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# Subset
(Redirected from Proper superset)
Euler diagram showing
A is a proper subset of B and conversely B is a proper superset of A
In mathematics, especially in set theory, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide. The relationship of one set being a subset of another is called inclusion or sometimes containment.
The subset relation defines a partial order on sets.
The algebra of subsets forms a Boolean algebra in which the subset relation is called inclusion.
## Definitions
If A and B are sets and every element of A is also an element of B, then:
• A is a subset of (or is included in) B, denoted by ${\displaystyle A\subseteq B}$,
or equivalently
• B is a superset of (or includes) A, denoted by ${\displaystyle B\supseteq A.}$
If A is a subset of B, but A is not equal to B (i.e. there exists at least one element of B which is not an element of A), then
• A is also a proper (or strict) subset of B; this is written as ${\displaystyle A\subsetneq B.}$
or equivalently
• B is a proper superset of A; this is written as ${\displaystyle B\supsetneq A.}$
For any set S, the inclusion relation ⊆ is a partial order on the set ${\displaystyle {\mathcal {P}}(S)}$ of all subsets of S (the power set of S) defined by ${\displaystyle A\leq B\iff A\subseteq B}$. We may also partially order ${\displaystyle {\mathcal {P}}(S)}$ by reverse set inclusion by defining ${\displaystyle A\leq B\iff B\subseteq A}$.
When quantified, A ⊆ B is represented as: ∀x{x∈A → x∈B}.[1]
## Property
• A finite set A is a subset of (or is included in) B, denoted by ${\displaystyle A\subseteq B}$,
If and only if the cardinality of their intersection is equal to the cardinality of A.
Formally:
${\displaystyle A\subseteq B\Leftrightarrow |A\cap B|=|A|}$
## ⊂ and ⊃ symbols
Some authors use the symbols ⊂ and ⊃ to indicate subset and superset respectively; that is, with the same meaning and instead of the symbols, ⊆ and ⊇.[2] So for example, for these authors, it is true of every set A that AA.
Other authors prefer to use the symbols ⊂ and ⊃ to indicate proper subset and superset, respectively, instead of ⊊ and ⊋.[3] This usage makes ⊆ and ⊂ analogous to the inequality symbols ≤ and <. For example, if xy then x may or may not equal y, but if x < y, then x definitely does not equal y, and is less than y. Similarly, using the convention that ⊂ is proper subset, if AB, then A may or may not equal B, but if AB, then A definitely does not equal B.
## Examples
The regular polygons form a subset of the polygons
• The set A = {1, 2} is a proper subset of B = {1, 2, 3}, thus both expressions A ⊆ B and A ⊊ B are true.
• The set D = {1, 2, 3} is a subset of E = {1, 2, 3}, thus D ⊆ E is true, and D ⊊ E is not true (false).
• Any set is a subset of itself, but not a proper subset. (X ⊆ X is true, and X ⊊ X is false for any set X.)
• The empty set { }, denoted by ∅, is also a subset of any given set X. It is also always a proper subset of any set except itself.
• The set {x: x is a prime number greater than 10} is a proper subset of {x: x is an odd number greater than 10}
• The set of natural numbers is a proper subset of the set of rational numbers; likewise, the set of points in a line segment is a proper subset of the set of points in a line. These are two examples in which both the subset and the whole set are infinite, and the subset has the same cardinality (the concept that corresponds to size, that is, the number of elements, of a finite set) as the whole; such cases can run counter to one's initial intuition.
• The set of rational numbers is a proper subset of the set of real numbers. In this example, both sets are infinite but the latter set has a larger cardinality (or power) than the former set.
Another example in an Euler diagram:
## Other properties of inclusion
A ⊆ B and B ⊆ C imply A ⊆ C
Inclusion is the canonical partial order in the sense that every partially ordered set (X, ${\displaystyle \preceq }$) is isomorphic to some collection of sets ordered by inclusion. The ordinal numbers are a simple example—if each ordinal n is identified with the set [n] of all ordinals less than or equal to n, then ab if and only if [a] ⊆ [b].
For the power set ${\displaystyle {\mathcal {P}}(S)}$ of a set S, the inclusion partial order is (up to an order isomorphism) the Cartesian product of k = |S| (the cardinality of S) copies of the partial order on {0,1} for which 0 < 1. This can be illustrated by enumerating S = {s1, s2, …, sk} and associating with each subset TS (which is to say with each element of 2S) the k-tuple from {0,1}k of which the ith coordinate is 1 if and only if si is a member of T.<|endoftext|>
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SEMATHS.ORG
Updated: 6 November 2021 08:42:00 AM
What does dilation mean in math?
A dilation (similarity transformation) is a transformation that changes the size of a figure. It requires a center point and a scale factor , k . The value of k determines whether the dilation is an enlargement or a reduction. If |k|>1 , the dilation is an enlargement. Simply, dilations always produce similar figures .
Considering this does dilated mean bigger or smaller?
When someone's eyes dilate, their pupils get bigger or smaller, but they always stay the same shape. When you dilate a figure, you change the size of the figure without changing its shape.
Keeping this in mind how do you create a dilation?
A dilation of an image is when the size of an image is changed. In order to create a dilation, we need a scale factor, which is the amount the image is changed, and the center of dilation, which is the point from which we are dilating an image. A reduction is when the scale factor is less than ''1''.
With this consideration in mind, should I be worried if one pupil is bigger than the other?
Is it serious? If a person's pupils are suddenly different sizes, it is best to seek medical attention. While not always harmful, a sudden change can indicate serious and dangerous medical conditions. It is especially important to seek medical attention if the change occurs after an injury or with other symptoms.
How do you dilate a area?
The perimeter of the dilated figure is the perimeter of the original figure multiplied by the scale factor. The area of the dilated figure is the area of the original figure multiplied by the square of the scale factor.
How do you dilate by a scale factor of 3?
The key thing is that the dilation value affects the distance between two points. As in the first example (dilation by a factor of 3), A is originally 1 unit down from P and 2 units to the left of P. 1*3 = 3, so A' (the dilated point) should be 3 units down from P. 2*3 = 6, so A' should be 6 units to the left of P.
How do you know if a shape is a dilation?
A dilation makes a figure larger or smaller, but has the same shape as the original. In other words, the dilation is similar to the original. All dilations have a center and a scale factor.
How do you write a dilation equation?
before you try to internalize the steps listed below and that explain the general formula for dilating a point with coordinates of (2, 4) by a scale factor of 12.Formula for Dilations.
1) Multiply both coordiantes by scale factor(2⋅12,4⋅12)
2) Simplify(1, 2)
3) Graph (if required)
How do you dilate by a scale factor of 2?
Dilation with scale factor 2, multiply by 2. Starting with quadrilateral ABCD (blue), draw the dilation image of the quadrilateral with a center at the origin and a scale factor of ½. Each vertex of ABCD is multiplied by ½. Dilation with scale factor ½, multiply by ½.
What is true about the dilation?
What is true about the dilation? It is an enlargement with a scale factor greater than 1.
What do large pupils mean?
The most common reason for dilated pupils is low light in a dark room since lower light causes your pupils to grow. Dilated pupils are also caused by drug use, sexual attraction, brain injury, eye injury, certain medications, or benign episodic unilateral mydriasis (BEUM).
Can emotions make your eyes dilate?
The processing of emotional signals usually causes an increase in pupil size, and this effect has been largely attributed to autonomic arousal prompted by the stimuli. Additionally, changes in pupil size were associated with decision making during non-emotional perceptual tasks.
Can stress cause uneven pupils?
Stimulation of the autonomic nervous system's sympathetic branch, known for triggering "fight or flight" responses when the body is under stress, induces pupil dilation.
What is center of dilation?
The center of a dilation is a fixed point on a plane. It is the starting point from which we measure distances in a dilation. In this diagram, point is the center of the dilation. A dilation is a transformation in which each point on a figure moves along a line and changes its distance from a fixed point.
What does it mean if my pupils are two different sizes?
Normally the size of the pupil is the same in each eye, with both eyes dilating or constricting together. The term anisocoria refers to pupils that are different sizes at the same time. The presence of anisocoria can be normal (physiologic), or it can be a sign of an underlying medical condition.
Can anxiety make your pupils different sizes?
Dilated or contracted pupils can precede, accompany, or follow an episode of nervousness, anxiety, fear, and elevated stress, or occur 'out of the blue' and for no apparent reason. The change in pupil size can range in degrees from slight, to moderate, to extreme.
How do you center a dilation at the origin?
Most dilations in the coordinate plane use the origin, (0,0), as the center of the dilation. Starting with ΔABC, draw the dilation image of the triangle with a center at the origin and a scale factor of two. Notice that every coordinate of the original triangle has been multiplied by the scale factor (x2).
How do you prove similarity by dilation?
Lesson Summary Dilations can be used to prove figures are similar by finding the scale factor between the two images and ensuring the sides are proportional. To find the scale factor, use the lengths of corresponding sides, set up a ratio and divide.
What stays the same in a dilation?
In dilation, the image and the original are similar, in that they are the same shape but not necessarily the same size. They are not congruent because that requires them to be the same shape and the same size, which they are not (unless the scale factor happens to be 1.0).
How do you dilate a function?
For instance, if we want to dilate a function by a factor of A in the x-direction and then shift C to the right, we do this by replacing x first by x/A and then by (x−C) in the formula.
How do you do similarity?
If two pairs of corresponding angles in a pair of triangles are congruent, then the triangles are similar. We know this because if two angle pairs are the same, then the third pair must also be equal. When the three angle pairs are all equal, the three pairs of sides must also be in proportion.
How do you plot dilation?
In order to graph a dilation, use the center of dilation and the scale factor. Find the distance between a point on the preimage and the center of dilation. Multiply this length by the scale factor.
What is the center point of a dilation?
The center of a dilation is a fixed point in the plane about which all points are expanded or contracted. The center is the only invariant (not changing) point under a dilation (k ≠1), and may be located inside, outside, or on a figure.
Is unequal pupil size an emergency?
Different sized pupils could indicate a serious health issue requiring urgent medical care. The pupil is the black hole in the center of the iris, the part that gives your eye its unique color.
How do you describe dilation?
A dilation is a transformation that enlarges or reduces the size of a figure. Therefore, the image and preimage will have the same shape but different sizes. Dilations also scale all sides of a figure by the same factor. As a result, dilations preserve angle measures and the ratio between corresponding parts.<|endoftext|>
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# How to solve for X math tutorial: introducing "Math with Margo"
Virginia
December 11, 2020
Solving for X...One of the most fundamental algebra concepts.
It’s also one of the most confusing!
Never fear, our very own iD Tech math superhero, Margo, is here to help.
Follow along in this easy tutorial and solving for x will be a snap! Read Margo’s notes and highlights for extra tips and tricks. (you’ll be able to check your work as you go.)
Meet Margo, Math Expert and Operations Manager at iD Tech
Hi there! My name is Margo Berry, and I was a middle school and high school math teacher for five years. I have an expertise in developing Common Core aligned math curriculum, a Master's Degree in Secondary Math Education, and a passion for making math engaging for kids.
Math is all around us! I like to find ways to provide opportunities for my students to interact with math and see it relate to the real world.
## Solve for X Math Tutorial
### Solving Two Step Equation Word Problems
Dan bought eight new baseball trading cards to add to his collection. The next day, his dog ate half of his collection. There are now only thirty eight cards left. How many cards did Dan start with?
#### Step One: Highlight important parts of the text
Go through the problem and identify the important pieces. These valuable details usually include all numbers and any indication that something is being added, subtracted, divided, or multiplied.
#### Step Two: Define your variable(s) or unknowns
The unknown, or what we are trying to solve for is C, or the number of cards Dan started with.
#### Step Three: Write your equation(s) by breaking down the text of the problem
Next, begin writing the equation by breaking down the important pieces of the problem.
First, Dan bought eight new cards, so we add C+8.
(Here is more on converting word problems into equations.)
Next, because Dan's dog ate half of the collection, we divide everything by 2.
Last, we know that Dan ends up with 38 cards in the end, so we set it equal to 38.
#### Step Four: Solve your equation!
Now, we are ready to solve! To get C by itself, we must perform inverse operations. In this case, we are dividing C+8 by 2, so we must multiply as the inverse. And then, whatever we do to one side of the equation we must do to the other side of the equation.
After multiplying both sides by 2, we are left with C+8 = 76...meaning we are very close to finding C on its own!
From there, we need to subtract 8 from both sides, ultimately leaving us with our pre-checked answer of C=68!
#### Step Five: Check your work
To check our work, take the answer of 68 and go through the different operations as described by the important pieces of the word problem.
68 original baseball cards (our answer) + 8 new baseball cards Dan bought = 76 total cards. We know Dan's dog ate half of the collection, so 76 divided by 2 = 38...which is the exact amount of cards the word problem told us Dan was left with!
After finding C and checking the work to get there, state the final answer in relation to the main question.
Congratulations! You did it! For more math resources and fun, check out these:
For support, extra help, and challenges in math, iD Tech offers live online math tutoring in algebra, pre-calculus, geometry and more!
Options include:
### Meet iD Tech!
Sign up for our emails to learn more about why iD Tech is #1 in STEM education! Be the first to hear about new courses, locations, programs, and partnerships–plus receive exclusive promotions! AI summer camps, coding classes for kids, and more!<|endoftext|>
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# { independent variable some property or restriction about independent variable } where the vertical line is read such that.
Size: px
Start display at page:
Transcription
1 Page 1 of 5 Introduction to Review Materials One key to Algebra success is identifying the type of work necessary to answer a specific question. First you need to identify whether you are dealing with an expression or an equation. Simply put, equations have an equal sign, expressions do not. Expressions are simplified or rewritten in a different, but equivalent form. Equations are solved, typically for a particular variable. Simplifying expressions and solving equations do use many of the same skills, though the ultimate goal of each is quite different. Below is a list of common tasks associated with expressions and equations. One term Multiply Divide Factor Distribute Evaluate Reduce or Simplify Expressions: Two or more terms Add Subtract Factor Evaluate Simplify Visualize Equations: Solve Definitions: Explanations of several mathematical terms and procedures are included here for your reference. Domain The domain is a list or set of all possible inputs that yield a real number output. There are three operations we can t do with real numbers in algebra. Each of these restrict the domain. Can t divide by zero. Can t take the square root (or any even-index radical) of a negative number. Can t take the logarithm of zero or a negative number. Two common notations to write the domain are set-builder and interval notation. 1. Set-builder notation: Sets are typically written in braces {}. The notation is { independent variable some property or restriction about independent variable } where the vertical line is read such that. Example: All real numbers x, less than.
2 Page of 5 { xx< } Example: All real numbers x, not equal to 9. { xx 9} Example: All real numbers n 4 n< 6 { } n, greater than or equal to 4 and less than 6.. Interval notation: A parenthesis indicates the starting or ending value is not included and a square bracket indicates the starting or ending value is included. Within the parentheses or square bracket, we indicate the smallest value of x followed by a comma and then the largest value of x. Example: All numbers x, less than. (,) Example: All numbers x, not equal to 9.,9 U 9, The mathematical symbol U means union or or. ( ) ( ) Example: All numbers 4,6 [ ) n, greater than or equal to 4 and less than 6. Equivalent Fractions Fractions that are equal when simplified. Example:,, 5, and are equivalent fractions because they all reduce to 1. Expression A collection of numbers, variables, grouping symbols and operations. An expression is made up of one or more terms. Factor (noun) Expressions that are multiplied together. A factor is any object (integer or polynomial) that exactly divides another object.
3 Page of 5 Factor (verb) To factor an integer means write the integer as a product of prime numbers. To factor a polynomial means to write the polynomial as the product of two or more polynomials of lower degree. Greatest Common Factor (GCF) The greatest common factor of two or more objects (integers or polynomials) is the largest quantity that divides (without remainder) all of the objects. Example: Find the GCF of 4 and 60. Start by factoring each expression completely. That is, write each number as a product of prime numbers. 4 = = 6 10 = ( ) 7 = ( ) ( 5) = 5 To build the GCF, identify the factors that are common to each integer. Notice 4 and 60 each have a factor of and, therefore the GCF is or 6. That is the largest number that divides evenly into both 4 and 60 is 6. Example: Find the GCF of 9x y and 0x y. Factor each expression completely. x y = x x y y 9 x y = x x x y 0 5 Each expression has one, two x s, and one y. Therefore the GCF is that divides evenly into 9x y and 0x y is x y. x y. Recall this means the largest expression Least Common Denominator (LCD) denominators. The least common denominator is the least common multiple of all involved
4 Page 4 of 5 Least Common Multiple (LCM) The least common multiple of two or more objects (integers or polynomials) is the smallest quantity that all the objects divide into evenly. Example: Find the LCM of 4 and 60. Factor each expression completely. 4 = = 6 10 = ( ) 7 = ( ) ( 5) = 5 The LCM is the product of the most number of times each factor occurs in any one of the objects. The factor appears once in 4 and twice in 60, therefore the LCM includes two s. The factor of appears once in 4 and once in 60, therefore the LCM includes one. The factor of 5 does not appear in 4 and once in 60, therefore the LCM includes one 5. Finally the factor of 7 appears once in 4 and does not appear in 60, so it appears once in the LCM. Therefore the LCM is 5 7 or 40. Thus 40 is the smallest integer that is exactly divisible by both 4 and 60. Example: Find the LCM of 9x y and Start by factoring each expression. 0x y. x y = x x y y 9 x y = x x x y 0 5 The LCM is the product of the most number of times each factor occurs in any of the objects. The factor does not appear in 9x y and appears once in 0x y. The LCM includes one. The factor of appears twice in 9x y and once in 0x y, so the LCM includes two s. The factor 5 does not appear in 9x y and appears once in 0x y, so the LCM includes one 5. The factor x appears twice in 9x y and three times in 0x y, so the LCM includes three x s. Finally, the factor y appears twice in 9x y and once in 0x y, so the LCM includes two y s. Thus the LCM is 5 x x x y yor 90x y. (Recall this means the smallest expression that both 9x y and 0x y divide evenly into is 90x y.)
5 Page 5 of 5 Perfect Square An expression is a perfect square if it can be written as some expression squared. Example: 9 is a perfect square because it can be written as. Example: 64x is a perfect square because it can be written as ( 8x ). n n 1 1 Polynomial A polynomial is an algebraic expression of the form an x + an 1 x a1x + a0, where an, an 1,..., a1, a0 are all real numbers and the exponents n, n 1,... are all whole numbers. Monomial A one-term polynomial. 7, x, 9 p q are examples of monomials. Binomial A two-term polynomial. x +1, 9t 5t, x + x are examples of binomials. Trinomial A three-term polynomial. 4 x + 7 x + 1, 9r 5r + r, x y xy + 5xy are examples of trinomials. Term May be composed of a number called the coefficient, variable(s), and perhaps exponents. Only multiplication and division occur within a term. Addition and subtraction separate terms. 9 x + 5 4xy 19xy+ 7 p( 4p 7) 1 p 1 p 1 term terms terms 1 term terms
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# How do you simplify sqrt(27/16)?
Jul 12, 2017
It is $\frac{3 \times \sqrt{3}}{4}$
#### Explanation:
$\frac{\sqrt{27}}{4}$
since $\sqrt{16} = 4$
You can further write
$\frac{\sqrt{9 \times 3}}{4} = \frac{3 \times \left(\sqrt{3}\right)}{4}$
$\frac{3 \times \left(\sqrt{3}\right)}{4}$
Jul 12, 2017
$\frac{3 \sqrt{3}}{4}$
#### Explanation:
Value $= \sqrt{\frac{27}{16}}$
Expressing the numerator and denominator as their prime factors:
Value $= \sqrt{\frac{3 \times 3 \times 3}{2 \times 2 \times 2 \times 2}}$
Taking each pair of factors once through the sqrt.
Value $= \frac{3 \sqrt{3}}{2 \times 2}$
$= \frac{3 \sqrt{3}}{4}$<|endoftext|>
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- 1 Definition
- 2 Description
- 3 History
- 4 Discussion 1
- 5 Discussion 2: The Common Good Bank approach to Interest
- 6 Key Books
- 7 References
"Interest is a fee paid on borrowed assets. It is the price paid for the use of borrowed money, or, money earned by deposited funds. Assets that are sometimes lent with interest include money, shares, consumer goods through hire purchase, major assets such as aircraft, and even entire factories in finance lease arrangements. The interest is calculated upon the value of the assets in the same manner as upon money. Interest can be thought of as "rent of money". For example, if you want to borrow money from the bank, there is a certain rate you have to pay according to how much you want loaned to you.
Interest is compensation to the lender for forgoing other useful investments that could have been made with the loaned asset. These forgone investments are known as the opportunity cost. Instead of the lender using the assets directly, they are advanced to the borrower. The borrower then enjoys the benefit of using the assets ahead of the effort required to obtain them, while the lender enjoys the benefit of the fee paid by the borrower for the privilege. The amount lent, or the value of the assets lent, is called the principal. This principal value is held by the borrower on credit. Interest is therefore the price of credit, not the price of money as it is commonly believed to be. The percentage of the principal that is paid as a fee (the interest), over a certain period of time, is called the interest rate." (http://en.wikipedia.org/wiki/Interest)
"Interest is the price paid for the use of borrowed money. Money itself does not pay interest...this is money functioning as stored of value, value lent by one party and borrowed by another that can be exchanged for productive assets. The need for borrowing implies scarcity. Therefore we can infer that interest is truly the price paid for accelerated access to scarce resources. Like all prices, an interest rate is a market signal that enables efficient allocation of these scarce resources - in this case resources being allocated through time, between consumption and investment. This analysis implies two preconditions for the existence of interest:
- Scarce resources
- Varying temporal preferences for consumption
Critically, these preconditions refer not only to the monetary system but to the constituents of the economy itself - its productive capabilities and the psychology of its participants. A monetary regime intended to eliminate interest would have to resolve at least one of these conditions in the economy itself." (http://onthespiral.com/the-role-of-interest-in-future-monetary-syste)
A Brief History of Interest in Europe
John Boik, in: Creating Sustainable Societies:
"Records of interest-based finance date back to the time of King Hummarabi in ancient Babylon (circa 1770 BC). The Code of Hummarabi stipulates various rules for loans, including a maximum allowable interest rate and the conditions under which debts must be forgiven.
The practice of charging interest continued into ancient Greece, although both Plato and later Aristotle condemned it.[23, 24] By the time of Aristotle (384–322 BC), interest-based loans had already precipitated social and economic unrest in Greece, as they had in Babylon before it.
Interest-based lending continued into the Roman era. With the fall of the Western Roman Empire (circa 476 AD) and the onset of the Middle Ages, a shift occurred. Based in part on the arguments of Aristotle, in part on the human suffering caused by loans under the Romans, and in part on prohibitions to usury in the Old Testament, interest-based lending was prohibited by the Catholic Church. The Church regarded usury as morally decrepit and sinful. Although Catholics were prohibited from lending with interest to other Catholics, Jewish law did not prohibit lending. As Catholic peasants and merchants continued to need loans, Jews, who were excluded from many other forms of commerce, became brokers who filled the need.
By the 1400s, alternative sources for loans became available. At the urging of Franciscans, public funds for the poor (montes pietatis) were established. Because they charged low interest, just enough to cover expenses, they were generally accepted by the Church. Also in that century, the Medici banking family rose to power in Florance. Along with several other banking innovations, their system of bills of exchange generated a profit without charging interest, and so was welcomed by the Church."
How Usury Drives Infinite Growth
Charles Eistenstein (in Sacred Economics:
"Because of interest, at any given time the amount of money owed is greater than the amount of money already existing. To make new money to keep the whole system going, we have to breed more chickens-in other words, we have to create more "goods and services." The principal way of doing so is to begin selling something that was once free. It is to convert forests into timber, music into product, ideas into intellectual property, social reciprocity into paid services.
Abetted by technology, the commodification of formerly nonmonetary goods and services has accelerated over the last few centuries, to the point today where very little is left outside the money realm. The vast commons, whether of land or of culture, has been cordoned off and sold-all to keep pace with the exponential growth of money. This is the deep reason why we convert forests to timber, songs to intellectual property, and so on. It is why two-thirds of all American meals are now prepared outside the home. It is why herbal folk remedies have given way to pharmaceutical medicines, why child care has become a paid service, why drinking water has been the number-one growth category in beverage sales.
The imperative of perpetual growth implicit in interest-based money is what drives the relentless conversion of life, world, and spirit into money. Completing the vicious circle, the more of life we convert into money, the more we need money to live. Usury, not money, is the proverbial root of all evil." (http://www.realitysandwich.com/sacred_economics_ch_6_usury)
The Cost of Interest
"The US Government at this point pays between 400 and 500 billion dollars in interest per year on the ‘National Debt’. The trillions that the FED have created and will create to buy up Treasuries are interest bearing.
If you buy a house you pay hundreds of thousands of dollars in interest for your mortgage. For money that was created by pushing a few buttons.
Forty percent of prices you pay are costs for capital. So just through prices for normal commodities you pay 40 % of your disposable income to banks and other financiers.
Who pays for all this? The 80% poorest of the population. The have nots pay interest, the haves receive it. We are talking a worldwide, yearly multi trillion wealth transfer from poor to rich through usury." (http://realcurrencies.wordpress.com/2010/10/10/in-defense-of-ellen-brown/)
Contemporary Christian condemnation of usury
"In Economics for Helen Hilaire Belloc outlines in his admirably lucid manner the following principles of usury.
1. Usury is both wrong morally and bad for society because it is the claim for an increase of wealth which is not really present at all. It is trying to get something where there is nothing out of which that something can be paid.
2. This action must therefore progressively and increasingly soak up the wealth which men produce into the hands of those who lend money, until at last all the wealth is so soaked up and the process comes to an end.
3. That is what has happened in the case of the modern world, largely through unproductive expenditure on war, which expenditure has been met by borrowing money and promising interest upon it although the money was not producing any further wealth.
4. The modern world has therefore reached a limit in this process and the future of usurious investment is in doubt.
Belloc always keeps in mind the thing modern men ignore. Modern men pretend that money is in and of itself productive, but money is simply a commodity that is conveniently traded and that can be used to price effort and production. Money is not magic. A loan of money does not always produce more money, for the money lent may not always go into a productive purpose–and it is production (effort plus resources) that makes wealth.
Thus usury is not merely charging exorbitant interest on a loan. It is charging any interest at all on a non-productive loan, for interest is a claim on an increase of wealth. And claiming an increase of wealth when an increase of wealth does not exist is usury. Thus, a consumer credit card loan even at 2% is usurious, for it is a claim of interest where no interest exists.
But if only credit cards limited their usury to 2%! That would indeed be usury by the strict definition of the term, but how much less of a sin that would be! For, as Bishop Paul Peter Jesep points out in Credit Card Usury and the Christian Failure to Stop It, these days there is even a bank that issues a credit card that charges (legally) 79% interest! " (http://distributistreview.com/mag/2011/07/christians-and-the-economy/)
Discussion 2: The Common Good Bank approach to Interest
Next contributions are from (http://commongoodbank.com/2009/10/general/the-evil-interest-fallacy:
William Spademan on the Evil Interest Fallacy
There is one bit of advice given to us by the ancient heathen Greeks, and by the Jews in the Old Testament and by the great Christian teachers of the Middle Ages, which the modern economic system has completely disobeyed. All these people told us not to lend money at interest: And lending money at interest — what we now call investment — is the basis of our whole system.
Those who devour usury will not stand except as stand one whom the Evil one by his touch Hath driven to madness.
Is interest evil? Many people who have become disillusioned with capitalism, see quite rightly that investment interest is how wealth gets funneled to those who already have the most. It is easy to think that interest is evil and must be done away with.
In the United States, our money is created by private companies lending it into existence and charging interest on it. Clearly this is not fair. But even worse, many people argue, is that the interest can never be repaid because it is not created as part of those loans! This argument is so popular that the search phrase “interest can never be repaid” gets 115,000 hits on Google.
But (1) interest is not evil in itself. And (2) the “interest can never be repaid” argument is seductively righteous and simple, but wrong.
Interest is not evil
People think interest is evil because the wealthy investor earns interest simply by being wealthy. The investor is not producing any useful goods and is not contributing any useful labor to society. Our current economic system rewards the investor for being wealthy much more than it rewards people for being productive. For example, let’s say Bill Gates earns $5 million a year doing productive work and let’s say, generously, that that amount is complete and fair compensation for all of his work for the year. In the same year, Mr. Gates’ $50 billion brings in another $5 billion or so in income (a thousand times as much as his paid work). Since we agreed that $5 million was fair pay for his actual work, the $5 billion of “unearned income” (as the IRS calls it) must be undeserved income.
When I gave this example to a colleague recently, he argued that Bill Gates might actually deserve those billions because of the great value that he has already given the world. I could argue against that, but the objection is missing the point. Surely there is SOME amount that is fair pay for his or anyone’s work. Then whatever investment income he gets beyond that fair amount is clearly unfair pay.
Here we come to the root of the problem. What triggers our moral outrage is the unfair pay, not the interest per se. What rankles is not that billions follow billions, but that someone is profiting unfairly. And perhaps, less obviously, that the rest of us are unfairly missing out on that profit.
The common good bank design rights this wrong by dedicating all profits to the common good."
The "Unpayable Debt" Fallacy
the “interest can never be repaid” argument is wrong
Like many attractive fallacies, this one has an element of truth. The error and the partial truth have to do with the fact that money is not designed to go just one way. It circulates.
Figure 1 shows a diagram of of how money is created and how at first it looks as though the interest is unpayable, since it never gets created. In the diagram, money paid as interest goes to the bank and never leaves except as additional loans. This makes it look as though interest is incompatible with sustainable economics.
The true situation is more complicated. In figure 2, I have added a crucial third party: the investors.
Most of the interest and fees that the bank receives goes to pay the expenses of operating a bank: salaries and wages for employees, utilities, legal fees, taxes, and so forth. Money for these expenses gets returned to the circulating money supply.
The remainder of the bank’s income is profit.
unpayable debt fallacy correction
Mutual banks (also called “cooperative banks”) and credit unions do in fact generally hold onto and relend their small profits — otherwise they cannot grow. This is a problem, but not a big one.
The vast majority of financial assets are held by stock-based banks, which are required by law to maximize profits. Profits go to the owners of the bank, the investors. The investors also receive profits from investment in other businesses.
Here again, it rankles that the investors are receiving all those profits without lifting a finger. But beyond our vague sense of unfairness, there are two very real problems.
Problem A: Investors typically receive more profits than they spend. This means that the buck stops there. The money stops circulating. It piles up.
Conceptually we can divide people into two groups:
(a) Investors — people who have more money than they need (and therefore have some extra that they can invest) and
(b) Non-investors — people who have less money than they need.
When investors receive more profits than they spend, the result is that people in group (a) who already have more money than they need end up with more and more of the money, leaving less and less for people in group (b) who already have less money than they need. This is a big problem. It is the root cause of poverty.
Problem B: Investors, being wealthy, typically spend and consume more than the average person. The big spenders are the worst offenders, but they are not alone. In fact, in the United States most of us — rich or poor — consume much more than we produce. For example, my family and I live on what is considered a “poverty level” income. And yet it would take us many years to produce for ourselves the goods and services that we blithely consume each year. This too is a big problem. It means that some people somewhere are working very very hard to produce the goods and services that we consume." (http://commongoodbank.com/2009/10/general/the-evil-interest-fallacy)
The Common Good Bank Solution
unpayable debt fallacy CGBs
Figure 3 shows how the common good bank system solves both problems, creating a sustainable economic system. Common good banks will charge interest, but the profit from that interest all goes back to the community as grants to schools and other nonprofit organizations. The money keeps circulating. None of the profits go to enrich individuals.
In fact, communities must dedicate half their profits to advance the common good outside their community. Wealthy communities will likely have larger deposits, larger loans, and larger profits than poor communities. So the wealth will gradually get distributed more evenly.
To clarify how interest can be repaid even though it is not explicitly created when the principal is lent into existence, here is an example:
Example of Paying Interest With No Problems
Imagine a world with just two people, Al and Betty, and one nonprofit bank.
Betty is a farmer. Al is a bank teller and tool-maker.
At first there is no money. Then one day Betty borrows $100 from the bank, to buy a plow from Al. The bank lends the money into existence, with interest of $1 per month. Betty plans to pay $11 a month, so that the loan will be paid off within ten months.
At first it looks as though Betty will only be able to pay back $100 (without interest) because there is only $100 in circulation. The interest will be unpayable. But since the money circulates, both principal and interest can be paid, without creating additional money. Figure 4 shows how it goes.unpayable debt fallacy Example
The first month, Al pays Betty $11 for food. Betty pays the bank $10 plus one dollar in interest. The bank pays Al $1 in wages and retires $10 of the debt. This leaves Al with $90. Betty and the bank each have nothing.
The second month, these transactions are all repeated, leaving Al with $80. The transactions are repeated again the next month, and so forth, each month leaving Al with $10 less.
In the ninth month, just after Al receives his pay, he notices that the world is about to run out of money, so he decides to spend his last $10 on food. Betty immediately pays off the loan. No additional interest is due and Al has already been paid for the month. The bank retires the final $10 of the loan. No money is left in circulation and there are no outstanding debts.
In this example, the bank makes no profit. If the bank does make a profit, say by paying Al only 50 cents a month, there is still no problem as long as the bank is a common good bank. The profits simply go to a nonprofit that (for example) pays Betty and Al to create works of art. The money stays in circulation.
In the common good bank system, interest is not evil and causes no problems. In the common good bank system, interest contributes to economic justice and sustainability. (http://commongoodbank.com/2009/10/general/the-evil-interest-fallacy)
- O Valor do Amanhã - Ensaio Sobre a Natureza dos Juros, by Eduardo Giannetti, ISBN 9788535907353
- C.S. Lewis, Mere Christianity
- Allah, the Qur’an (Surah Baqarah, 2:275)
- Why demurrage is better than interest
- A Short Review of the Historical Critique of Usury, by Wayne A.M. Visser and Alastair McIntosh - Centre for Human Ecology
- Some thoughts on usury, money and the banking industry
- Evil Is Interest article by John G Root Jr
- Usury And Evil article by John G Root Jr
- The Facts About Usury: Why Islam Is Against Lending Money At Interest<|endoftext|>
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An exploration and challenge with some less usual cubes
A number exploration that gives the opportunity to develop a systematic approach.
An exploration involving number sequences and numbers associated with shapes - triangles, squares, pentagons etc.
Explore these arrangements of circles. This task challenges you to consider what your idea of the 'next size up' might be.
What happens when you overlap pieces of paper? You might want to look at shape and areas. It's an exploration that can lead ... who knows where?
Have a go at arranging numbers in a special way to get a certain total. The adventure starts when you try to find all the possible ways of doing this - how will you know you haven't left out any possibilities?
Investigate the number of squares or lines that make up these spirals as they grow. This task encourages you to create new spirals of your own to explore in similar ways.
Investigate the paths taken by a squirrel travelling to the corners of a quadrilateral but only going half-way each time. A wild exploration that may involve direction, area, length and shape!
An exploration involving quarters of shapes. You could take a look at some ways in which other people have been creative in response to this task!
Create your own grid of numbers following these simple rules. What fascinating patterns and connections can you find in the numbers? Be prepared to discover something new and perhaps surprising!<|endoftext|>
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Inside: A free set of sorting worksheets for preschool.
Sorting and categorizing are beginning math skills that are practiced during preschool years a lot. Therefore I created this set of sorting worksheets for preschool to provide parents and teachers with a free and reliable resource.
You might also like: Fun activities for developing critical thinking skills in preschoolers
Sorting is an important skill for future more complex math learning. It teaches children about similarities and differences, grouping objects together, logical thinking and more.
Many preschool-aged children naturally sort and organize toys during their free play. And we can build on this interest even further and help them out with providing more structured categorizing activities such as sorting worksheets.
Sorting worksheets for preschool
My sorting worksheets for preschool are based on sorting objects by various attributes.
If your children have already mastered sorting by the basic characteristics such as color, size or shapes, today’s printable will allow you to introduce other concepts.
Whether they are learning about farm animals or about healthy foods, this activity is a great addition to their learning.
Also visit: Tracing circles worksheets and shapes worksheets for preschool
To download my sorting preschool worksheets, simply click on the download link at the very bottom. Then save or print right away.
Have fun with your preschooler!
These worksheets are for personal use only. Any re-distribution or altering are not allowed.
Other ideas for sorting activities
There are many toys and toy sets available these days for hands-on learning. But you can always use everyday objects to teach or reinforce sorting skills in preschoolers. Here are just a few ideas:
- For sorting by color use colorful buttons, pom poms, lego pieces or blocks.
- For sorting by shape make your own shapes like one mama on this blog or get these shapes kids’ buttons that will work great for sorting purposes as well as future crafts or activities.
- To sort animals by their habitat these five tubes of different animals work just right.<|endoftext|>
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# Question #39436
Jan 1, 2017
$9 \text{ and } 15$
#### Explanation:
Let one number be represented by x
Then the other number will be $2 x - 3$ That is 3 less than twice the other which is x.
Forming an equation.
$\Rightarrow x + 2 x - 3 = 24 \leftarrow \text{ sum of numbers is 24}$
$\Rightarrow 3 x - 3 = 24$
add 3 to both sides of the equation.
$3 x \cancel{- 3} \cancel{+ 3} = 24 + 3$
$\Rightarrow 3 x = 27$
To solve for x, divide both sides by 3
$\frac{\cancel{3} x}{\cancel{3}} = \frac{27}{3}$
$\Rightarrow x = 9$
The 2 numbers are.
$x = 9 \text{ and } 2 x - 3 = \left(2 \times 9\right) - 3 = 18 - 3 = 15$
$\textcolor{b l u e}{\text{As a check }} 9 + 15 = 24$<|endoftext|>
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You are Here: Home >< Maths
# Simultaneuos Equation Help watch
1. Hi there I'm struggling to do this simple process could anyone walk me through it please? The answer is given but not sure how to get there.
θ = 25/Vm at P=10 mbar
θ = 41/Vm at P=18 mbar
and θ = KP/(1+KP)
Thus 25/Vm = 10K/(1+10K) and 41/Vm = 18K/(1+18K)
Rearranging:
1/K = (10Vm - 250)/25
1/K = (18Vm - 738)/41.
Solve simultaneous equations for 1/K Vm = 205 cm3
2. (Original post by Mitty1990)
Rearranging:
1/K = (10Vm - 250)/25
1/K = (18Vm - 738)/41.
Solve simultaneous equations for 1/K Vm = 205 cm3
Since 1/K equals both of those, we can cut out the middle man and get:
(10Vm - 250)/25 = (18Vm - 738)/41.
Then it's just a question of multiplying through, collecting terms,...
Does that cover it, or are you concerned about a different part of the process?
3. Thank you but I'm not sure how to get to the 1/K to start with.
4. (Original post by Mitty1990)
Thank you but I'm not sure how to get to the 1/K to start with.
OK. I suspect a full answer might be best in this case, so:
Spoiler:
Show
I''ll use T rather than theta to simplify my typing.
So, T=KP/(1+KP)
Multiplying through we have T(1+KP) = KP
Expanding brackets T+TKP=KP
Collect terms in K together T=KP-TKP
Factor out the K, so K(P-TP)=T
And divide through by K and T, to get:
1/K = (P-TP)/T
At this stage we could substitute in the values given, and on the right we would multiply the top and bottom of the fraction by "Vm" to simplify it and get it in the form given.
OR we could carry on with:
Now theta is given as "something/Vm", I'll call the something H, so theta = H/Vm
Substituting in we have 1/K = (P - PH/Vm)/(H/Vm)
Multiplying the top and bottom of the fraction on the right by Vm, we get:
1/K=(PVm-PH)/H where H is the given numerical part theta.
5. Hey thank you very much for the reply. I'm following your instruction up until the something/vm part.
If I write it out with the numbers, I get:
1/K = 10 - 10 25 vm / 25 vm.
I don't think this is correct though sadly.
6. (Original post by Mitty1990)
Hey thank you very much for the reply. I'm following your instruction up until the something/vm part.
If I write it out with the numbers, I get:
1/K = 10 - 10 25 vm / 25 vm.
I don't think this is correct though sadly.
That should be 1/K = (10 - 10x25/vm) / (25/vm).
Then multiply top and bottom by Vm on the right hand side.
7. (Original post by ghostwalker)
That should be 1/K = (10 - 10x25/vm) / (25/vm).
Then multiply top and bottom by Vm on the right hand side.
Doesn't that just remove vm from the equation?
8. (Original post by Mitty1990)
Doesn't that just remove vm from the equation?
I haven't really been following but you will still have 10vm
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# NCERT Solutions For Class 6 Maths Chapter 8 Exercise 8.2
## Ncert Solutions for Class 6 Maths Chapter 8 Decimals Exercise 8.2:-
Exercise 8.2 Class 6 maths NCERT solutions Chapter 8 Decimals pdf download:-
### Ncert Solution for Class 6 Maths Chapter 8 Decimals Exercise 8.2 Tips:-
Hundredths
David was measuring the length of his room.
He found that the length of his room is 4 m
and 25 cm.
He wanted to write the length in metres.
Can you help him? What part of a metre will
be one centimetre?
1 cm = ( ) 1
100 m or one-hundredth of a metre.
This means 25 cm =
25
100 m
Now ( ) 1
100 means 1 part out of 100 parts of a whole. As we have done for
1
10 , let us try to show this pictorially.
Take a square and divide it into ten equal parts.
What part is the shaded rectangle of this square?
It is
1
10 or one-tenth or 0.1, see Fig (i).
Now divide each such rectangle into ten equal parts.
We get 100 small squares as shown in Fig (ii).
Then what fraction is each small square of the whole
square?
Each small square is ( ) 1
100 or one-hundredth of the
whole square. In decimal notation, we write ( ) 1
100 = 0.01
and read it as zero point zero one.
What part of the whole square is the shaded portion, if
we shade 8 squares, 15 squares, 50 squares, 92 squares of
the whole square?
Take the help of following figures to answer.
What have we discussed?
1. To understand the parts of one whole (i.e. a unit) we represent a unit by a block. One
block divided into 10 equal parts means each part is
1
10 (one-tenth) of a unit. It can
be written as 0.1 in decimal notation. The dot represents the decimal point and it
comes between the units place and the tenths place.
2. Every fraction with denominator 10 can be written in decimal notation and vice-versa.
3. One block divided into 100 equal parts means each part is ( ) 1
100 (one-hundredth) of
a unit. It can be written as 0.01 in decimal notation.
4. Every fraction with denominator 100 can be written in decimal notation and
vice-versa.
5. In the place value table, as we go from left to the right, the multiplying factor becomes
1
10 of the previous factor.
The place value table can be further extended from hundredths to
1
10 of hundredths
i.e. thousandths (
1
1000 ), which is written as 0.001 in decimal notation.
6. All decimals can also be represented on a number line.
7. Every decimal can be written as a fraction.
8. Any two decimal numbers can be compared among themselves. The comparison can
start with the whole part. If the whole parts are equal then the tenth parts can be
compared and so on.
9. Decimals are used in many ways in our lives. For example, in representing units of
money, length and weight.
#### Test Paper Of Class 8th
• Maths 8th Class
• Science 8th class
• Sst 8th Class
• #### Test Paper Of Class 7th
• Maths 7th Class
• Science 7th class
• #### Test Paper Of Class 6th
• Maths 6th Class
• Science 6th class<|endoftext|>
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What Is Diagonal Matrix in Data Structure?
//
Heather Bennett
A diagonal matrix is a special type of square matrix where all the elements outside the main diagonal are zero. The main diagonal of a matrix consists of elements that have the same row and column index. In other words, a diagonal matrix has non-zero elements only on its main diagonal, and all other elements are zero.
Properties of Diagonal Matrix
A diagonal matrix has several interesting properties:
• 1. Scalar Multiplication: When you multiply a scalar value by a diagonal matrix, each element on the main diagonal is multiplied by the scalar, while all other elements remain zero.
• 2.
Addition and Subtraction: Adding or subtracting two diagonal matrices is as simple as adding or subtracting their corresponding elements on the main diagonals.
• 3. Matrix Multiplication: Multiplying two diagonal matrices results in another diagonal matrix, where each element on the main diagonal is obtained by multiplying the corresponding elements from both matrices.
Example
To understand better, let’s consider an example of a 3×3 diagonal matrix:
```1 0 0
0 4 0
0 0 -2
```
In this example, the first element (1) corresponds to row 1 and column 1, second element (4) corresponds to row 2 and column 2, and so on. All other elements outside the main diagonal are zero.
Scalar Multiplication Example
If we multiply this matrix by a scalar value of 3:
```3 * (1 0 0)
(0 4 0)
(0 0 -2)
```
The resulting matrix will be:
```3 0 0
0 12 0
0 0 -6
```
Let’s consider another example where we add two diagonal matrices:
```(1 0 0) + (2 0 0) = (3 0 0)
(0 4 0) + (0 -1 0) = (3 -1 0)
(0 2 -2) + (1 -1 -2) = (1 -1 -4)
```
Matrix Multiplication Example
Lastly, let’s multiply two diagonal matrices:
```(1 0 ) * (4 5 ) = (4 5 )
( ) * ( -2) = ( )
( ) * (-6 ) = (-6 )
```
The resulting matrix will also be a diagonal matrix:
```4
What Is Matrix in Data Structure?
What Is Matrix in Data Structure? A matrix is a two-dimensional data structure that consists of a collection of elements arranged in rows and columns. It is often used to represent mathematical or tabular data.
What Is Matrix in Data Structure With Example?
What Is Matrix in Data Structure With Example? A matrix is a two-dimensional data structure that represents a collection of elements arranged in rows and columns. It is an essential concept in computer science and is widely used to solve various computational problems.
What Is Matrices in Data Structure?
What Is Matrices in Data Structure? In the field of data structure, a matrix is a rectangular array of elements arranged in rows and columns. It is a fundamental concept used in various applications, such as mathematics, computer science, physics, and engineering.
What Is Band Matrix in Data Structure?
What Is Band Matrix in Data Structure? A band matrix is a special type of matrix that has non-zero elements only in a specific band around its diagonal. In other words, most of the elements in a band matrix are zero, except for those within a certain number of diagonals from the main diagonal.
What Is Tri Diagonal Matrix in Data Structure?
A tri diagonal matrix is a special type of square matrix where the elements outside the main diagonal and the two diagonals adjacent to it are all zero. In other words, a tri diagonal matrix has non-zero elements only in the main diagonal, the diagonal above it, and the diagonal below it. Tri diagonal matrices find application in various fields, including numerical analysis, computational mathematics, and computer science.
Which Data Structure Is Best for Matrix?
The choice of the right data structure is crucial when working with matrices. A matrix is a two-dimensional array that consists of rows and columns, and it is commonly used in various fields such as mathematics, computer graphics, and machine learning. In this article, we will explore different data structures and determine which one is best for handling matrices.
What Is Matrix Data Structure?
The Matrix Data Structure: A Comprehensive Overview
Matrices are an essential part of computer science and mathematics. They provide a structured way to organize and store data in a two-dimensional grid format. In this article, we will explore the concept of a matrix data structure, its properties, and its applications.
What Is Matrix Transpose in Data Structure?
Matrix transpose, also known as matrix transposition, is an important concept in the field of data structures. It involves rearranging the elements of a matrix such that the rows become columns and vice versa. This operation is denoted by the superscript ‘T’ or by writing the matrix with its rows and columns interchanged.
What Is Transpose Matrix in Data Structure?
What Is Transpose Matrix in Data Structure? A transpose matrix is a fundamental concept in data structures that involves rearranging the rows and columns of a given matrix. This operation essentially flips the matrix over its main diagonal, resulting in a new matrix where the rows become columns and the columns become rows.
What Is a Matrix Data Structure?
A matrix data structure is a two-dimensional array that represents a collection of elements arranged in rows and columns. It is commonly used to store and manipulate data in various applications, such as mathematical operations, computer graphics, and scientific simulations. In this article, we will explore the concept of a matrix data structure and its significance in programming.
```<|endoftext|>
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In 1740, the death of the Holy Roman Emperor, Charles IV, set of the War of Austrian Succession. The War would have ripple effects felt around the world in Rochester. When Charles IV died his daughter, Maria Theresa was left to take his place. France and Prussia challenged her authority declaring she was not eligible to assume the various thrones held by the Hapsburgs because she was a woman. The British and Dutch who had long been enemies of the French supported Austria. Great Britain did not get involved in the war until late 1743. In March 1744, war was officially declared between France and Great Brittan. In May, the news reached the French colony at Nova Scotia. The French wasted little time in attacking British ports. The war soon spread to British holdings in New York, New Hampshire and Massachusetts. The war front in the American colonies is known as King George’s War.
Native Americans were often drawn in to colonial wars as allies for the colonists. War could be a valuable source of income for natives but could also be devastating to native families because Native American men suffered high mortality rates in conflicts.
Native Americans also sided with the French during colonial conflicts with the British. Eastern Abenaki in Maine often sided with the French but by the outbreak of King George’s War the Abenaki were suffering from internal conflicts and the southern Abenaki known as the Pigwacket sided with the British.
However, not all of the Pigwacket wished to take sides and fight in the war. In July 1744, several Pigwacket leaders went to Boston to ask the Governor for a safe place to settle during the duration of the war. The Pigwacket wanted to locate to an area in which they had friends. The colonial government denied this request instead choosing a settlement where they could keep a close eye on and make sure they did not get involved in the war against the British. The other option given to the Pigwacket people was to return to where they came from and face a harsh treatment from both sides of the war parties.
The Pigwacket were moved to Castle Island where they were put to work making snowshoes. A colonial committee had been charged with investigating the situation at Castle Island and decided to send the Pigwacket to “English Families, as shall be willing on reasonable Conditions to receive them…” The colonial government wanted to move the Pigwacket further away from the war front, ideally south of Boston. However, they had difficulty finding a town that would welcome them.
By 1746, the Pigwacket found a home in Rochester. The people of Rochester were willing to host the war refugees and provided some land at Attansawomuck Neck now known as Mattapoisett Neck for the Pigwacket to live. Local residents Noah Sprague and Benjamin Hammond, Jr. were appointed by the colonial committee to act as guardians. These men provided the Pigwacket with necessary tools such as axes, hoes and a fishing boat with funds given by the committee.
Noah Sprague sent bills to the committee to have them pay for materials and goods used by the Pigwacket people including wood cut from his swamp that was used to make baskets and dishes, cedar shingles and picked green apples. Sprague even charged the committee thirty pounds for “extradinary Travlle & care” he had provided.
The Pigwacket people felt the reservation they had been placed on was too confining and they were not happy with their situation. A Rochester resident complained that the Pigwacket were “insolent and surly” and asked the General Court to remove them from Rochester. A General Court committee investigated the situation and accused local residents of selling liquor to the Pigwacket and providing poor guardianship.
The Pigwacket stayed in Rochester but were moved to another tract of land northwest of the Witch Rock on New Bedford Road. By the early 1900s, this area of land had been “given up to woods and huckleberry pastures” and was known in Rochester as Pigwacket.
In 1748 many of the Pigwacket left and returned home. However, some settled with Native Americans in Dartmouth, Freetown and Middleboro. The name Pigwacket survives today in Mattapoisett as Pigwacket Lane but the location of this street does not correspond with the location of the Pigwacket settlement over two centuries ago.<|endoftext|>
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This publication is now archived.
The March 2008 anti-government clashes in Tibet and other regions in China brought the decades-long dispute once more into the international spotlight demonstrating the depth of historical disagreement over the territory. Tensions between China and Tibet have persisted since People’s Republic of China was founded in 1949. China says Tibet has been a part of China for many centuries now, a claim refuted by many Tibetans. Chinese authorities use this claim to support their sovereignty over the territory while proponents of the Tibetan independence point to periods in Tibetan history when it enjoyed self-rule. Meanwhile, Chinese government policies in Tibet have fed the conflict. These inlude restrictions on cultural and religious freedoms of Tibetans, attempts to change the demographics of the region through migration of ethnic Chinese, and an unwillingness to open dialogue with Tibet’s exiled spiritual leader, the Dalai Lama. Experts believe the dispute over Tibet will persist as long as China refuses to speak to the Dalai Lama, who has been in exile in neighboring India since 1959. China, however, has sought to bypass the 73-year-old Dalai Lama and concentrated instead on efforts to control the process that will determine his successor.
Unresolved Political Status
The contemporary dispute over Tibet is rooted in religious and political disputes starting in the thirteenth century. China claims that Tibet has been an inalienable part of China since the thirteenth century under the Yuan dynasty. Tibetan nationalists and their supporters counter that the Chinese Empire at that time was either a Mongol (in Chinese, Yuan) empire or a Manchu (Qing) one, which happened to include China too, and that Tibet was a protectorate, wherein Tibetans offered spiritual guidance to emperors in return for political protection. When British attempts to open relations with Tibet culminated in the 1903-04 invasion and conquest of Lhasa, Qing-ruled China, which considered Tibet politically subordinate, countered with attempts to increase control over Tibet’s administration. But in 1913, a year after the Qing dynasty collapsed, Tibet declared independence and all Chinese officials and residents in Lhasa were expelled by the Tibetan government. Tibet thenceforth functioned as a de facto independent nation until the Chinese army invaded its eastern borders in 1950.
But even during this period, Tibet’s international status remained unsettled. China continued to claim it as sovereign territory. Western countries, including Britain and the United States, did not recognize Tibet as fully independent. After founding the People’s Republic of China in 1949, the new communist government in China sought reunification with Tibet and decided to invade it in 1950. A year later, in 1951, the Dalai Lama’s representatives signed a seventeen-point agreement with Beijing, granting China sovereignty over Tibet for the first time. The agreement stated that the central authorities “will not alter the existing political system in Tibet” or “the established status, functions and powers of the Dalai Lama.” While the Chinese government points to this document to prove Tibet is part of Chinese territory, proponents of Tibetan independence say Tibet was coerced into signing this document and surrendering its sovereignty.
“Experts point to the years from 1913 to 1950, a time when Tibet behaved like a de facto independent state, to argue that Tibet was not always part of China.”
Experts also point to the years from 1913 to 1950, a time when Tibet behaved like a de facto independent state, to argue that Tibet was not always part of China. But China blames the British influence at the time for provoking the idea of Tibetan independence and refuses to be bound by any treaties signed between Tibet and Britain during that period. This includes the 1914 Simla convention where the British recognized Tibet as an autonomous area under the suzerainty of China.
The political status question is also complicated by uncertainty about what constitutes Tibet’s borders. The Chinese only accept the term Tibet for the western and central areas, the area which is now called the Tibet Autonomous Region (TAR). This area was directly ruled by the Lhasa government when the Chinese invaded in 1950. But Tibetan exiles have been demanding a Greater Tibet which includes political Tibet in modern times (TAR) as well as ethnic Tibetan areas east of TAR, most of which Tibet had lost in the eighteenth century. These areas, earlier known as Amdo and Kham, are now scattered among parts of Chinese provinces of Sichuan, Qinghai, Yunnan and Gansu. The March 2008 anti-government protests, which started in Lhasa, soon spread among the ethnic Tibetan areas in these provinces.
Experts say there is no document in which the Tibetan people or their government explicitly recognizes Chinese sovereignty before the invasion of 1950. But Robert Barnett, a Tibet specialist at Columbia University, says the importance of this argument lies not in its role in the legal debate, but in what it indicates in terms of the political realities on the ground. “The fact is that most Tibetans seem to have experienced themselves and their land as distinct from China,” he says.
Conflict with China
Since China’s invasion, Barnett says, “China’s policies towards the Tibetans can perhaps best be described as a mix of brutality and concession.” The first Tibetan uprising of 1959 resulted in the flight of the Dalai Lama and about 80,000 Tibetans. During these years thousands of Tibetans were allegedly executed, imprisoned, or starved to death in prison camps. So far no Chinese official has publicly acknowledged these atrocities. This period also included a policy of induced national famines that resulted from tenets of the so-called Great Leap Forward, when Beijing set up communes in agricultural and pastoral areas. The Cultural Revolution, the next phase of Mao’s revolutionary politics, followed in 1966 and continued in effect until 1979 in Tibet. During these years, all religious activities were prohibited and the monastic system in Tibet was dismantled. The campaign included an attempt to eradicate the ethnic minority’s culture and distinctive identity as a people.
“If India is indeed a liberal democracy, it must be willing to speak out about gross Chinese human rights violations.” -- Sumit Ganguly, Indiana University
Deng Xiaoping’s rise to power in China in 1978 brought forth a new initiative to resolve the Tibet question. Besides reaching out to the Dalai Lama in exile in India, the Chinese authorities also initiated a more conciliatory ethnic and economic development policy. Tibetans were encouraged to revitalize their culture and religion. Infrastructure was developed to help Tibet grow. But pro-independence protests in Tibet that started in 1987 led to the declaration of martial law in the region in 1989. After martial law was lifted in May 1990, Chinese authorities adopted a more hard-line policy with stricter security measures, curtailing religious and cultural freedoms. At the same time, a program of rapid economic development was adopted which included much resented incentives encouraging an influx of non-Tibetans, mostly Han Chinese, into Tibet. This, Beijing hopes, will result in a new generation of Tibetans who will be less influenced by religion and consider being part of China in their interest, wrote Tibet expert Melvyn C. Goldstein in Foreign Affairs in 1998. “Even if such an orientation does not develop, the new policy will so radically change the demographic composition of Tibet and the nature of the economy that Beijing’s control over Tibet will not be weakened.”
Government-in-exile in India
When the Dalai Lama sought exile in Dharamsala in northern India in 1959, India arguably became a key player in the conflict. India now is home to about 120,000 Tibetans, the world’s largest Tibetan community outside of Tibet. But since 1952, India has always regarded Tibet as an integral part of China and does not encourage overt criticism of China by Tibetans in exile. Sumit Ganguly, a professor of political science at Indiana University, is openly critical of the Indian policy. “If India is indeed a liberal democracy,” he says, “it must be willing to speak out about gross Chinese human rights violations.”
Ganguly believes India’s administration can exert pressure on China by allowing Indian Tibetans to demonstrate peacefully without interference, and by treating the Dalai Lama as a head of state instead of a spiritual leader. But there are many Indian analysts who believe otherwise. “There is interest on both sides, very deep interest, to see that what is happening is not allowed to upset the apple cart—the present momentum of India-China relations,” says Mira Sinha Bhattacharjea, former director of the Institute of Chinese Studies in New Delhi. Relations between India and China, long fraught with resentments including a short border war in 1962, recently have warmed. China became India’s biggest trading partner in 2007. The two countries have also seen a thaw in diplomatic relations.
The United States and the West
Experts say U.S. policy has done little to help resolve the Tibet issue. According to A. Tom Grunfeld, a professor of history at Empire State College, Washington’s policy is inherently contradictory. “While officially recognizing Tibet as part of China,” he writes, “the U.S. Congress and White House unofficially encourage the campaign for independence.”
“While officially recognizing Tibet as part of China, the U.S. Congress and White House unofficially encourage the campaign for independence.” -- A. Tom Grunfeld, Empire State College
Goldstein writes Washington has been opportunistic in its dealings (PDF) with Tibet. During the Cold War in the 1950s and 1960s, the U.S. Central Intelligence Agency (CIA) covertly funded and armed Tibetan guerilla forces to fight against communist China. But even during this period of covert support, Washington’s official position on Tibet did not change. It continued to recognize it as a part of China. CIA’s covert funding stopped in 1971 as U.S. interest in Tibet waned due to warmer relations with China. But pressure from the Tibet lobby complicated the policy environment, argues Grunfeld. In the 1980s, Tibetans in exile launched a new strategic initiative with an aim to secure increased political support from the United States and the West to exert pressure on China.
An important element in this new strategy was visits and speeches by the Dalai Lama in the West. In September 1987, the Dalai Lama spoke before the Congressional Human Rights Caucus in Washington. The following June, he made another important address at the European Parliament in Strasbourg. For the first time publicly, he laid out a willingness to accept something less than independence for Tibet. Calling for genuine autonomy for Tibet within the framework of China, the Dalai Lama proposed that Tibet have full control over its domestic affairs but that China could remain responsible for Tibet’s defense and foreign affairs. He reiterated this “middle-way approach” in a 2001 address to the European parliament. The Tibet issue has also won popular sympathy in the west including interest of Hollywood actors like Richard Gere who actively lobby for the Tibetan cause. But the success of the international campaign for Tibet has bolstered hard-liners within the Chinese government, experts say, thereby worsening conditions for the Tibetan people.
A Difficult Solution
Tibet is very important to China’s sense of nationhood, says CFR’s China expert Adam Segal. “There is a fear that if Tibet gets independence, Uighurs and Taiwan will want independence.” Segal notes that Chinese authorities have frequently suggested that they are just waiting for the Dalai Lama to die, expecting Tibetan nationalism to disappear after his death, but says this may be a miscalculation. “I think the more radical Tibetans would direct the movement for independence after Dalai Lama’s death.”
Experts agree that unless there is political reform within China, the resolution of the Tibetan question remains bleak. "The historical question was never unsolvable," says Barnett. "It would not have been a problem necessarily if China had been able to develop policies for Tibet that were acceptable to most Tibetans." In November 2008, the Dalai Lama said his efforts to bring autonomy to Tibet had failed so far and called for a meeting of Tibetans from around the world to consider the future of the Tibetan movement. The meeting, which took place Nov. 17-22 in Dharamsala, India, drew more than five hundred Tibetans. Though the meeting closed with what was described as a "strong endorsement" of the Dalai Lama’s "middle-way" approach, participants also "clearly stated" they might seek independence if talks with China do not bring progress "in the near future."<|endoftext|>
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Investigation of Parametric Curves
By: Denise Natasha Brewley
Consider the following parametric equations of the following form for 0 < t < 2p :
x = a cos(t)
y = b sin(t)
We will begin this investigation by considering different values of a and b. First let us look at the case when we have a < 0 < b. Namely when a = -1/2 and b = 1
Notice that the parametric equations give us what appears to be an ellipse centered at the origin. An ellipse is the set of all points P in a plane such that the sum of the distances of P from two fixed points in the plane is constant. What we now want to do is verify that this is an ellipse. Recall that each value of t determines a value of x and y in rectangular coordinates. To eliminate the parameter t, we solve the system of parametric equations and substitute our respective values of cos(t) and sin(t) into the Pythagorean identity cos2t + sin2t = 1. So it follows that we have
cos(t) = -2x and sin(t) = y
(-2x)2 + (y)2 = 1
4x2 + y2 = 1
(x/(1/2))2 + (y/1)2 = 1
The result is an ellipse in rectangular form with major axis of length = 1 and minor axis of length = 1/2 just as we conjectured. The major axis is longest distance found through the center and foci of an ellipse. Similarly the minor axis is the shortest distance found through the center of the ellipse. This means that the distance from the origin to the major vertices is 1 and the distance from origin to the co-vertices is 1/2. In general we can determine the length of the major axis and minor axis of the ellipse by simply looking at our parametric equations. The major axis is the the longest length between a and b. And the minor is the shortest length between a and b. Since we are given that [x = -0.5 cost and y = sint] with a = -1/2 and b = 1. It follows that the length of our minor axis is |a|= 1/2 and our major axis is |b|= 1; 1/2 < 1. This also tells us if the major and minor axis will be vertical or horizontal. Notice that for this parametric curve it has a major axis that is vertical and a minor axis that is horizontal.
Because we have the equation of an ellipse, as indicated above, we can make a conjecture. But before that, let's ask some questions. What will happen if we have the case a < 0 < b and 0 < a < b? Will this give us the same parametric curve? Let us see what will happen. If we are given the following, x = a cos(t) and y = b sin(t), it follows that
cos(t) = x/a and sin(t) = y/b
(x/a)2 + (y/b)2 = 1
x2/a2 + y2/b2 = 1
So we can say for values a < 0 < b and 0 < a < b such that, |a|< |b|, we will have the same parametric curves in t and equation in rectangular form in x and y. Try this for the parametric equations [x = -0.5 cos(t) and y = sin(t)] and [x = 0.5 cos(t) and y = sin(t)]. Now let's look at a family of parametric curves that satisfies this claim.
Using this model we will continue our exploration of other values of a and b. We will now consider when a = b, specifically when a = b = -1 < 0 If we continue this investigation as we did in the previous example, we will obtain an ellipse, where the major and minor axis are the same. We can also say that the distance from origin to the vertices and co-vertices are also the same. But this is just a circle centered at the origin with radius = 1, namely x2 + y2 = 1It is important to note here that in the case when a = b > 0 , the resulting graph would be the same as in the negative case which was already discussed.
So for values of a and b such that |a|=|b|, we can consider the family of the parametric curves. Can you guess what the equation of each curve is based on our discussion?
Now let us look at the case when 0 < b < a and b < 0 < a. We will consider case a = 1 and b = 1/2 and generalize. Repeating the steps above, we obtain the following:
cos(t) = x and sin(t) = 2y
x2 + (2y)2 = 1
x2 + 4y2 = 1
x2 + (y/(1/2))2 = 1
In this case the major axis is horizontal and the minor axis is vertical. Which follows since |b|= 1/2 < |a|= 1.
So we can generalize for this case as well. That is, when |b|<|a|.
BACK TO THE HOMEPAGE<|endoftext|>
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A nanometer is one-billionth of a meter. That's impossibly small. A single sheet of paper is 100,000 nanometers. Your fingernail grows approximately 1 nanometer every second. Even a strand of your DNA is 2.5 nanometers wide [source: NANO.gov]. To construct materials at the "nano" scale would seem impossible, but using cutting-edge techniques like electron-beam lithography, scientists and engineers have successfully created tubes of carbon with walls that are only 1 nanometer thick.
When a larger particle is divided into increasingly smaller parts, the proportion of its surface area to its mass increases. These carbon nanotubes have the highest strength-to-weight ratio of any material on Earth and can be stretched a million times longer than their thickness [source: NBS]. Carbon nanotubes are so light and strong that they can be embedded into other building materials like metals, concrete, wood and glass to add density and tensile strength. Engineers are even experimenting with nanoscale sensors that can monitor stresses inside building materials and identify potential fractures or cracks before they occur [source: NanoandMe.org].<|endoftext|>
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Markov's Marbles A container holds 2 green marbles and 9 red marbles. Two players, A and B, alternately pick a marble from the container. If it's red, the marble is replaced. If it's green, it is kept. The player who gets the second green marble wins. What are the odds of winning for the player who draws first? Problems like this can be solved by means of a simple Markov model. The game is either in State 1 (no greens have yet been drawn) or State 2 (one of the greens has been drawn and removed). In State 1, each draw has probability 2/11 of going to State 2, and 9/11 of staying in State 1. In State 2, each draw has probability 1/10 of ending the game (by drawing the second green) and 9/10 of staying in State 2. So, if we let P1[n] and P2[n] denote the probability of being in states 1 and 2 respectively after the nth draw, we begin with P1[0] = 1 and P2[0] = 0. Thereafter, the probabilities can be computed by the recurrence relation Letting W[n] denote the probability that the game has been won by someone after the nth draw, we obviously have Now, the recurrence relation can be written in matrix form as P[n] = M P[n−1] where P[n] is the column vector of probabilities and M is the transition matrix From this we also have the simple closed-form expression for the nth probability vector P[n] = Mn P[0]. We want to know the probability of winning for the player who draws first. The two players alternate, so the one who draws first will also draw 3rd and 5th and so on. Thus, the question is: What is the probability that the game will end on an odd-numbered draw? The probability of ending the game on the first draw is W[1] − W[0], and of winning on the 3rd draw is W[3] − W[2], and so on. In general, the probability of winning on the (2n+1)th draw is So, the sum of all the probabilities of ending the game on an odd-numbered draw is given by the sum of the components of the vector P[0] − P[1] + P[2] − P[3] + ..., and this equals the geometric series Since P[0] is just [1,0]T, we want the sum of the left-hand column of the matrix So the probability of a win on the odd draws is 11/20 − 1/19, which equals 189/380 = 0.49736... Of course, we could have computed the probability of a win on the even draws, simply by bumping the index up one number, i.e., multiplying by M, to give which confirms that the "even" probability is, as expected, Obviously this approach can be extended to cover any number of red and green marbles. If there are N green marbles, the transition matrix will be of size N x N. Return to MathPages Main Menu<|endoftext|>
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# What is 51/139 as a decimal?
## Solution and how to convert 51 / 139 into a decimal
51 / 139 = 0.367
51/139 or 0.367 can be represented in multiple ways (even as a percentage). The key is knowing when we should use each representation and how to easily transition between a fraction, decimal, or percentage. Decimals and Fractions represent parts of numbers, giving us the ability to represent smaller numbers than the whole. The difference between using a fraction or a decimal depends on the situation. Fractions can be used to represent parts of an object like 1/8 of a pizza while decimals represent a comparison of a whole number like \$0.25 USD. If we need to convert a fraction quickly, let's find out how and when we should.
## 51/139 is 51 divided by 139
The first step of teaching our students how to convert to and from decimals and fractions is understanding what the fraction is telling is. 51 is being divided into 139. Think of this as our directions and now we just need to be able to assemble the project! Fractions have two parts: Numerators on the top and Denominators on the bottom with a division symbol between or 51 divided by 139. To solve the equation, we must divide the numerator (51) by the denominator (139). This is our equation:
### Numerator: 51
• Numerators are the portion of total parts, showed at the top of the fraction. 51 is one of the largest two-digit numbers you'll have to convert. The bad news is that it's an odd number which makes it harder to covert in your head. Large numerators make converting fractions more complex. Now let's explore the denominator of the fraction.
### Denominator: 139
• Denominators represent the total parts, located at the bottom of the fraction. 139 is one of the largest two-digit numbers to deal with. But the bad news is that odd numbers are tougher to simplify. Unfortunately and odd denominator is difficult to simplify unless it's divisible by 3, 5 or 7. Have no fear, large two-digit denominators are all bark no bite. So without a calculator, let's convert 51/139 from a fraction to a decimal.
## Converting 51/139 to 0.367
### Step 1: Set your long division bracket: denominator / numerator
$$\require{enclose} 139 \enclose{longdiv}{ 51 }$$
Use long division to solve step one. Yep, same left-to-right method of division we learned in school. This gives us our first clue.
### Step 2: Extend your division problem
$$\require{enclose} 00. \\ 139 \enclose{longdiv}{ 51.0 }$$
Uh oh. 139 cannot be divided into 51. So that means we must add a decimal point and extend our equation with a zero. Even though our equation might look bigger, we have not added any additional numbers to the denominator. But now we can divide 139 into 51 + 0 or 510.
### Step 3: Solve for how many whole groups you can divide 139 into 510
$$\require{enclose} 00.3 \\ 139 \enclose{longdiv}{ 51.0 }$$
How many whole groups of 139 can you pull from 510? 417 Multiply by the left of our equation (139) to get the first number in our solution.
### Step 4: Subtract the remainder
$$\require{enclose} 00.3 \\ 139 \enclose{longdiv}{ 51.0 } \\ \underline{ 417 \phantom{00} } \\ 93 \phantom{0}$$
If there is no remainder, you’re done! If you have a remainder over 139, go back. Your solution will need a bit of adjustment. If you have a number less than 139, continue!
### Step 5: Repeat step 4 until you have no remainder or reach a decimal point you feel comfortable stopping. Then round to the nearest digit.
In some cases, you'll never reach a remainder of zero. Looking at you pi! And that's okay. Find a place to stop and round to the nearest value.
### Why should you convert between fractions, decimals, and percentages?
Converting fractions into decimals are used in everyday life, though we don't always notice. Remember, they represent numbers and comparisons of whole numbers to show us parts of integers. Same goes for percentages. Though we sometimes overlook the importance of when and how they are used and think they are reserved for passing a math quiz. But each represent values in everyday life! Without them, we’re stuck rounding and guessing. Here are real life examples:
### When you should convert 51/139 into a decimal
Sports Stats - Fractions can be used here, but when comparing percentages, the clearest representation of success is from decimal points. Ex: A player's batting average: .333
### When to convert 0.367 to 51/139 as a fraction
Pizza Math - Let's say you're at a birthday party and would like some pizza. You aren't going to ask for 1/4 of the pie. You're going to ask for 2 slices which usually means 2 of 8 or 2/8s (simplified to 1/4).
### Practice Decimal Conversion with your Classroom
• If 51/139 = 0.367 what would it be as a percentage?
• What is 1 + 51/139 in decimal form?
• What is 1 - 51/139 in decimal form?
• If we switched the numerator and denominator, what would be our new fraction?
• What is 0.367 + 1/2?<|endoftext|>
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# GRAPH INTEGERS ON HORIZONTAL AND VERTICAL NUMBER LINES
## About "Graph integers on horizontal and vertical number lines"
Graph integers on horizontal and vertical number lines :
Before going to know about how to graph integers on horizontal and vertical lines, first we have to know about what is horizontal number line and what is vertical number line.
Horizontal number line :
Draw a line horizontally and mark some points at equal distance on it as shown in the figure.
Mark a point as zero on it. Points to the right of zero are positive integers and are marked + 1, + 2, + 3, etc. or simply 1, 2, 3 etc.
Points to the left of zero are negative integers and are marked – 1, – 2, – 3 etc. In order to mark – 6 on this line, we move 6 points to the left of zero.
Vertical number line :
Draw a line vertically and mark some points at equal distance on it as shown in the figure.
Mark a point as zero on it. Points to the upward of zero are positive integers and are marked + 1, + 2, + 3, etc. or simply 1, 2, 3 etc.
Points to the upward of zero are negative integers and are marked – 1, – 2, – 3 etc. In order to mark – 6 on this line, we move 6 points to the left of zero.
Let us see some example problems to understand how to graph the given integers on horizontal and vertical number lines.
Example 1 :
The below vertical number line, representing integers. Observe it and locate the following points :
(a) If point D is + 8, then which point is – 8?
(b) Is point G a negative integer or a positive integer?
Solution :
(a) To find the position of the number -8, first let us mark down the points vertically on the given number line.
By marking the point on the given number line, we come to know that -8 is at the position F.
(b) By observing the number line "G" is below 0. Hence it is negative.
Example 2 :
Following is the list of temperatures of five places in India on a particular day of the year.
Place Temperature New yorkChicagoBoston 10°C below 0°C2°C below 0°C30°C above 0°C
Plot the name of the city against its temperature.
From this we come to know that New york is the coolest place.
After having gone through the stuff given above, we hope that the students would have understood "Graph integers on horizontal and vertical number lines".
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WORD PROBLEMS
HCF and LCM word problems
Word problems on simple equations
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Algebra word problems
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Area and perimeter word problems
Word problems on direct variation and inverse variation
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Word problems on sets and venn diagrams
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OTHER TOPICS
Profit and loss shortcuts
Percentage shortcuts
Times table shortcuts
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Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
Sum of all three four digit numbers formed using 0, 1, 2, 3
Sum of all three four digit numbers formed using 1, 2, 5, 6<|endoftext|>
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Interpersonal communication is a dynamic and complex human phenomenon that includes at least two communicators. These communicators intentionally orient toward each other as both subject and object whose actions embody each other’s perspectives both toward self and toward other. In essence, interpersonal communication is a goal-driven interaction between at least two people that typically occurs in a face-to-face environment. However, scholarly trends are moving toward studying mediated interpersonal communication via communication technologies. Interpersonal communication in organizations represents an interaction process including a variety of relational situations. These internal situations involve superior-subordinate and peer communication. This article centers on internal interpersonal communication. First, an overview of the process of interpersonal communication will be provided. Second, interpersonal communication is situated in organizations by examining superior-subordinate communication and peer communication. Finally, the process of interpersonal communication is contextualized by reviewing the impact of trust and technology on interpersonal communication in organizations.
The Process of Interpersonal Communication
The process of interpersonal communication is viewed from a general communication perspective provided by Claude Shannon and Warren Weaver. This model, in its most basic format, includes the sender, the message, the channel, and the receiver. Noise provides an additional component.
The first two components of interpersonal communication are the sender and the message. The sender mentally composes a message to relay to another person, taking into account the reason, or intention, for sending the message. Perhaps it is meant to persuade, or to inform. The act of transferring this message from thought to words is called encoding.
The channel in this model refers to the mode of communication used to relay the message. Familiar channels include television, radio, and newspaper. However, interpersonal communication differs from mass communication in this respect because the channel used is face-to-face communication in which messages are relayed through verbal interaction at one location.
The fourth component of this model is the receiver. This person is responsible for taking the sender’s message and decoding it. The action of decoding results in the assignment of meaning by the receiver.
The exchange described is one basic unit of interaction between communicators. Once the receiver decodes the message and gives meaning to it, that person can encode another message to relay to the sender. The resulting action is characterized as feedback. Feedback helps to clarify the original message or to enhance it. In the feedback process, the original receiver then becomes the sender who encodes the message, and the original sender becomes the receiver who decodes the message. Again, the channel of communication remains face-to-face. This process can continue in a cyclical manner, creating a dialogue between both people.
An additional component affecting the interaction represented in this model is noise. Noise refers to anything that could interfere with the transmission of the message from the sender to the receiver, and it can be attributed to a number of sources. Physical sources are often much easier to recognize and would include a loud truck driving by while the sender was talking to the receiver during a meeting, or if the receiver was having difficulty with his hearing aid while listening to the sender speak.
Noise related to differences in perception can also interfere with the ability for communicators to relay a message. This type of noise is attributed to a number of factors, including nonverbal communication and cultural differences. Differences in perception can lead to conflict among the communicators.
The supervisory-subordinate relationship is the primary interpersonal relationship structured by the organization. Individuals’ relationship with their supervisor is one of the most important communication facets of their organizational life. This relationship is so critical that it may determine how individuals identify with the organization, as well as the individuals’ job and organizational satisfaction and commitment. Particularly, the quality of supervisory communication and information exchanges have been linked to revenue and productivity measures of the overall organization.
Most organizations typically have superior-subordinate relationships among organizational members. Generally, research in the area of superior-subordinate interpersonal communication centers on exchanges of information and influence between organizational members, at least one of whom has formal authority, granted by the organizational structure, to direct and evaluate the activities of other organizational members. Daniel Katz and Robert Kahn suggested that superior to subordinate communication typically centers on information regarding organizational procedures and practices, indoctrination of goals, job instructions, job rationale, or feedback on performance. Similarly, subordinate to superior communication typically focuses on information about the subordinates themselves, their colleagues, and their work-related or personal problems; information about tasks to accomplish; or about organizational policies and practices.
- F. Smith and S. A. Hellweg found in 1985 that subordinates are more satisfied with their work when communication between subordinate and supervisor is good. A strong predictor of subordinate satisfaction is the superior’s ability to listen, respond quickly to messages, and be sensitive, empathic, and understanding.
- R. Waldron and M. D. Hunt further posited in 1992 that subordinates reporting high-quality relationships with their supervisors were more likely to engage in informal, friendly interactions with their supervisors, to conform to formal and informal requests, to attempt to clarify expectations, and to accept criticism from supervisors than were individuals reporting lower-quality relationships.
Leader-member exchange (LMX) theory frequently informs superior-subordinate relationships. The LMX theory has been linked to a variety of communication behaviors and suggests that leaders have limited time and resources and share both personal and positional resources differently with their subordinates. In sum, Jaesub Lee and colleagues suggested in 1999 that leaders tend to develop and maintain exchanges with their subordinates that vary in degrees of quality. These relationships range from high (in-group) to low (out-group) exchanges. In-group exchange is considered a high-quality relationship reflected by high levels of information exchange, mutual support, informal influence, and trust, and greater negotiating latitude and input in decision influence. Alternatively, out-group exchange reflects a low-quality relationship characterized by formal supervision, less support, and less trust and attention from the supervisor.
Research on Superior-Subordinate Relationships
There are several areas of research examining issues of superior-subordinate communication. These include the following:
- Interaction patterns. Research that studies the communication patterns between supervisors and their subordinates. How much time is spent communicating with each other? Who initiates the communication? What is the importance of the interactions?
- Openness in communication. This line of research examines two dimensions of openness in the superior-subordinate relationship: message sending (delivering bad news, candor in communication, providing important company facts) and message receiving (encouraging frank expressions of alternative views).
- Upward distortion. This occurs when persons of lower hierarchical rank in organizations communicate with persons of higher rank. Upward distortion falls into four general categories:
- Subordinates tend to distort upward information, saying what they think will please their supervisors.
- Subordinates tend to filter information and tell their supervisors what they, the subordinates, want them to know.
- Subordinates often tell supervisors what they think the supervisor wants to hear.
- Subordinates tend to pass personally favorable information to supervisors while not transmitting unfavorable information about themselves to supervisors.
- Upward influence. This line of research focuses on two dimensions of influence: (a) the effects a superior’s influence in the hierarchy has on his or her relationships with subordinates and (b) subordinates’ use of influence with their supervisors.
- Semantic-information distance. This research describes the gap in agreement and/or understanding on specific issues between superiors and subordinates (e.g., job duties and leaders’ authority).
- Effective versus ineffective superiors. Examines prescriptive characteristics of effective and ineffective communication behaviors among organizational supervisors, as well as communication qualities of effective leaders.
- Personal characteristics. These study the mediating effects of personal characteristics of superiors and subordinates (e.g., communication apprehension, communication competence, locus of control, and communicator style).
- Feedback. Research focusing on relationship between feedback and performance, feedback and motivation, feedback and attributional processes, the use of rewards and punishments as feedback, and the feedback-seeking behavior of individuals.
- Conflict. Research examining the role of communication in superior-subordinate conflict (e.g., conflict management style, organizational level, power, perceptions of skills, perceptions of subordinate’s personality).
Peer communication is an important interpersonal facet in everyday organizational life. This area of study focuses on coworker communication within and between work groups. Peer communication is important for three reasons:
- Peer interpersonal communication differs from superior-subordinate communication (e.g. relationship rules, message strategy choices).
- Peer communication and the use of groups to accomplish work goals in organizations is increasing.
- Peer interpersonal communication is an important source of support, friendship, and job satisfaction and commitment.
Peers communicate about job requirements, provide social support, and are in a position to give advice without formally evaluating performance. Peers also may help each other solve organizational problems or issues and utilize the best strategies to use with supervisors. However, peer communication is not without problems. Peers can withhold information from one another, which makes accomplishing individual and group goals difficult.
Research on Interpersonal Communication in Organizations
Interpersonal communication is complex. It is a difficult proposition to communicate effectively with others while maintaining an authentic sense of self. Communication may be difficult with others owing to the wide array of interactions on a regular basis. Communication partners have different interpersonal communication experiences that contribute to how they communicate and interact with others. Exposure to multiple communication partners can be confusing if one is not familiar with recognizing and adjusting to different styles and patterns of communication.
Several factors contribute to the interpersonal communication process in organizations. They include interpersonal trust, the use of nonverbal communication, cultural differences between the partners, and technology in interpersonal relationships.
Interpersonal Trust in Organizations
The role of interpersonal communication in the development of relationships is a popular area of study for communication researchers. Interpersonal communication may occur between people who have had continual interaction or between people who do not have past experiences with each other, allowing a reduction in drawing on a historical frame of reference. Regardless of the interpersonal situation, trust is a critical factor in all interpersonal relations. Although a general term, trust is defined as positive expectations about the behavior of others based on roles, relationships, experiences, and interdependencies, as noted by Pamela Shockley-Zalabak in 2002. Shockley-Zalabak, Kathleen Ellis, and Ruggero Cesaria discussed in 2000 the central role that organizational communication plays in the behavior components of trust. These scholars highlight three primary areas of organizational trust that strengthens communication:
- Accurate information. Information flow that is forthcoming
- Explanations for decisions. Adequate and timely feedback on decisions
- Managers and supervisors freely exchange thoughts and ideas with their employees
Technology and Interpersonal Communication
Interpersonal communication is typically restricted to communication that occurs in a face-to-face environment. However, with an increase in the use and access of technologies in organizations, mediated interpersonal communication is becoming a salient area of inquiry. Knowledge of interpersonal communication has become more important in recent years, especially as organizations have expanded their activities to other countries and relied on computer-mediated communication to overcome physical distances. The rapidly increasing use of computer-mediated communication to connect members of an organization has resulted in more research relating to both computer-mediated communication and globalization. It raises questions regarding key assumptions of face-to-face interaction and highlights the need to understand interpersonal communication. This higher level of awareness is more likely to produce organizational members who recognize their own and others’ communication needs, resulting in communicators who are more effective.
Technology is changing the way we view and engage each other in our relationships. Communication technologies have eradicated boundaries of brick-and-mortar buildings, where face-to-face interactions were predominant, to expand time and spatial restrictions that inform interpersonal and work communication. Individuals accomplish work through various time zones, cultural differences, and particularly geographic locations. Because of this, we work with people without much information about their background, history, or experiences, much less their worldviews, values, and ideology. This may create opportunities for effective interpersonal communication or may greatly hinder it, depending on how well individuals react to this new way of working. Teleworking (individuals who work at home or in other organizationally controlled spaces) and virtual teams (individuals who work as part of a team remotely solely using communication technologies) are new interpersonal communication configurations informed by technology.
- Cupach, W. R., & Spitzberg, B. H. (Eds.). (1994). The dark side of interpersonal communication. Hillsdale, NJ: Lawrence Erlbaum.
- Jablin, F. M., & Krone, K. J. (1994). Task/work relationships: A life-span perspective. In M. L. Knapp & G. R. Miller (Eds.), Handbook of interpersonal communication (pp. 621-675). Thousand Oaks, CA: Sage.
- Lee, J., Jares, S. M., & Heath, R. L. (1999). Decision-making encroachment and cooperative relationships between public relations and legal counselors in the management of organizational crisis. Journal of Public Relations Research, 11(3), 243-270.
- Littlejohn, S. W. (2002). Communication in relationships. In Theories of human communication (7th ed., pp. 234262). Belmont, CA: Wadsworth.
- Miller, K. (1995). Conflict management processes. In Organizational communication: Approaches and processes (pp. 231-250). Belmont, CA: Wadsworth.
- Shockley-Zalabak, P. (Ed.). (2002). Fundamentals of organizational communication: Knowledge, sensitivity, skills, values. Boston: Allyn & Bacon.
- Shockley-Zalabak, P., Ellis, K., & Cesaria, R. (2000). Measuring organizational trust. San Francisco: International Association of Business Communicators.
- Smith, A. F., & Hellweg, S. A. (1985, May). Work and supervisor satisfaction as a function of subordinate perceptions of communication competence of self and supervisor. Paper presented to the Organizational Communication Division of the International Communication Association Convention, Honolulu, HI.
- Trenholm, S., & Jensen, A. (2004). Interpersonal communication (5th ed.). New York: Oxford University Press.
- Waldron, V. R., & Hunt, M. D. (1992). Hierarchical level, length, and quality of supervisory relationships as predictors of subordinates’ use of maintenance tactics. Communication Reports, 5, 82-89.<|endoftext|>
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# 3.11 The Secant, Cosecant, and Cotangent Functions
Kashvi Panjolia
Kashvi Panjolia
So far, you have learned about the three basic and their inverse functions. In this guide, you will learn about the reciprocal functions of the three trig functions. In trigonometry, the reciprocal functions play a crucial role in understanding the relationships between the different trigonometric functions. The three reciprocal functions are , , and , denoted by csc(x), sec(x), and cot(x) respectively.
## The Cosecant Function
The cosecant function, denoted by csc(x), is a trigonometric function that is defined as the reciprocal of the sine function. In other words, csc(x) = 1/sin(x).
Image courtesy of Wolfram MathWorld.
That's a strange graph! Let's break it down by exploring the main characteristics of the cosecant function. The of the cosecant function is all real numbers, except for x = (n+1)𝛑, where n is an integer. These values of x correspond to the vertical asymptotes of the cosecant function, which means that the function becomes infinitely large at every integer multiple of 𝛑, so 2𝛑, 3𝛑, 4𝛑, etc. At every integer multiple of 𝛑, sin(x) = 0, and since cosecant is defined as 1/sin(x), that means we would attempt to compute 1/0, which is not possible. Therefore, we have a vertical asymptote at these values. The range of the cosecant function is (-∞, -1] U [1, ∞).
The period of the cosecant function is 2𝛑, which means that the function repeats every 𝛑 units. This is the same period as the sine function, which makes sense because the cosecant function is defined as the reciprocal of the sine function.
In terms of the unit circle, the cosecant function can be understood as the ratio of the length of the hypotenuse to the length of the y-coordinate. The hypotenuse is always equal to 1, so csc(x) = 1/sin(x) can also be written as csc(x) = 1/y-coordinate. The cosecant function is related to the sine function in that it is the reciprocal of the sine function. In other words, csc(x) = 1/sin(x). This means that when the sine function is at its minimum or maximum values, the cosecant function is at its maximum or minimum values, respectively.
## The Secant Function
The secant function, denoted by sec(x), is a trigonometric function that is defined as the reciprocal of the cosine function. In other words, sec(x) = 1/cos(x).
Image courtesy of Wikimedia Commons.
The domain of the secant function is all real numbers, and the range is the set of all real numbers greater than or equal to 1. The secant function has vertical asymptotes at x = (2n + 1)𝛑/2, where n is an integer. This means that the secant function becomes infinitely large at these values of x. The expression (2n + 1) will always yield an odd integer, so the vertical asymptotes of the cosecant function are at 3𝛑/2, 5𝛑/2, 7𝛑/2, etc. As you might have already noticed, these values are where cos(x) = 0, and since we cannot divide 1 by 0, we have a vertical asymptote.
The of the secant function is 2𝛑, which means that the function repeats every 𝛑 units. This is the same period as the cosine function, which makes sense because the secant function is defined as the reciprocal of the cosine function. In terms of the , the secant function can be understood as the ratio of the length of the to the length of the . The hypotenuse is always equal to 1, so sec(x) = 1/cos(x) can also be written as sec(x) = 1/x-coordinate.
The secant function is related to the cosine function in that it is the reciprocal of the cosine function. In other words, sec(x) = 1/cos(x). This means that when the cosine function is at its minimum or maximum values, the secant function is at its maximum or minimum values, respectively.
## The Cotangent Function
The cotangent function, denoted by cot(x), is a trigonometric function that is defined as the reciprocal of the . In other words, cot(x) = 1/tan(x).
Image courtesy of Voovers.
The domain of the cotangent function is all real numbers, except for **x = (n + 1)**𝛑, where n is an integer. These values of x correspond to the vertical asymptotes of the cotangent function, which means that the function becomes infinitely large at these points. At every integer multiple of 𝛑, the tangent function is 0, so trying to compute 1/0 yields a value that is undefined, and therefore, a vertical asymptote. Also, since tan(x) = sin(x)/cos(x), taking the reciprocal of the function yields cot(x) = cos(x)/sin(x). This also means that when sin(x) = 0, there is a vertical asymptote. The range of the cotangent function is (-∞, -1] U [1, ∞).
The period of the cotangent function is 𝛑, which means that the function repeats every 𝛑 units. This is the same period as the tangent function, which makes sense because the cotangent function is defined as the reciprocal of the tangent function. In terms of the unit circle, the cotangent function can be understood as the ratio of the x-coordinate to the y-coordinate. This means that cot(x) = x-coordinate/y-coordinate.
The cotangent function is related to the tangent function in that it is the reciprocal of the tangent function. In other words, cot(x) = 1/tan(x). This means that when the tangent function is at its minimum or maximum values, the cotangent function is at its maximum or minimum values, respectively. While the tangent function was always increasing, the cotangent function is always decreasing because we took the reciprocal of the tangent function.
** CHOSHACAO: You can use the acronym CHOSHACAO to remember the reciprocal functions. CHOCosecant is Hypotenuse over Opposite. SHASecant is Hypotenuse over Adjacent. CAOCotangent is Adjacent over Hypotenuse. In case you didn't notice, this acronym is the reciprocal of SOHCAHTOA!**
## Key Terms to Review (14)
Cosecant: The cosecant of an angle in a right triangle is the ratio of the length of the hypotenuse to the length of the side opposite that angle.
Cot(x): Cotangent, abbreviated as cot(x), is another trigonometric function that represents the reciprocal of tangent. It calculates the ratio between adjacent side and opposite side in a right triangle.
Cotangent: Cotangent is defined as one over tangent. It represents ratios between adjacent and opposite sides in right triangles.
Csc(x): The cosecant function, denoted as csc(x), is a trigonometric function that represents the reciprocal of the sine of an angle. It gives the ratio of the hypotenuse to the length opposite a given angle in a right triangle.
Domain: The domain of a function refers to the set of all possible input values (x-values) for which the function is defined and produces an output.
Hypotenuse: The hypotenuse is the longest side of a right triangle, and it is opposite the right angle. It connects the two other sides of the triangle.
Period: The period of a function is the distance between two consecutive points on the graph that have the same value. It represents the length of one complete cycle of the function.
Sec(x): The secant function, represented as sec(x), is a trigonometric function that gives us the reciprocal of cosine. It calculates the ratio of the hypotenuse to the adjacent side in a right triangle.
Secant: In trigonometry, secant refers to one over cosine. It can also refer to a straight line that intersects a curve at two or more points.
Tangent Function: The tangent function relates the ratio between the length of an angle's opposite side and its adjacent side in a right triangle. It is defined as tan(theta) = opposite/adjacent.
Trigonometric Functions: Trigonometric functions are mathematical functions that relate angles in a right triangle to ratios of side lengths. Common trigonometric functions include sine, cosine, and tangent.
Unit Circle: The unit circle is a circle with a radius of 1 unit centered at the origin (0,0) on a coordinate plane. It is used to understand trigonometric functions and their relationships.
X-coordinate: The x-coordinate represents the horizontal position or value of a point on a coordinate plane. It indicates how far left or right the point is from the origin (0,0).
Y-coordinate: The y-coordinate represents the vertical position or value of a point on a coordinate plane. It indicates how far up or down the point is from the origin (0,0).<|endoftext|>
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Imagination plays a key role in the creative process of pinhole photography, as a pinhole camera has no viewfinder or lens. Specific attributes of the pinhole camera create a softening of detail, a lessening of surface glare and reflection in the image, together with an infinite depth of field, natural vignetting and a modulation of colour.
These characteristics are fundamental as they emphasise light over surface detail and facilitate a subtle shift in the reality normally observable with the naked eye, imbuing images with an atmospheric quality conducive to contemplation and wonder.
Time is recorded slowly in one image.
What is a Pinhole Camera?
A pinhole camera consists of a blackened, lightproof box with a tiny pinhole on one side. Light enters through the pinhole sized aperture, strikes the opposite wall of the box and records an image upside down on light sensitive paper or film. Exposure times are usually long, from seconds to minutes and even to hours.
Pinhole images are soft.
What is a Zone Plate?
A zone plate is a plate of glass marked out into concentric zones or rings alternately transparent and opaque, used like a lens to bring light to a focus. Unlike lenses or curved mirrors, the zone plate uses diffraction rather than refraction or reflection.
Zone Plate images glow.
What is a Camera Obscura?
The pinhole camera utilises a naturally occurring phenomenon, which is now known as a camera obscura.
According to the Encyclopaedia Britannica, the camera obscura was the ancestor of the photographic camera. The Latin name means “dark chamber,” and the earliest versions, dating to antiquity, consisted of small darkened rooms with light admitted through a single tiny hole. The result was that an inverted image of the outside scene was cast on the opposite wall, which was usually whitened.
For centuries the technique was used for viewing eclipses of the Sun without endangering the eyes and, by the 16th century, as an aid to drawing; the subject was posed outside and the image reflected on a piece of drawing paper for the artist to trace. Portable versions were built, followed by smaller and even pocket models; the interior of the box was painted black and the image reflected by an angled mirror so that it could be viewed right side up.
The introduction of a light-sensitive plate by J.-N. Niepce created photography.<|endoftext|>
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# Search by Topic
#### Resources tagged with Fractions similar to Eureka!:
Filter by: Content type:
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### There are 51 results
Broad Topics > Fractions, Decimals, Percentages, Ratio and Proportion > Fractions
### How Long Is the Cantor Set?
##### Stage: 3 Challenge Level:
Take a line segment of length 1. Remove the middle third. Remove the middle thirds of what you have left. Repeat infinitely many times, and you have the Cantor Set. Can you find its length?
### History of Fractions
##### Stage: 2 and 3
Who first used fractions? Were they always written in the same way? How did fractions reach us here? These are the sorts of questions which this article will answer for you.
### The Greedy Algorithm
##### Stage: 3 Challenge Level:
The Egyptians expressed all fractions as the sum of different unit fractions. The Greedy Algorithm might provide us with an efficient way of doing this.
### The Cantor Set
##### Stage: 3 Challenge Level:
Take a line segment of length 1. Remove the middle third. Remove the middle thirds of what you have left. Repeat infinitely many times, and you have the Cantor Set. Can you picture it?
### Egyptian Fractions
##### Stage: 3 Challenge Level:
The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions.
### Couples
##### Stage: 3 Challenge Level:
In a certain community two thirds of the adult men are married to three quarters of the adult women. How many adults would there be in the smallest community of this type?
### Keep it Simple
##### Stage: 3 Challenge Level:
Can all unit fractions be written as the sum of two unit fractions?
### Diminishing Returns
##### Stage: 3 Challenge Level:
In this problem, we have created a pattern from smaller and smaller squares. If we carried on the pattern forever, what proportion of the image would be coloured blue?
### Bull's Eye
##### Stage: 3 Challenge Level:
What fractions of the largest circle are the two shaded regions?
### F'arc'tion
##### Stage: 3 Challenge Level:
At the corner of the cube circular arcs are drawn and the area enclosed shaded. What fraction of the surface area of the cube is shaded? Try working out the answer without recourse to pencil and. . . .
### Unit Fractions
##### Stage: 3 Challenge Level:
Consider the equation 1/a + 1/b + 1/c = 1 where a, b and c are natural numbers and 0 < a < b < c. Prove that there is only one set of values which satisfy this equation.
### Fractions and Coins Game
##### Stage: 2 Challenge Level:
Work out the fractions to match the cards with the same amount of money.
### Twisting and Turning
##### Stage: 3 Challenge Level:
Take a look at the video and try to find a sequence of moves that will take you back to zero.
### Water Lilies
##### Stage: 3 Challenge Level:
There are some water lilies in a lake. The area that they cover doubles in size every day. After 17 days the whole lake is covered. How long did it take them to cover half the lake?
### Cuisenaire Without Grid
##### Stage: 1 and 2 Challenge Level:
An environment which simulates working with Cuisenaire rods.
### Rod Fractions
##### Stage: 3 Challenge Level:
Pick two rods of different colours. Given an unlimited supply of rods of each of the two colours, how can we work out what fraction the shorter rod is of the longer one?
### More Twisting and Turning
##### Stage: 3 Challenge Level:
It would be nice to have a strategy for disentangling any tangled ropes...
##### Stage: 2 Challenge Level:
Use the fraction wall to compare the size of these fractions - you'll be amazed how it helps!
### Fractional Wall
##### Stage: 2 Challenge Level:
Using the picture of the fraction wall, can you find equivalent fractions?
### Fraction Match
##### Stage: 1 and 2 Challenge Level:
A task which depends on members of the group noticing the needs of others and responding.
### Fraction Lengths
##### Stage: 2 Challenge Level:
Can you find combinations of strips of paper which equal the length of the black strip? If the length of the black is 1, how could you write the sum of the strips?
### Paper Halving
##### Stage: 1 and 2 Challenge Level:
In how many ways can you halve a piece of A4 paper? How do you know they are halves?
### What Do You See Here?
##### Stage: 2 Challenge Level:
An activity for teachers to initiate that adds to learners' developing understanding of fractions.
### Exploring Fractions
##### Stage: 1 and 2
This article, written for primary teachers, links to rich tasks which will help develop the underlying concepts associated with fractions and offers some suggestions for models and images that help. . . .
##### Stage: 2 Challenge Level:
Can you find ways to make twenty-link chains from these smaller chains?
### Peaches Today, Peaches Tomorrow....
##### Stage: 3 Challenge Level:
Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?
### Bryony's Triangle
##### Stage: 2 Challenge Level:
Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?
### Matching Fractions
##### Stage: 2 Challenge Level:
Can you find different ways of showing the same fraction? Try this matching game and see.
##### Stage: 3 Challenge Level:
Can you work out which drink has the stronger flavour?
### Matching Fractions, Decimals and Percentages
##### Stage: 3 Challenge Level:
An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.
### Rectangle Tangle
##### Stage: 2 Challenge Level:
The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the ten numbered shapes?
### Count the Beat
##### Stage: 1 and 2
This article, written by Nicky Goulder and Samantha Lodge, reveals how maths and marimbas can go hand-in-hand! Why not try out some of the musical maths activities in your own classroom?
### Dividing a Cake
##### Stage: 2 Challenge Level:
Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?
### Doughnut
##### Stage: 2 Challenge Level:
How can you cut a doughnut into 8 equal pieces with only three cuts of a knife?
### Mathematical Swimmer
##### Stage: 3 Challenge Level:
Twice a week I go swimming and swim the same number of lengths of the pool each time. As I swim, I count the lengths I've done so far, and make it into a fraction of the whole number of lengths I. . . .
### Fraction Fascination
##### Stage: 2 Challenge Level:
This problem challenges you to work out what fraction of the whole area of these pictures is taken up by various shapes.
### Cuisenaire Environment
##### Stage: 1 and 2 Challenge Level:
An environment which simulates working with Cuisenaire rods.
### Tangles
##### Stage: 3 and 4
A personal investigation of Conway's Rational Tangles. What were the interesting questions that needed to be asked, and where did they lead?
### Do Unto Caesar
##### Stage: 3 Challenge Level:
At the beginning of the night three poker players; Alan, Bernie and Craig had money in the ratios 7 : 6 : 5. At the end of the night the ratio was 6 : 5 : 4. One of them won \$1 200. What were the. . . .
### Ratio Sudoku 3
##### Stage: 3 and 4 Challenge Level:
A Sudoku with clues as ratios or fractions.
### Farey Sequences
##### Stage: 3 Challenge Level:
There are lots of ideas to explore in these sequences of ordered fractions.
### 3388
##### Stage: 3 Challenge Level:
Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.
### Chocolate
##### Stage: 2 and 3 Challenge Level:
There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time?
### Chocolate Bars
##### Stage: 2 Challenge Level:
An interactive game to be played on your own or with friends. Imagine you are having a party. Each person takes it in turns to stand behind the chair where they will get the most chocolate.
### Teaching Fractions with Understanding: Part-whole Concept
##### Stage: 1, 2 and 3
Written for teachers, this article describes four basic approaches children use in understanding fractions as equal parts of a whole.
### Racing Odds
##### Stage: 3 Challenge Level:
In a race the odds are: 2 to 1 against the rhinoceros winning and 3 to 2 against the hippopotamus winning. What are the odds against the elephant winning if the race is fair?
### Light Blue - Dark Blue
##### Stage: 2 Challenge Level:
Investigate the successive areas of light blue in these diagrams.
### Fractional Triangles
##### Stage: 2 Challenge Level:
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
### Plutarch's Boxes
##### Stage: 3 Challenge Level:
According to Plutarch, the Greeks found all the rectangles with integer sides, whose areas are equal to their perimeters. Can you find them? What rectangular boxes, with integer sides, have. . . .<|endoftext|>
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- NASA scientists watching material that emerged from the sun
- Comet ISON may have evaporated, experts says
- Spacecraft lose sight of the comet
- Comet was making its closest approach to sun
Something emerged from the sun after Comet ISON made its closest approach today. Is it the ISON?
NASA scientists, professional and amateur astronomers are analyzing images from NASA satellites to learn more about comet's fate.
"We haven't seen any definite nucleus yet," said Padma Yanamandra-Fisher with the Space Science Institute and NASA's Comet ISON Observing Campaign.
Members of the group's Facebook page spotted what may be the remnants of ISON in satellite images soon after experts at NASA's Google Hangout on ISON said it looked like the comet had broken up and melted into the sun.
Comet watchers will have to wait until ISON, or what's left of it, are a bit further from the sun to get more information.
"What we see here is the dust tail emerging first, pointing away from the sun," Yanamandra-Fisher said.
But it is not clear if the comet's core, or nucleus, is intact, or if it's just a bunch of dust.
Observers were hoping that ISON would survive its Thanksgiving Day close encounter with the sun and emerge to put on a big sky show in December.
A fleet of spacecraft watched ISON plunge toward the sun, including NASA's STEREO satellite, the European Space Agency/NASA SOHO spacecraft and the Solar Dynamics Observatory.
Comets are giant snowballs of frozen gases, rock and dust that can be several miles in diameter. When they get near the sun, they warm up and spew some of the gas and dirt, creating tails that can stretch for thousands of miles.
Most comets are in the outer part of our solar system. When they get close enough for us to see, scientists study them for clues about how our solar system formed.
Astronomers Vitali Nevski and Artyom Novichonok discovered ISON in September 2012 using a telescope near Kislovodsk, Russia, that is part of the International Scientific Optical Network.
ISON -- officially named C/2012 S1 -- was 585 million miles away at the time. Its amazing journey through the solar system had been chronicled by amateur astronomers and by space telescopes.<|endoftext|>
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# Question Video: Solving Linear Inequalities with One Unknown on Both Sides Mathematics • 7th Grade
Solve the inequality 10𝑥 + 16 ≤ 8(𝑥 − 19) in ℚ.
02:18
### Video Transcript
Solve the inequality 10𝑥 plus 16 is less than or equal to eight multiplied by 𝑥 minus 19 in the set of rational numbers.
And as we said when reading out the question, this ℚ means rational numbers. And what we mean by rational numbers are any numbers that can be represented using a fraction. Okay, so now let’s solve our inequality.
Well, the first step or stage in our multistep inequality is to distribute across our parentheses. And what this means is we’re gonna multiply the eight by both terms inside our parentheses. So we’re gonna get 10𝑥 plus 16 is less than or equal to. Then we’ve got eight 𝑥 cause eight multiplied by 𝑥 is eight 𝑥. And then we’re gonna get minus 152. And that’s cause eight multiplied by negative 19 gives this negative 152.
So now what we can do to make sure that we have the 𝑥s on one side of our inequality and numerical values on the other side of our inequality is to subtract eight 𝑥 and 16 from each side. So when I do this, what I’m gonna get is two 𝑥 is less than or equal to negative 168. And then all we need to do is divide both sides of the inequality by two. And we get 𝑥 is less than or equal to negative 84.
So what this means is, 𝑥 is any value that’s less than negative 84 but also including negative 84. Well, we’ve just shown the answer using inequality notation cause 𝑥 is less than or equal to negative 84. We could also use some interval notation as I’ve shown here, where we’ve got a parenthesis. Then we’ve got negative ∞, then comma negative 84. And then we’ve got a square bracket. And what this means is, the values can take any value from negative ∞, but not including negative ∞, all the way up to negative 84, and including negative 84.
And then we also have this other way of representing our answer that tells us that 𝑥 is an element or a member of the rational numbers such that 𝑥 is less than or equal to negative 84.<|endoftext|>
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## What is the definition of same side interior angles?
Same side interior angles are two angles that are on the same side of the transversal and on the interior of (between) the two lines. Same Side Interior Angles Theorem: If two parallel lines are cut by a transversal, then the same side interior angles are supplementary.
## Are the same side exterior angles always congruent?
All angles that are either exterior angles, interior angles, alternate angles or corresponding angles are all congruent.
## What is the definition of exterior of an angle?
Definition of exterior angle 1 : the angle between a side of a polygon and an extended adjacent side. 2 : an angle formed by a transversal as it cuts one of two lines and situated on the outside of the line.
## How many pairs of same side exterior angles are there?
Each pair of exterior angles are outside the parallel lines and on the same side of the transversal. There are thus two pairs of these angles.
## What is the difference between same side interior angles and same side exterior angles?
The same side interior angles are the angles inside the parallel lines on the same side of the transversal and the same side exterior angles are the angles outside the parallel lines on the same side of the transversal.
## Are exterior angles equal?
What is the Exterior Angle Theorem? The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle. The remote interior angles are also called opposite interior angles.
## What does exterior mean in maths?
The angle between any side of a shape, and a line extended from the next side.
## How do you write an exterior angle?
Exterior angle = sum of two opposite non-adjacent interior angles. Simplify. Subtract 120° from both sides.
## What is exterior angle example?
An exterior angle of a triangle is equal to the sum of the two opposite interior angles. Example: Find the values of x and y in the following triangle. y + 92° = 180° (interior angle + adjacent exterior angle = 180°.)
## What is exterior angle property class 8?
CBSE NCERT Notes Class 8 Maths Understanding Quadrilaterals. For a polygon, the sum of the exterior angles is always 360°regardless of the number of sides of the polygon. The sum of angles in a linear pair is always 180°.
## What is exterior angle property class 9?
Exterior angle property – Exterior angle is equal to sum of interior.
## What is the formula for the exterior angle theorem?
The exterior angle theorem states that the exterior angle formed when you extend the side of a triangle is equal to the sum of its non-adjacent angles. The theorem tells us that the measure of angle D is equal to the sum of angles A and B.
## What do the exterior angles of a triangle equal?
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles of the triangle.
## How many degrees is a triangle?
180°Learn the formal proof that shows the measures of interior angles of a triangle sum to 180°.
## What is the name of the exterior angle in the figure?
Answer. The Exterior Angle is the angle between any side of a shape, and a line extended from the next side. When we add up the Interior Angle and Exterior Angle we get a straight line 180°. They are “Supplementary Angles“.
## What is the sum of two exterior angles on the same side of the transversal?
Two angles that are exterior to the parallel lines and on the same side of the transversal line are called same-side exterior angles. The theorem states that same-side exterior angles are supplementary, meaning that they have a sum of 180 degrees.
## Why does the sum of exterior angles equal 360?
Summed, the exterior angles equal 360 degreEs. A special rule exists for regular polygons: because they are equiangular, the exterior angles are also congruent, so the measure of any given exterior angle is 360/n degrees.<|endoftext|>
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# whats the next two terms in order are p+q, p , p-q
Question
whats the next two terms in order are p+q, p , p-q
in progress 0
2 years 2021-07-20T21:22:00+00:00 1 Answers 3 views 0
p – 2q and p – 3q
Step-by-step explanation:
A Series is given to us and we need to find the next two terms of the series . The given series to us is ,
$$\rm\implies Series = p+q , p , p – q$$
Note that when we subtract the consecutive terms we get the common difference as “-q” .
$$\rm\implies Common\ Difference = p – (p + q )= p – p – q =\boxed{\rm q}$$
Therefore the series is Arithmetic Series .
Arithmetic Series: The series in which a common number is added to obtain the next term of series .
And here the Common difference is -q .
Fourth term :
$$\rm\implies 4th \ term = p – q – q = \boxed{\blue{\rm p – 2q}}$$
Fifth term :
$$\rm\implies 4th \ term = p – 2q – q = \boxed{\blue{\rm p – 3q}}$$
Therefore the next two terms are ( p 2q) and ( p 3q ) .<|endoftext|>
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# How do you use the half angle formulas to determine the exact values of sine, cosine, and tangent of the angle 165^circ?
Jan 5, 2018
$\sin \left({165}^{\circ}\right) = \frac{\sqrt{2 - \sqrt{3}}}{2}$,
$\cos \left({165}^{\circ}\right) = - \frac{\sqrt{2 + \sqrt{3}}}{2}$,
$\tan \left({165}^{\circ}\right) = - \sqrt{7 - 4 \sqrt{3}}$
#### Explanation:
${165}^{\circ}$ is in QII, so we know that $\sin \left({165}^{\circ}\right)$ is positive and $\cos \left({165}^{\circ}\right)$ is negative.
${165}^{\circ} = \frac{{330}^{\circ}}{2}$, so we'll use ${330}^{\circ}$ in the half angle formulas. $\cos \left({330}^{\circ}\right) = - \frac{\sqrt{3}}{2}$.
$\sin \left(\frac{x}{2}\right) = \pm \sqrt{\frac{1 - \cos \left(x\right)}{2}}$
$\cos \left(\frac{x}{2}\right) = \pm \sqrt{\frac{1 + \cos \left(x\right)}{2}}$
Combining what we know so far we can find sine:
$\sin \left({165}^{\circ}\right) = \sin \left({330}^{\circ} / 2\right) = \sqrt{\frac{1 - \cos \left({330}^{\circ}\right)}{2}}$
$= \sqrt{\frac{1 - \left(- \frac{\sqrt{3}}{2}\right)}{2}} = \sqrt{\frac{\frac{2 - \sqrt{3}}{2}}{2}}$
$= \sqrt{\frac{2 - \sqrt{3}}{4}} = \frac{\sqrt{2 - \sqrt{3}}}{2}$
Now let's find cosine in much the same way:
$\cos \left({165}^{\circ}\right) = \cos \left({330}^{\circ} / 2\right) = - \sqrt{\frac{1 + \cos \left({330}^{\circ}\right)}{2}}$
$= - \sqrt{\frac{1 + \left(- \frac{\sqrt{3}}{2}\right)}{2}} = - \sqrt{\frac{\frac{2 + \sqrt{3}}{2}}{2}}$
$= - \sqrt{\frac{2 + \sqrt{3}}{4}} = - \frac{\sqrt{2 + \sqrt{3}}}{2}$
So we've found:
$\sin \left({165}^{\circ}\right) = \frac{\sqrt{2 - \sqrt{3}}}{2}$
and
$\cos \left({165}^{\circ}\right) = - \frac{\sqrt{2 + \sqrt{3}}}{2}$
To find $\tan \left({165}^{\circ}\right)$ we'll use the identity:
$\tan \left(x\right) = \sin \frac{x}{\cos} \left(x\right)$.
So,
$\tan \left({165}^{\circ}\right) = \sin \frac{{165}^{\circ}}{\cos} \left({165}^{\circ}\right)$
=(sqrt(2-sqrt(3))/2)/(- sqrt(2+sqrt(3))/2) = -sqrt(2-sqrt(3))/(sqrt(2+sqrt(3))
we can do more work on this, if we want, although that's finished answer for many people:
$- \frac{\sqrt{2 - \sqrt{3}}}{\sqrt{2 + \sqrt{3}}} = - \sqrt{\frac{2 - \sqrt{3}}{2 + \sqrt{3}}}$
$= - \sqrt{\frac{2 - \sqrt{3}}{2 + \sqrt{3}} \cdot \frac{2 - \sqrt{3}}{2 - \sqrt{3}}}$
$= - \sqrt{\frac{7 - 4 \sqrt{3}}{1}} = - \sqrt{7 - 4 \sqrt{3}}$<|endoftext|>
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# RAP - Editorial
Contest
Practice
Author : Ranjan Kumar
Editorialist : Ranjan Kumar
Difficulty :–
Easy-Medium.
Pre-Requisites:
Maths, Bit Manipulation.
Problem Statement :–
The problem is to find all the even coefficient of a binomial expression (1+x)^N for a given value of N, the power raised to the expression (1+x).
Quick Solution:–
As we know that for the expression (1+x)^N has N+1 terms which are:—
C(N,0) + C(N,1)x + C(n,2)x^2 +………………+ C(N,N)x^N.
So in very short explanation I say that for finding the number even coefficient we can find the odd coefficient and subtract that from the N+1 so that we can get the number of even coefficients.
Now we come to a problem of finding the number of odd coefficient. For finding the number of odd coefficient we know that will count number of 1s in the Binary value of N and the final answer will be 2 to the power number of 1s.
Detailed Approach:–
We are provided with a value N that is the power of the term (1+x).
This will lead to the N+1 terms which are
C(N,0) + C(N,1)x + C(n,2)x^2 +………………+ C(N,N)x^N.
In which the coefficients are C(N,0), C(N,1), C(n,2), ………………,C(N,N)
Suppose the number of odd coefficients is o.
Then number of even coefficients is e=N+1-o.
Now for finding the number of odd coefficients we find the binary form of N.
Let us take a counter c and initialize it by 0.
Now we perform subsequent division by 2 and increase the counter when the remainder is 1 and perform this operation until the value of N is not 0.
Then o=power(2,c);
Now e=N+1-o.
Hence the required answer is e.
Time Complexity :–
O(logN)
Solution :–
Setter’s Solution can be found here.
Feel free to post comments if anything is not clear to you.
1 Like
//<|endoftext|>
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Rome’s Mediterranean Empire, 753 B.C.E.–600 C.E.
A. A Republic of Farmers, 753–31 B.C.E.
1. Rome was inhabited at least as early as 1000 B.C.E. According to legend, it was ruled by seven kings between 753 B.C.E. and 507 B.C.E. Kingship was eliminated in 507 B.C.E. when representatives of the senatorial class of large landholders overthrew the last king and established a republic.
2. The centers of political power were the two consuls and the Senate. In practice, the Senate made laws and governed.
3. The Roman family consisted of several generations living under the absolute authority of the oldest living male, the paterfamilias.
4. Society was hierarchical. Families and individuals were tied together by patron/client relationships that institutionalized inequality and gave both sides of the relationship reason to cooperate and to support the status quo.
5. Roman women had relatively more freedom than Greek women, but their legal status was still that of a child, subordinate to the paterfamilias of their own or their husband’s family. Eventually procedures evolved that made it possible for some women to become independent after the death of their fathers.
6. Romans worshiped a large number of supernatural spirits as well as major gods such as Jupiter and Mars. Proper performance of ritual ensured that the gods continued to favor the Roman state.
B. Expansion in Italy and the Mediterranean
1. Rome began to expand, at first slowly and then very rapidly, in the third and second centuries B.C.E. until it became a huge Mediterranean empire. Possible explanations for this expansion include greed, aggressiveness, the need for consuls to prove themselves as military commanders during their single year in office, and a constant fear of being attacked.
2. During the first stage of expansion, Rome conquered the rest of Italy (by 290 B.C.E.). Rome won the support of the people of Italy by granting them Roman citizenship. As citizens, these people then had to provide soldiers for the military.
3. In the next stages of expansion, Rome first defeated Carthage to gain control over the western Mediterranean and Sicily, Sardinia, and Spain (264–202 B.C.E.). Next, between 200 and 30 B.C.E., Rome defeated the Hellenistic kingdoms to take over the lands of the eastern Mediterranean. Between 59 and 51 B.C.E., Gaius Julius Caesar conquered the Celts of Gaul.
4. The Romans used local elite groups to administer and tax the various provinces of their rapidly expanding and far-flung empire. A Roman governor, who served a single one-year term in office, supervised the local administrators. This system was inadequate and prone to corruption.
C. The Failure of the Republic
1. As Rome expanded, the social and economic bases of the Roman republic in Italy were undermined. While men from independent farming families were forced to devote their time to military service, large landowners bought up their land to create great estates called latifundia. This meant both a decline in Rome’s source of soldiers and a decline in food production because latifundia owners preferred to grow cash crops like grapes rather than staple crops such as wheat.
2. Because slave labor was cheap in an expanding empire, Italian peasants, driven off the land and not employed by the latifundia, drifted into the cities where they formed a fractious unemployed underclass.
3. As the independent farming family that had been the traditional source of soldiers disappeared, Roman commanders built their armies from men from the underclass who tended to give their loyalty, not to the Roman state, but to their commander. This led to generals taking control of politics, to civil wars, and finally to the end of the republican system of government.
D. The Roman Principate, 31 B.C.E.–330 C.E.
1. Julius Caesar’s grandnephew Octavian (also known as Augustus) took power in 31 B.C.E., reorganized the Roman government, and ruled as a military dictator.
2. During the reign of Augustus, Egypt, parts of the Middle East, and Central Europe were added to the empire. He created a paid civil service from a class of wealthy merchants and landowners to manage the growing empire.
3. After Augustus died, several members of his family succeeded him. However, the position of emperor was not necessarily hereditary; in the end, armies chose emperors.
4. Rather than laws developing through a senate and assemblies, as it had during the Republic, the emperor became a major source of laws during the Principate. The development of Roman law culminated in the sixth century C.E. and became the foundation of European law.
E. An Urban Empire
1. About 80 percent of the 50 to 60 million people of the Roman Empire were rural farmers, but the empire was administered through and for a network of cities and towns. In this sense, it was an urban empire. Rome had about a million residents, other large cities (Alexandria, Antioch, and Carthage) had several hundred thousand each, while many Roman towns had populations of several thousand.
2. In Rome, the upper classes lived in elegant, well-built, well-appointed houses; many aristocrats also owned country villas. The poor lived in dark, dank, fire-prone wooden tenements in squalid slums built in the low-lying parts of the city.
3. Provincial towns imitated Rome both in urban planning and in urban administration. The local elite, who served the interests of Rome, dominated town councils. The local elite also served their communities by using their wealth to construct amenities such as aqueducts, baths, theatres, gardens, temples, and other public works and entertainment projects.
4. Rural life in the Roman Empire involved lots of hard work and very little entertainment. Rural people had little contact with representatives of the government. By the early centuries C.E., absentee landlords who lived in the cities owned most rural land, while the land was worked by tenant farmers supervised by hired foremen.
5. Manufacture and trade flourished under the pax romana. Grain had to be imported to feed the huge city of Rome. Rome and the Italian towns (and later, provincial centers) exported glass, metalwork, pottery, and other manufactures to the provinces. Romans also imported Chinese silk and Indian and Arabian spices.
6. One of the effects of the Roman Empire was Romanization. In the western part of the Empire, the Latin language, Roman clothing, and the Roman lifestyle were adopted by local people; and indigenous cultures had an effect on Rome through cultural interaction. As time passed, Roman emperors gradually extended Roman citizenship to all free male adult inhabitants of the empire.
F. The Rise of Christianity
1. Jesus lived in a society marked by resentment against Roman rule, which had inspired the belief that a Messiah would arise to liberate the Jews. When Jesus sought to reform Jewish religious practices, the Jewish authorities in Jerusalem turned him over to the Roman governor for execution.
2. After the execution, Jesus’ disciples continued to spread his teachings; they also spread their belief that Jesus had been resurrected. At this point, the target of their proselytizing was their fellow Jews.
3. The target of proselytizing changed from Jews to non-Jews in the 40s–70s C.E. First, Paul of Tarsus, an Anatolian Jew, discovered that non-Jews (gentiles) were much more receptive to the teachings of Jesus than Jews were. Second, a Jewish revolt in Judaea (66 C.E.) and the subsequent Roman reconquest destroyed the original Jewish Christian community in Jerusalem.
4. Christianity grew slowly for two centuries, developing a hierarchy of priests and bishops, hammering out a commonly accepted theological doctrine, and resisting the persecution of Roman officials. By the late third century, Christians were a sizeable minority in the Roman Empire.
5. The expansion of Christianity in the Roman Empire came at a time when Romans were increasingly dissatisfied with their traditional religion. This dissatisfaction inspired Romans to become interested in a variety of mystery cults and universal creeds that had their origins in the eastern Mediterranean.
G. Byzantines and Germans
1. While Roman rule and the traditions of Rome died in the west, they were preserved in the Byzantine Empire and in its capital, Constantinople.
2. The popes in Rome were independent of secular power, but the Byzantine emperor was appointed the patriarch of Constantinople and intervened in doctrinal disputes. Religious differences and doctrinal disputes permeated the Byzantine Empire; nonetheless, polytheism was quickly eliminated.
3. While the unity of political and religious power prevented the Byzantine Empire from breaking up, the Byzantines did face serious foreign threats. The Goths and Huns on the northern frontier were not difficult to deal with, but on the east, the Sasanids harassed the Byzantine Empire for almost three hundred years.
II. The Origins of Imperial China, 221 B. C. E.–220 C. E.
A. Resources and Populations
B. Hierarchy, Obedience, and Belief
1. The family was the basic unit of society. The family was conceived as an unbroken chain of generations, including ancestors as well as current generations. Ancestors were thought to take an active interest in the affairs of the current generation, and they were routinely consulted, appeased, and venerated.
2. Chinese society believed that a hierarchy in the family, dominated by the elder male, reflected a hierarchy in society, dominated by rulers, with interdependent relationships more important than the individual. The status and authority of women depended upon their social status. Women of the royal family could have some political influence. A young wife was expected to be obedient and recognize her mother-in-law’s authority over her. All women were expected to be obedient, but their quality of life depended upon economic circumstances.
C. The First Chinese Empire, 221–207 B.C.E.
1. By 221 B.C.E., the state of Qin had unified all of northern and central China into the first Chinese “empire.” Success for the Qin came from long experience in defending against “barbarian” neighbors, the adoption of severe Legalist methods, and the ambition of the ruthless young king Shi Huangdi and his advisors.
2. Upon uniting China, the Qin established a strong centralized state by eliminating rival centers of authority, establishing primogeniture, and creating a strong bureaucracy. It standardized law, measurements, coinage, and writing. Following the advice of his prime minister, Li Si, Shi Huangdi followed the Legalist view and suppressed Confucianism.
3. To secure the empire’s borders from northern raiders, the Qin sent a large military force to drive the nomads north. To ensure they would not lose the newly gained territory, they constructed connections and extensions to walls built earlier to defend the kingdoms, the ancestor of the Great Wall of China. Shi Huangdi’s attack on the nomads inadvertently united the fragmented nomads under the Xiongnu Confederacy, a source of threat to China for centuries to come.
4. To fill their military and labor needs, the Qin government instituted an oppressive program of compulsory military and labor services.
5. Shi Huangdi died in 210 B.C.E. and was buried in a monumental tomb guarded by a terracotta clay army of seven thousand soldiers. His son secured the throne but proved to be a weak leader who could not withstand the uprisings that broke out from the resentment of different groups. Qin rule was over by 206 B.C.E.
D. The Long Reign of the Han, 206 B.C.E.–220 C.E.
1. Gaozu (the throne name of Liu Bang) was a peasant who defeated all other contestants for control of China, establishing the Han dynasty. The Han established a political system that drew on both Confucian philosophy and Legalist techniques.
2. Han rulers faced challenges at first from residual resentments of the ruthless rule of the Qin. To ease their transition and help the economy, the Qin reduced taxes and government spending, and collected and stored surplus grain for times of shortage. For those who had aided him, Gaozu restored the system of feudal grants abolished by the Qin.
3. Confrontation with the Xiongnu confederacy nomads of the north revealed the inadequacy of Han troops, leading Gaozu to develop a policy of appeasement, buying them off with annual gifts.
4. The Han went through a period of territorial expansion under Emperor Wu (r. 141–87 B.C.E.) who increased the power of the emperor. During his rule, he expanded the empire into areas as far as northern Vietnam, Manchuria, and North Korea. Instead of appeasing the Xiongnu, he built his military to fight the northern nomads.
5. Wu’s reign saw the expansion of Chinese territory into the northwest and the foundations of the Silk Road, which would later affect the economic health of Asia. To pay for the military buildup, government monopolies on high-profit commodities added to the treasury, though not without controversy. The state also adopted Confucianism, using Confucian scholars as officials of the government, who in turn expected exemplary ethical behavior from their rulers.
E. Technology and Trade
F. Decline of the Han Empire
1. An ambitious high official seized power from 9 to 23 C.E. but was killed in his palace, and a member of the Han royal family was again installed as emperor. At this time the capital was moved east to Luoyang.
2. The Han Empire was undermined by a number of factors. First, the imperial court was plagued by weak leadership and court intrigue. Second, nobles and merchants built up large landholdings at the expense of the small farmers, and peasants sought tax relief, reducing revenues for the empire. Third, the system of military conscription broke down and the central government had to rely on mercenaries whose loyalty was questionable.
3. These factors, compounded by factionalism at court, official corruption, peasant uprisings, and nomadic attacks, led to the fall of the dynasty in 220 C.E. China entered a period of political fragmentation that lasted until the late sixth century.
1. The Han and Roman Empires were similar relative to agriculture being their fundamental economic activity. Both empires received revenue from a percentage of the annual harvests. And both empires strengthened their central rule by breaking the power of old aristocratic families, reducing their land holdings. Both empires saw their authority eroding at the end of their reigns by the reversal of this process.
2. Both empires spread out from an ethnically homogeneous core to encompass widespread territories of diverse cultures. Many in the conquered lands adopted the cultural elements of the core, and the core also adopted some of the cultural traditions of their far-flung regions. The extent of their empires forced both empires to create a well-trained bureaucracy and to make use of local officials to administer their interests.
3. Both empires built roads to facilitate military movement that later became routes to spread commerce and culture. While the majority of populations in both empires lived in the countryside, those living in urban centers enjoyed the more cosmopolitan advantages of empire.
4. Both empires faced common problems in terms of defense and found their domestic economies undermined by their military expenditures.
5. Both empires were overrun by new peoples who had been so deeply influenced by the imperial cultures of Rome and of China that they maintained some of that culture during their own reigns.
1. In China, the imperial model was revived and the territory of the Han Empire re-unified. The former Roman Empire was never again reconstituted.
2. Differences between China and the Roman world can be located in the concept of the individual, the greater degree of economic mobility for the middle classes in Rome than in Han China, the make-up and hierarchy of their armies, and the different political ideologies and religions of the two empires.
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24 Scouting Knots To Know
A knot is a method of fastening or securing linear material such as rope by tying or interweaving. It may consist of a length of one or several segments of rope, string, webbing, twine, strap, or even chain interwoven such that the line can bind to itself or to some other object . Knots have been the subject of interest for their ancient origins, their common uses, and the area of mathematics known as knot theory.
There is a large variety of knots, each with properties that make it suitable for a range of tasks. Some knots are used to attach the rope to other objects such as another rope, cleat, ring, or stake. Some knots are used to bind or constrict objects. Decorative knots usually bind to themselves to produce attractive patterns.
While some people can look at diagrams or photos and tie the illustrated knots, others learn best by watching how a knot is tied. Knot tying skills are often transmitted by sailors, scouts, climbers, cavers, arborists, rescue professionals, fishermen, linemen and surgeons.
Truckers in need of securing a load may use a trucker’s hitch, gaining mechanical advantage. Knots can save a spelunker from finding himself buried under rock. Many knots can also be used as makeshift tools, for example, the bowline can be used as a rescue loop, and the munter hitch can be used as a belay. The diamond hitch was widely used to tie packages on to donkeys and mules.
In hazardous environments such as mountains, knots are very important. In the event of someone falling into a ravine or a similar terrain feature, with the correct equipment and knowledge of knots a rappel system can be set up to lower a rescuer down to a casualty and set up a hauling system to allow a third individual to pull both the rescuer and the casualty out of the ravine.
Further application of knots includes developing a high line, which is basically equivalent to a zip line. Using the high line supplies, injured people, or those lacking training in rappelling and rock climbing can be moved across a river or a large crevice or ravine. Note the systems mentioned typically require carabineers and the use of multiple appropriate knots.
These knots include the bowline, double figure eight, munter hitch, munter mule, prusik, autoblock, and clove hitch. Thus any individual who goes into a mountainous environment should have basic knowledge of knots and knot systems to increase safety and the ability to undertake activities such as rappelling.
Page 1 of 2 – See the knots<|endoftext|>
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Many people believe that cats became domesticated in Egypt, but a genetic study suggests that feline ancestors originally came from more humble roots.
Researchers traced the mitochondrial DNA in nearly a thousand domestic and wild cats. Looks like the ancestors of domestic cats lived in the Fertile Crescent about 130,000 years ago.
The Fertile Crescent was the location where humans first settled and began farming, as opposed to hunting and gathering. It’s a belt of land stretching east from the Mediterranean Sea, and down into what is now Iraq.
When agriculture began and humans started storing grain, cats became useful for catching rodents. The humans appreciated the cats killing rodents, and the cats put up with the humans in exchange for food and shelter.
In other words, the wild cats domesticated themselves.
Archaeologists also found cats from 9500 years ago buried with humans on the island of Cyprus. Since the island had no cats before that, and it was settled by farmers from Turkey, scientists think the farmers brought cats with them.<|endoftext|>
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# Percents as Decimals
## Rewrite percents as decimals.
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Percents as Decimals
Credit: Dakota Ray
Source: https://www.flickr.com/photos/dakotaray/5855339649
The school is fundraising for a new gym. An amusement park owner has agreed to have a fundraiser at his park. He plans to donate 15% of every dollar spent at the park to the gym fund. How much of every dollar will be donated to the school? Write the amount as a decimal.
In this concept, you will learn how to write percents as decimals.
### Writing Percents as Decimals
Percents and decimals are parts of a whole. A percentage is a quantity out of 100. A decimal number with two decimal digits also represents a quantity out of 100.
Compare 34% and 0.34.
34% is 34 out of 100.The decimal 0.34 is 34 hundredths or 34 out of 100. Both quantities represent the same ratio.
A percents can be written as a decimal by replacing “out of 100” with “hundredths.” Remove the percent symbol and move the decimal point two places to the left.
Here is a percent:
\begin{align*}45\%.\end{align*}
Write 45% as a decimal.
First, remove the percent symbol.
\begin{align*}45\end{align*}
Then, move the decimal point two places to the left. Remember that the decimal point is located between the ones and the tenths place.
\begin{align*}0.45\end{align*}
45% is written as 0.45.
Let’s look at another percent.
\begin{align*}5\%\end{align*}
Write 5% as a decimal.
First, remove the percent symbol.
\begin{align*}5\end{align*}
Then, move the decimal point in two places to the left. There is no number to the left of 5. Use zero as a place holder.
\begin{align*}0.05\end{align*}
5% is written as 0 .05
### Examples
#### Example 1
Earlier, you were given a problem about the school fundraiser at the amusement park.
15% of every dollar will be donated towards the school. Convert the percent to a decimal to find how much per dollar will be donated.
Write 15% as a decimal.
First, remove the percent symbol.
\begin{align*}15\end{align*}
Next, move the decimal point two places to the left.
\begin{align*}0.15\end{align*}
0.15 of every dollar will be donated to the school. Then, multiply 1 by 0.15. \begin{align*}\1\times 0.15 = \ 0.15\end{align*}0.15 or 15 cents of every dollar will go to the school.
#### Example 2
Write 15% as a decimal.
First, remove the percent symbol.
\begin{align*}15\end{align*}
Then, move the decimal point two places to the left.
\begin{align*}0.15\end{align*}
15% is written as 0 .15
Write the following percents as a decimal.
#### Example 3
Write 17% as a decimal.
First, remove the percent symbol.
\begin{align*}17\end{align*}
Then, move the decimal point in two places to the left.
\begin{align*}0.17\end{align*}
17% is written as 0.17.
#### Example 4
Write 25% as a decimal.
First, remove the percent symbol.
\begin{align*}5\end{align*}
Then, move the decimal point in two places to the left.
\begin{align*}0.25\end{align*}
25% is written as 0.25.
#### Example 5
Write 75% as a decimal.
First, remove the percent symbol.
\begin{align*}75\end{align*}
Then, move the decimal point in two places to the left.
\begin{align*}0.75\end{align*}
75% is written as 0.75.
### Review
Write each percent as a decimal.
1. 54%
2. 11%
3. 6%
4. 12%
5. 89%
6. 83%
7. 19%
8. 4%
9. 9%
10. 32%
11. 65%
12. 88%
13. 78%
14. 67.5%
15. 18.2%
To see the Review answers, open this PDF file and look for section 8.11.
### Notes/Highlights Having trouble? Report an issue.
Color Highlighted Text Notes
### Vocabulary Language: English
TermDefinition
Decimal In common use, a decimal refers to part of a whole number. The numbers to the left of a decimal point represent whole numbers, and each number to the right of a decimal point represents a fractional part of a power of one-tenth. For instance: The decimal value 1.24 indicates 1 whole unit, 2 tenths, and 4 hundredths (commonly described as 24 hundredths).<|endoftext|>
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LESSON PLAN FOR THE EXTRAORDINARY EGG
An Extraordinary Egg Lesson Plan - Written Reality
Drawing Conclusions lesson for this book. However, an ordinary chicken egg along with pictures of various eggs would work just as easily for this activity. ! Using the ostrich egg, I had students predict everything from baby chicks to dinosaurs. That would be one large chicken! !! Before Reading— ! Take a few moments to feel and even shake the egg.
Extraordinary Egg Lesson Plans & Worksheets Reviewed by
Find extraordinary egg lesson plans and teaching resources. From an extraordinary egg worksheets to leo lonni extraordinary egg videos, quickly find teacher-reviewed educational resources.
Lesson Plans: Extensions to An Extraordinary Egg by Leo
Whole group discussion walking through the reading process steps for the book An Extraordinary Egg(predicting story content, clarifying and checking; making personal connections) 7. read the story An Extraordinary Egg by Leo Lionni(This is an amusing story about an alligator that hatches from an egg.
An Extraordinary Egg by Leo Lionni | Scholastic
Another declares it a chicken egg. But what happens when a baby alligator hatches i. Teachers. Teachers Home Lessons and Ideas Books and Authors Top Teaching Blog Teacher's Tool Kit Student Activities The Teacher Store An Extraordinary Egg. By Leo Lionni, Leo Lionni. Grades. PreK-K,
Download Extraordinary Egg Comprehension Questions
collection of social emotional lesson plans activities, June 2015 dive into a lesson plan book, Art museum packet 1, An extraordinary egg lesson plan, Title author year genre. An Extraodinary Egg Quiz One little frog wants to impress her friends and brings home a very interesting egg
Extraordinary In The Ordinary - Lesson Worksheets
Extraordinary In The Ordinary. Displaying all worksheets related to - Extraordinary In The Ordinary. Worksheets are Extension activity 8, An extraordinary egg lesson plan, Ordinary people do extraordinary things connecting, , Primary mentor text ordinary mary, , Do unto others extraordinary acts of ordinary people, Rule child support guidelines rule.
Teaching With Leo Lionni | Scholastic
Lesson Directions. We share our observations. Step 5: Talk about what is inside the egg. Break open an egg in a glass bowl. Let the students come up and identify the different parts of the egg. Label the parts of an egg together on the Parts of an Egg printable. Next, show them the egg that has soaked in
TeachingBooks | An Extraordinary Egg
An Extraordinary Egg by Leo Lionni To help put the right book in each reader's hands, consider the following comprehensive text complexity analyses within your instructional plans.
Extraordinary Eggs | Education World
Extraordinary Eggs. pre-cutting egg shapes. Divide each shape with a jagged cut. On one side write a number; on the other side draw a corresponding number of dots. Mix up the halves and let children match the correct number to the corresponding number of dots. giving each child a pre-cut lower case e shape.[PDF]
An Extraordinary Egg - Manchester University
reading a book about three frogs. One of the frogs finds an egg. Tell them, “I wonder what is going to be so special about this egg or if it is even an egg at all.” Step-by-Step Plan: 1. Show the students the cover of the book. (Gardner’s visual/spatial) 2. Begin reading the story. 3.
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The rotation of the earth causes the oceans to continuously move and the winds to blow. There are five large rotating ocean currents that are called ‘gyres’. These are huge vortexes in which all floating objects are slowly sucked into the middle. It is comparable to the kitchen sink drain.
There are five major gyres on earth: the North Pacific, South Pacific, Indian Ocean, North Atlantic and the South Atlantic Gyre. They are in sub-tropical areas, above and below the equator. All five gyres have higher concentrations of plastic rubbish compared to other parts of the oceans. In the North Atlantic Gyre, 20,328 pieces of plastic were found per square kilometre, while in the North Pacific Gyre, this can be as high as 334,271 pieces per square kilometre. These pieces are largely made up of tiny fragments of less than 5 mm that we can barely see with the naked eye. These are the microplastics.
In the centre of the gyres there is no wind. These areas have traditionally been avoided by shipping. But in 1997 captain Charles Moore sailed from Hawaii to Southern California through the North Pacific Gyre. There, in the middle of the ocean, he saw pieces of plastic floating by every day. Later he returned to the area to do closer research. There appeared to be a significantly higher concentration of plastic then elsewhere in the ocean. The plastic appeared to not only float, but also to hang suspended below the surface. Moore called the phenomena plastic soup, the term now used worldwide.<|endoftext|>
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In mice, specialized cells monitor for allergens and pass intel to response-triggering immune cells
H.W. Choi et al/Science 2018
Within minutes of biting into peanut-tainted food, people with a peanut allergy may find their pulse quickening, blood pressure plummeting and throat closing up. They’re experiencing a rapid and sometimes fatal allergic reaction called anaphylaxis.
New research in mice explains how even a small amount of an allergen can quickly trigger such a strong, full-body reaction. The culprit is a type of cell that probes the bloodstream for allergens and then broadcasts the invaders’ presence to anaphylaxis-inducing immune cells, researchers report in the Nov. 9 Science.
When these immune cells, called mast cells, detect an allergen that they’re sensitized to, they flood the body with inflammatory proteins that set off an allergic reaction. But how mast cells, which line the space surrounding blood vessels, are so efficient at detecting allergens floating along in the blood has been a long-standing question, says Stephen Galli, an immunologist at Stanford University who wasn’t involved in the research. In the case of a snakebite, fangs can pierce blood vessels and make it easy for venom, which also activates mast cells, to reach the cells. But with a food allergy, the vessels are usually intact.
In the study, researchers systematically lowered the levels of different types of immune cells in mice to see how the animals’ response to egg allergens changed.
“We found that the mast cells didn't really pick up the allergens,” says study coauthor Soman Abraham, a pathologist at Duke University School of Medicine. “Instead, there was an intermediary cell.”
When the number of intermediary cells was reduced, the mice didn’t seem to experience anaphylactic symptoms, Abraham and his colleagues noticed. Those cells were a type of dendritic cell, which like mast cells are located outside of the bloodstream.
Usually, a dendritic cell detects foreign molecules, takes them in and processes them, and then displays proteins on its surface to advertise the invaders’ presence to other immune cells. Using a technique called two-photon microscopy, which visualizes cells in action in live animals, Abraham and his colleagues showed that this group of dendritic cells has a different, quicker way of alerting mast cells to allergens.
These dendritic cells extend protrusions into blood vessels to periodically sample the blood. Then, the cells bud off tiny packets called microvesicles that carry potential allergens that are found. Those packets get distributed to mast cells and other immune cells, which may then trigger an allergic response.
“When the dendritic cells capture the [allergen] from the blood, they don't internalize it,” Abraham says. Instead, the microvesicles quickly distribute allergen advertisements in all directions — like posting flyers around a neighborhood, rather than displaying a yard sign. By unleashing the microvesicles, the dendritic cells can reach a larger audience than they would by showing a warning protein on their surface.
A 2013 study showed that mast cells can also extend protrusions into the bloodstream, and suggested that these cells might directly detect allergens. But “the fact that one cell can do something doesn't necessarily prove that it's the main responsible cell type,” Galli says. The new research builds a “very thorough” case for dendritic cells being the main messengers between allergens in the blood and mast cells, he says.
These dendritic cells could someday be a target for treating and preventing allergic reactions, Abraham says, though that’s a long way away for humans.
H.W. Choi et al. Perivascular dendritic cells elicit anaphylaxis by relaying allergens to mast cells via microvesicles. Science. Vol. 362, November 9, 2018, p. 656. doi:10.1126/science.aao0666.
L. Cheng et al. Perivascular mast cells dynamically probe cutaneous blood vessels to capture immunoglobulin E. Immunity. Vol. 38, January 24, 2013, p. 166. doi:10.1016/j.immuni.2012.09.022.
L. Beil. Little by little. Science News. Vol. 176, September 12, 2009, p. 20.
N. Seppa. Role change: Mast cells show an anti-inflammatory side. Science News. Vol. 172, September 8, 2007, p. 149.<|endoftext|>
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Can they get where the need to go? (Dan Majka / The Nature Conservancy)
As the global climate gets hotter both people and animals will have to adapt to changes in their local environments. However, while people can shed clothes or turn up the A/C, animals have fewer options to maintain the conditions they need to survive...
If their home habitats change too much, they’ll be forced to migrate in search of new territory. “Migration” sounds like a simple fix, and in some cases it might be, if not for one big problem: There are, literally, a lot of things in the way.
Nearly every path that animals would naturally travel is blocked by roads, fences, houses and other man-made barriers. According to research published earlier this year in PNAS (paywall), “only 41% of natural land area retains enough connectivity to allow plants and animals to maintain climatic parity as the climate warms.” In some parts of the eastern US, as little as 2% of the land remains well-connected.
To illustrate the problems this will cause, Nature Conservancy cartographer Dan Majka created an animated map of the paths animals would likely try to follow in order to stay within their ecological niches as the climate changes. Both the map and the PNAS study are driven by data from earlier research (paywall), which used algorithms designed for predicting electricity flow through circuits to estimate the most efficient migration path for each of nearly 3,000 different species across North and South America.
A portion of The Nature Conservancy’s animated map. (Dan Majka / The Nature Conservancy)
Each line on the map represents the likely migration path for a single species. Pink paths are mammals, blue are birds, and yellow are amphibians. To view the full map, click here.
Migration barriers are not a new problem, nor one that is solely driven by climate change. Animal populations isolated by roads or other barriers are at greater risk of danger from disease or invasive predators. If a species only exists in one location, it could go extinct entirely. The climate change dimension brings new urgency to this issue as it could cause the near-simultaneous, and permanent, need for a large number of species to relocate. Those that are find themselves trapped could simply die out.
Fortunately, some promising solutions to this problem already exist. Many countries have already established wildlife corridors to connect isolated natural regions. Often, these are wide tracts of undeveloped state or federal land that are reserved for animals to travel across; they can also be narrow easements or passageways that bypass human infrastructure.
In Canada, overpasses in Banff National Park allow wolves, bears, deer, and other animals to cross highways. In India, protected lands keep traveling elephants safe. Other corridors don’t require giving up any land at all. In Oslo, a network of rooftop flower pots allows bees to wander across the city.
Though they are certainly not a solution for all our environmental woes, wildlife corridors have the benefit of extensive scientific support. The research suggests that connecting lands separated by 10 km (6.2 miles) or less could increase the total amount of connected land from 41% to 60%.
Sadly, wildlife corridors can also be difficult and expensive to implement. So, as with climate change in general, saving the diversity of animals will require more economic concessions from humans—the animals that created the problems in the first place.
Sign up for the Global Warming Blog for free by clicking here. In your email you will receive critical news, research and the warning signs for the next global warming disaster.
Click here to learn how global warming has become irreversible and what you can do to protect your family and assets.
To share this blog post: Go to the original shorter version of this post. Look to lower right for the large green Share button.
To view our current agreement or disagreement with this blog article, click here.<|endoftext|>
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# Graph Incident Adjacent With Code Examples
Graph Incident Adjacent With Code Examples
We will use programming in this lesson to attempt to solve the Graph Incident Adjacent puzzle. This is demonstrated by the following code.
```The node can be incident to other edges,
but a pair can be ONLY be adjacent.```
Using a variety of different examples, we have learned how to solve the Graph Incident Adjacent.
## What is adjacent and incident in graph?
If two vertices in a graph are connected by an edge, we say the vertices are adjacent. If a vertex v is an endpoint of edge e, we say they are incident.
## What does adjacent mean graph?
In a graph, two vertices are said to be adjacent, if there is an edge between the two vertices. Here, the adjacency of vertices is maintained by the single edge that is connecting those two vertices. In a graph, two edges are said to be adjacent, if there is a common vertex between the two edges.
## What is incidence and adjacency?
Note: An incidence matrix is a matrix that shows the relationship between two classes of objects. If the first class is X and the second is Y, the matrix has one row for each element of X and one column for each element of Y. An adjacency matrix is a square matrix utilized to describe a finite graph.
## How can you tell if two graph nodes are adjacent?
Any two nodes connected by an edge or any two edges connected by a node are said to be adjacent.
## Which edges are incident on v1?
Although each edge must have either one or two endpoints, a vertex need not be an endpoint of an edge. b. e1, e2, and e3 are incident on v1.
## What is incident on a graph?
In graph theory, a vertex is incident with an edge if the vertex is one of the two vertices the edge connects. An incidence is a pair where is a vertex and is an edge incident with. Two distinct incidences and are adjacent if either the vertices or the edges.
## What is the meaning of adjacent side?
If two sides share a common angle, then they are called adjacent sides.
## What is adjacency data structure?
An adjacency list represents a graph as an array of linked lists. The index of the array represents a vertex and each element in its linked list represents the other vertices that form an edge with the vertex.
## How do you find adjacency and incidence matrix?
The number of ones in the adjacency matrix of a directed graph is equal to the number of edges. Example: Consider the directed graph shown in fig. Determine its adjacency matrix MA. The number of ones in an incidence matrix is equal to the number of edges in the graph.<|endoftext|>
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By Alexis Dunnum, NFU Intern
As stated in the NFU Climate Column on extreme precipitation, “Projected increases in heavy precipitation combined with milder winters is expected to increase total runoff and peak stream flow during the winter and spring, which may increase the magnitude or frequency of flooding.” With heavy rainfall likely to occur more often, contour farming may be a solution to lessen the severity of heavy precipitation.
According to NRCS, contour farming is generally used on sloping land where tillage, planting, and cultivation are used to grow annual crops. In a properly designed contour farming system the tillage furrows intercept runoff and allow more moisture to infiltrate into the soil.
By planting across the slope, rather than up and down a hill, the contour ridges slow or stop the downhill flow of water. Water is then held in between these contours, thus reducing water erosion and increasing soil moisture.
This farming technique is most effective on slopes between 2 and 10 percent. Contour farming’s effects on annual soil loss rates vary with slope steepness; however, typically soil loss rates are reduced by half when the slope is between 4 and 7 percent.
Conservation benefits may include, but are not limited to reduced sheet and rill erosion, reduced transport of sediment, other solids and the contaminants attached to them, and increased water infiltration.
Are you a farmer that practices contour farming? How has this practice worked for you? Let us know in the comments section!
Like what you’ve read? Check out our Climate Leaders home page, join the conversation in the NFU Climate Leaders Facebook Group, and keep up-to-date with NFU climate action by signing up for the mailing list.<|endoftext|>
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Temperature calibration provides a means of quantifying uncertainties in temperature measurement in order to optimise sensor and/or system accuracies. Uncertainties result from various factors including:
a) Sensor tolerances which are usually specified according to published standards and manufacturers specifications.
b) Instrumentation (measurement) inaccuracies, again specified in manufacturers specifications.
c) Drift in the characteristics of the sensor due to temperature cycling and ageing.
d) Possible thermal effects resulting from the installation, for example thermal voltages created at interconnection junctions.
A combination of such factors will constitute overall system uncertainty. Calibration procedures can be applied to sensors and instruments separately or in combination. Calibration can be performed to approved recognised standards (National and International) or may simply constitute checking procedures on an “in-house” basis. Temperature calibration has many facets, it can be carried out thermally in the case of probes or electrically (simulated) in the case of instruments and it can be performed directly with certified equipment or indirectly with traceable standards. Thermal (temperature) calibration is achieved by elevating (or depressing) the temperature sensor to a known, controlled temperature and measuring the corresponding change in its associated electrical parameter (voltage or resistance). The accurately measured parameter is compared with that of a certified reference probe; the absolute difference represents a calibration error. This is a comparison process. If the sensor is connected to a measuring instrument, the sensor and instrument combination can be effectively calibrated by this technique. Absolute temperatures are provided by fixed point apparatus and comparison measurements are not used in that case. Electrical Calibration is used for measuring and control instruments which are scaled for temperature or other parameters. An electrical signal, precisely generated to match that produced by the appropriate sensor at various temperatures is applied to the instrument which is then calibrated accordingly. The sensor is effectively simulated by this means which offers a vary convenient method of checking or calibration. A wide range of calibration “simulators” is available for this purpose; in many cases, the operator simply sets the desired temperature and the equivalent electrical signal is generated automatically without the need for computation. However this approach is not applicable to sensor calibration for which various thermal techniques are used.
The International Temperature Scale of 1990
The International Temperature Scale of 1990 was adopted by the International Committee of Weights and Measures at its meeting in 1989, in accordance with the request embodied in Resolution 7 of the 18th General Conference of Weights and Measures of 1987. This scale supersedes the International Practical Temperature Scale of 1968 (amended edition of 1975) and the 1976 Provisional 0.5 K to 30 K Temperature Scale.
1. Units of Temperature
The unit of the fundamental physical quantity known as thermodynamic temperature, symbol T, is the kelvin, symbol K, defined as the fraction 1/273.16 of the thermodynamic temperature of the triple point of water1.
Because of the way earlier temperature scales were defined, it remains common practice to express a temperature in terms of its difference from 273.15 K, the ice point. A thermodynamic temperature, T, expressed in this way is known as a Celsius temperature, symbol t, defined by:
t / °C = T/K - 273.15 . (1)
The unit of Celsius temperature is the degree Celsius, symbol °C, which is by definition equal in magnitude to the kelvin. A difference of temperature may be expressed in kelvins or degrees Celsius.
The International Temperature Scale of 1990 (ITS-90) defines both International Kelvin Temperatures, symbol T90, and International Celsius Temperatures, symbol t90. The relation between T90 and t90, is the same as that between T and t, i.e.:
t90 / °C = T90/K - 273.15 . (2)
The unit of the physical quantity T90 is the kelvin, symbol K, and the unit of the physical quantity t90, is the degree Celsius, symbol °C, as is the case for the thermodynamic temperature T and the Celsius temperature t.
ITS 90 Fixed points include:
Boiling point of Nitrogen -195.798°C
Mercury triple point -38.8344°C
Triple point of water 0.01°C
Melting point of Gallium 29.7646°C
Freezing point of Indium 156.5985°C
Freezing point of Tin 231.928°C
Freezing point of Lead 327.462°C
Freezing point of Zinc 419.527°C
Freezing point of Antimony 630.63°C
Freezing point of Aluminium 660.323°C
Freezing point of Silver 961.78°C<|endoftext|>
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In our last post, we described the transdisciplinary framework in the International Baccalaureate Primary Years Program. Teaching and learning within this framework cultivates curiosity into inquiry, develops soft leadership skills (IB Learner Traits), and engages students at both conceptual and practical levels. The rationale for this framework is both developmental appropriateness and preparation to solve complex, unknown problems for the betterment of all people.
The IB Middle Years Program builds on the PYP framework by shifting to an interdisciplinary approach. The same rationale for the framework applies in the middle years. Students are ready to engage with the dominant structures (concepts, skills, essential questions) of the disciplines. They have a broadening sense of social justice and independence. And middle school students have a penchant to get deeply engaged in relevant content for short bursts at a time.
MYP students take eight core classes:
- Design Thinking: In this course, students apply practical and creative thinking skills to solve design problems. They explore the role of design in both historical and contemporary contexts. And they consider their responsibilities when making design decisions and taking action.
- Sciences: As they investigate real examples of science application, students discover the tensions and dependencies between science and morality, ethics, culture, economics, politics, and the environment.
- Mathematics: The MYP Mathematics framework encompasses number, algebra, geometry and trigonometry, statistics and probability. Students learn how to represent information, to explore and model situations, and to find solutions to familiar and unfamiliar problems.
- Individuals and Societies: This course integrates multiple subject areas: history, geography, economics, global politics and international relations, civics, philosophy, sociology, business management, anthropology. The subjects build understanding and skills to inquire into all factors that affect individuals and societies in local and global contexts.
- Language and Literature: Language is central to the development of critical thinking. This course aims to provide individual and collaborative exploration and practice in six key areas: listening, speaking, reading, writing, viewing, presenting.
- Language Acquisition: The study of additional languages provides students with the opportunity to develop insights into the features, processes and crafts of language and the concept of culture, and to realize that there are diverse ways of living, viewing and behaving in the world.
- The Arts: The arts stimulate young imaginations, challenge perceptions and develop creative and analytical skills. Involvement in the arts encourages students to understand the arts in context and the cultural histories of artworks, supporting the development of an inquiring and empathetic world view. Arts challenge and enrich personal identity and build awareness of the aesthetic in a real-world context.
- Physical and Health Education: PHE focuses on both learning about and learning through physical activity. Both dimensions help students to develop Approaches To Learning (for another post) skills across the curriculum.
Each of these eight courses are connected through the practice of the IB Learner Profile Traits, Global Contexts, Key Concepts, and Essential Debatable Questions.
The Global Contexts ground units of study in real issues and applications. These are lens through which students see the content:
- Identities and Relationships
- Personal and Cultural Identity
- Orientations in Space and Time
- Scientific and Technical Innovation
- Fairness and Development
- Globalization and Sustainability
Through the subject area, topic, and global context, we determine the "key concepts" for a unit. They can be one to three of the following: aesthetics, change, communication, communities, connections, creativity, culture, development, form, global interactions, identity, logic, perspective, relationships, time, place, and space, and systems.
A unit culminates as students consider the subject area (and connections to others), global context, key concepts, subject specific concepts and skills and grapple with an essential and debatable question or attempt to solve a complex problem.
Here are examples of MYP units happening at Soundview today:
When students complete the MYP grade 8 at Soundview, they engage in The Community Project, a student-directed, service-learning experience. Students participate in a sustained inquiry within a global context. One goal is to generate new insights and deepen understanding through in-depth investigation. Students are responsible for community-oriented action as a demonstration of their knowledge, skills, and attitudes. This is leadership.
The Soundview MYP experience is a deep-dive into the core disciplines, explored through relevant global contexts, with opportunities to apply skills and knowledge to real issues and problems in our communities. As a result of the PYP and MYP, students are intellectually curious, able to ask critical questions, apply lenses of the academic disciplines, and connect and apply their learning to finding innovative solutions - great preparation for high school and life!<|endoftext|>
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“Declaration of Independence” by painter John Trumbull.
We all know Thomas Jefferson’s famous words immortalized in the Declaration of Independence: “We hold these truths to be self-evident, that all men are created equal.” But when did the world start thinking about equality?, a distinguished research professor at UCLA, and author of the book , says we haven’t always recognized basic human rights, and the very concept wasn’t spoken much about until the end of the 1700s. We explore its origins.
- The surging popularity of the novel in the 18th century led to a greater connection between people of different genders and classes, creating a push for the idea of human equality. Even if they were fictional, novels offered up full-formed, sympathetic portraits of peasants and slaves; aristocratic readers were able to see in these characters reflections of their own humanity.
- Hunt describes the advancement of human rights as a process of, “Two steps forward, one step back,” because there will always be people who are threatened or upset by a change in social orders.
- In ten or twenty years, how will we look back on our views of human rights? Hunt says we will always reflect on the struggles of our generation and generations before us and think, “How could that be?”
- Lynn Hunt gives a talk on
- NPR's tweeting of the Declaration of independence
- Here’s our interview with Nancy Malkiel about<|endoftext|>
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Tourette syndrome (TS or simply Tourette's) is a common neuropsychiatric disorder with onset in childhood, characterized by multiple motor tics and at least one vocal (phonic) tic. These tics characteristically wax and wane, can be suppressed temporarily, and are typically preceded by an unwanted urge or sensation in the affected muscles. Some common tics are eye blinking, coughing, throat clearing, sniffing, and facial movements. Tourette's does not adversely affect intelligence or life expectancy. Tourette's is defined as part of a spectrum of tic disorders, which includes provisional, transient and persistent (chronic) tics. While the exact cause is unknown, it is believed to involve a combination of genetic and environmental factors. There are no specific tests for diagnosing Tourette's; it is not always correctly identified because most cases are mild and the severity of tics decreases for most children as they pass through adolescence. Extreme Tourette's in adulthood, though sensationalized in the media, is a rarity; tics are often unnoticed by casual observers.<|endoftext|>
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1. 1. Copyright © 2007 Pearson Education, Inc. Slide 2-1 2.3 Stretching, Shrinking, and Reflecting Graphs Vertical Stretching of the Graph of a Function If c > 1, the graph of is obtained by vertically stretching the graph of by a factor of c. In general, the larger the value of c, the greater the stretch. )(xfcy ⋅= )(xfy = .1units,stretched )(ofgraphGeneral > = cc xfy .2.3and,4.2 ,3.4,ofgraphThe 43 21 xyxy xyxy == ==
2. 2. Copyright © 2007 Pearson Education, Inc. Slide 2-2 2.3 Vertical Shrinking Vertical Shrinking of the Graph of a Function If the graph of is obtained by vertically shrinking the graph of by a factor of c. In general, the smaller the value of c, the greater the shrink. ,10 << c )(xfcy ⋅= )(xfy = .10units,shrunk )(ofgraphGeneral << = cc xfy . 3 4 3 3 3 2 3 1 3.and,5. ,1.,ofgraphThe xyxy xyxy == ==
3. 3. Copyright © 2007 Pearson Education, Inc. Slide 2-3 2.3 Reflecting Across an Axis Reflecting the Graph of a Function Across an Axis For a function (a) the graph of is a reflection of the graph of f across the x-axis. (b) the graph of is a reflection of the graph of f across the y-axis. )(xfy −= ),(xfy = )( xfy −=
4. 4. Copyright © 2007 Pearson Education, Inc. Slide 2-4 2.3 Example of Reflection Given the graph of sketch the graph of (a) (b) Solution (a) (b) ),(xfy = )(xfy −= )( xfy −= ).,(isso ,graphon theis),(pointIf ba ba − If point ( , ) is on the graph, so is ( , ). a b a b−
5. 5. Copyright © 2007 Pearson Education, Inc. Slide 2-5 2.3 Reflection with the Graphing Calculator ).( and, ,126Set 13 12 2 1 xyy yy xxy −= −= ++= .andofgraphthehaveWe 21 yy .andofgraphthehaveWe 31 yy
6. 6. Copyright © 2007 Pearson Education, Inc. Slide 2-6 2.3 Combining Transformations of Graphs Example Describe how the graph of can be obtained by transforming the graph of Sketch its graph. Solution Since the basic graph is the vertex of the parabola is shifted right 4 units. Since the coefficient of is –3, the graph is stretched vertically by a factor of 3 and then reflected across the x-axis. The constant +5 indicates the vertex shifts up 5 units. 5)4(3 2 +−−= xy .2 xy = ,2 xy = 2 )4( −x 2 )4(3 −− x 2 ) 53( 4xy −−= + shift 4 units right shift 5 units up vertical stretch by a factor of 3 reflect across the x-axis
7. 7. Copyright © 2007 Pearson Education, Inc. Slide 2-7 Graphs: 5)4(3 2 +−−= xy 2 ( 4)y x= − 2 3( 4)y x= − 2 3( 4)y x= − −
8. 8. Copyright © 2007 Pearson Education, Inc. Slide 2-8 2.3 Caution in Translations of Graphs • The order in which transformations are made is important. If they are made in a different order, a different equation can result. – For example, the graph of is obtained by first stretching the graph of by a factor of 2, and then translating 3 units upward. – The graph of is obtained by first translating horizontally 3 units to the left, and then stretching by a factor of 2. 32 += xy xy = 32 += xy
9. 9. Copyright © 2007 Pearson Education, Inc. Slide 2-9 2.3 Transformations on a Calculator- Generated Graph Example The figures show two views of the graph and another graph illustrating a combination of transformations. Find the equation of the transformed graph. Solution The first view indicates the lowest point is (3,–2), a shift 3 units to the right and 2 units down. The second view shows the point (4,1) on the graph of the transformation. Thus, the slope of the ray is Thus, the equation of the transformed graph is xy = First View Second View .3 1 3 43 12 = − − = − −− =m .233 −−= xy
10. 10. Copyright © 2007 Pearson Education, Inc. Slide 2-9 2.3 Transformations on a Calculator- Generated Graph Example The figures show two views of the graph and another graph illustrating a combination of transformations. Find the equation of the transformed graph. Solution The first view indicates the lowest point is (3,–2), a shift 3 units to the right and 2 units down. The second view shows the point (4,1) on the graph of the transformation. Thus, the slope of the ray is Thus, the equation of the transformed graph is xy = First View Second View .3 1 3 43 12 = − − = − −− =m .233 −−= xy<|endoftext|>
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Last blog articles
The Falcon Races
Categories : , , Blog
The Falcon Races
Birds are not correctly classifiedas predators, but they are an indispensable part of the food chain. Although there is a bird that can easily be considered a predator or the most dangerous because when it isaway from the ground, it difficult to avoid. I'm talking about the Hawks, birds that are characterized by their large size and the fastest animal on earth reaching speeds over 230 to 360 kilometers per hour in a tailspin, while in its normal displacement is over 96 km/h on average.
Its scientific name is Falcon Longipennis, and thisbird can be foundin the regions of the Australian continent, the origin of its name comes from there, although it can also be foundin Indonesia and Papua New Guinea. It has dark plumage and is common to see in forests or areas where vegetation is usually very abundant. On average, it can measure up to 36 centimeters high, although the female can become larger. This falcon is capable of making its nest and appropriating others. Its food is mainly based on invertebrates, other birds and insects.
Scientifically, this bird is called Falco Vespertinus which is a bird of prey of the family Falconidae family. This bird is found mainly by the wooded areas of Europe and Asia, during winter time, they usually emigrate to Africa. Its average size is between 28 to 34 centimeters long, reaching a height of up to 75 centimeters. The male has bluish-grayplumage, and thefemale has gray wings, the head and parts of the chest areorange. It tends to make a shortbite on its prey. It feeds mainly on big insects but also small mammals like mice.
It belongs to the Falconidae family; thisbirdis called Falco Sparverius which is also known colloquially as the Weehawk Colorado or Cuyaya It is a species present in the American continent. One of the peculiarities of this bird is that it is usedfor the falconry which is the hunting with trained birds. This species can measure up to 27 centimeters long. Its characteristic color is light greyish and has black dots in the wings, its tail is reddish with a black granaja and has small white tips. This bird has a diet that includes large insects, rodents, reptiles, amphibians, and other little birds.
Scientifically, it is known as the Falco femoralis, and it is one of the medium-sized hawks that exist all over the world.
This falcon prevails throughout the American contain, andits common name is due to the color of the plumage since it has areas of bluish grey. It can be found in the wooded regions of America. This bird feeds on insects, small birds andmammals. A bird that can be quick in a tailspin no doubt.
The Columbarium Falco is one of the smallest hawks in the whole family. However, it doesn`t mean it isnot dangerous for their prey. This bird can be found mainly in the Northern hemisphere. This bird is also known with another name: Falcon Palomo in the North American zone. This Falco tends to emigrate to the tropics of America to spend the winterseason there. Its diet is usually basedon insects, small birds, androdents.
The Brown Hawk, Falcon Falcon or Falco Falcon is a bird that is characterized by having its brown plumage andwhite color on its chest, dark brown wings. This species is also knownwith the name of Spotted Hawk, striped Hawk or Western Falcon. Indeed, this last name is because it is presented in Western Australia and its name Falcon is derived from its aboriginal name.
This bird is locatedon the African continent. This species has a characteristic that makes to stand out among the entire Falco family since it is a very sedentary bird, it means it is likely that is on the top of a tree than flying. The hobby Falco lives in the woods, as long as the vegetation is not very high. Another of its characteristics is that it usually invades the nests of other birds; itis not a bird that likes to build its own nest. Females can measure up to 80 centimeters, being the main difference inregards to a male.
The red-headed Merlin or TURUMTI is the Chicquera Falco is consideredas a prey bird of the Halon family. It can be foundin India and Africa in the sub-Saharan region. It has been adapted to live in semi-deserted areas, savannas and other places where the prevailing climate is dry with some trees. Although it has also been foundin riparian forests. This bird can lay five eggs in its nest. Its diet is basedon rodents, reptiles, andinsects.
The Rusticolus Falco is a bird found in the areas of North America, specifically on the Arctic coast and nearby islands. As well as it is possible to see it in Europe and Asia. It has been adapted to cold weather conditions.
They are known as smoke hawks; thesebirds belong to the region of Australia and have a medium size. It is a species that only has a population of 1000 specimens and is not because it is endangered, but it is a low-density species. However, its populationalso decreases by traps and pesticide poisoning.
The Falco Newton is originally from Madagascar, hence its common name. This species can reach 30 centimeters in length and weigh up to 128 grams. Present plumage in reddish-grey colors with dark streaks, grey with black or dark brown spots.<|endoftext|>
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Q. What is ‘e-waste’? Discuss its impact on the environment and human health. What are the steps taken by the government to tackle the problem of e-waste? (250 words)01 Mar, 2019 GS Paper 1 Geography
- Explain what is e-waste in introduction.
- Discuss its impact on the environment and human health
- Mention steps taken by the government to tackle the problem of e-waste
- Give a way forward.
- E-waste or electronic waste refers to all waste from electronic and electrical appliances which have reached their end- of- life period or are no longer fit for their original intended use and are destined for recovery, recycling or disposal. It includes computer and its accessories monitors, printers; typewriters, mobile phones and chargers, remotes, batteries, LCD/Plasma TVs, air conditioners, refrigerators and other household appliances etc.
- India’s annual electronic waste (e-waste) generation was 1.8 million MTs in 2016 and is expected to reach 5.2 million MTs by 2020.
- Rapid growth of technology, upgradation of technical innovations, and a high rate of obsolescence in the electronics industry have led to one of the fastest growing waste streams in the world.
Impact on the environment and human health
- Pollutants in e-waste: Many of these substances are toxic and carcinogenic. Some are Arsenic, Brominated flame-proofing agent, Cadmium, Cobalt, Chrome, Lead etc.
- Lead: A neurotoxin that affects the kidneys and the reproductive system. It affects mental development in children.
- Chromium: Inhaling hexavalent chromium can damage liver and kidneys and cause bronchial maladies including asthmatic bronchitis and lung cancer.
- Mercury: Affects the central nervous system, kidneys and immune system.
- Cadmium: A carcinogen. Long-term exposure causes Itai-itai disease, which causes severe pain in the joints and spine.
- Non-biodegradable: The materials are complex and have been found to be difficult to recycle in an environmentally sustainable manner causing health hazard.
- Harmful substances from e-wastes can leach into the surrounding soil, water and air during waste treatment or when they are dumped in landfills or left to lie around near it. It adversely affects human health and ecology.
- The impact is found to be worse in developing countries like India where people are engaged in recycling E-Waste are mostly in the unorganised sector, living in close proximity to dumps or landfills of untreated E-Waste. It can enter their body through respiratory tracts, skin, or the mucous membrane of the mouth and the digestive tract.
Steps taken by the government to tackle the problem of e-waste:
- The Ministry of Environment & Forests (MoEFCC) of the government of India is responsible for environmental legislation and its control. The Central Pollution Control Board (CPCB), an autonomous body under the MoEF, plays an important role in drafting guidelines and advising the MoEF on policy matters regarding environmental issues.
- Government of India announced the e-waste (Management and Handling) Rules in 2011. These Rules came into effect from 1st May, 2012.
- E-waste Management Rules (2016): These rules apply to every manufacturer, producer, consumer, bulk consumer, collection centres, dealers, e-retailer, refurbisher, dismantler and recycler involved in manufacture, sale, transfer, purchase, collection, storage and processing of e-waste or electrical and electronic equipment.
- Deposit Refund System (DRS): The implementation of a DRS would involve collecting a deposit from consumer that is refundable when consumer deposits the e-waste for safe recycling.
- Extended Producer Responsibility: The new rules present a more stringent version of Extended Producer Responsibility as compared to the Rules of 2011. The authorized EPR entities now have obligation to declare targets of how much e-waste they will recycle which should be 30% of the e-waste they are likely to generate based on past sales.
- Build consumer awareness and define their roles and responsibilities around E-waste disposal through a regulatory framework.
- Recognise End-of Life (EOL) range for all Electrical and Electronic Equipment after due industry consultation.
- Adopt 'Informal Sector Franchisee Model' aimed to move the unorganised sector to an organised one
- Introduction of Advanced Recycling Fee (ARF) will help build a sound infrastructure, provide quality service for the public, and manage the backlog of old products, while placing the least financial burden on local communities.<|endoftext|>
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Title
Beginning Algebra
Tutorial 20: The Rectangular Coordinate System
Learning Objectives
After completing this tutorial, you should be able to: Plot points on a rectangular coordinate system. Identify what quadrant or axis a point lies on. Tell if an ordered pair is a solution of an equation in two variables or not. Complete an ordered pair that has one missing value.
Introduction
This section covers the basic ideas of graphing: rectangular coordinate system, ordered pairs and solutions to equations in two variables. Graphs are important in giving a visual representation of the correlation between two variables. Even though in this section we are going to look at it generically, using a general x and y variable, you can use two-dimensional graphs for any application where you have two variables. For example, you may have a cost function that is dependent on the quantity of items made. If you needed to show your boss visually the correlation of the quantity with the cost, you could do that on a two-dimensional graph. I believe that it is important for you learn how to do something in general, then when you need to apply it to something specific you have the knowledge to do so. Going from general to specific is a lot easier than specific to general. And that is what we are doing here looking at graphing in general so later you can apply it to something specific, if needed.
Tutorial
Rectangular Coordinate System
The following is the rectangular coordinate system:
It is made up of two number lines: The horizontal number line is the x- axis. The vertical number line is the y- axis. The origin is where the two intersect. This is where both number lines are 0. It is split into four quadrants which are marked on this graph with Roman numerals. Each point on the graph is associated with an ordered pair. When dealing with an x, y graph, the x coordinate is always first and the y coordinate is always second in the ordered pair (x, y). It is a solution to an equation in two variables. Even though there are two values in the ordered pair, be careful that it associates to ONLY ONE point on the graph, the point lines up with both the x value of the ordered pair (x-axis) and the y value of the ordered pair (y-axis).
Example 1: Plot the ordered pairs and name the quadrant or axis in which the point lies. A(2, 3), B(-1, 2), C(-3, -4), D(2, 0), and E(0, 5).
Remember that each ordered pair associates with only one point on the graph. Just line up the x value and then the y value to get your location.
A(2, 3) lies in quadrant I. B(-1, 2) lies in quadrant II. C(-3, -4) lies in quadrant III. D(2, 0) lies on the x-axis. E(0, 5) lies on the y-axis.
Example 2: Find the x- and y- coordinates of the following labeled points
Remember that each ordered pair associates with only one point on the graph. Just line up the x value and then the y value to get your ordered pair. Since point A corresponds to 2 on the x-axis and -3 on the y-axis, then A’s ordered pair is (2, -3). Since point B corresponds to 3 on the x-axis and 2 on the y-axis, then B’s ordered pair is (3, 2). Since point C corresponds to -2 on the x-axis and 3 on the y-axis, then C’s ordered pair is (-2, 3). Since point D corresponds to -3 on the x-axis and - 4 on the y-axis, then D’s ordered pair is (-3, - 4). Since point E corresponds to -3 on the x-axis and 0 on the y-axis, then E’s ordered pair is (-3, 0). Since point F corresponds to 0 on the x-axis and 2 on the y-axis, then F’s ordered pair is (0, 2).
Solutions of Equations in Two Variables
The solutions to equations in two variables consist of two values that when substituted into their corresponding variables in the equation, make a true statement. In other words, if your equation has two variables x and y, and you plug in a value for x and its corresponding value for y and the mathematical statement comes out to be true, then the x and y value that you plugged in would together be a solution to the equation. Equations in two variables can have more than one solution. We usually write the solutions to equations in two variables in ordered pairs. Example 3: Determine whether each ordered pair is a solution of the given equation. y = 5x - 7; (2, 3), (1, 5), (-1, -12)
Let’s start with the ordered pair (2, 3). Which number is the x value and which one is the y value? If you said x = 2 and y = 3, you are correct! Let’s plug (2, 3) into the equation and see what we get:
*Plug in 2 for x and 3 for y
This is a TRUE statement, so (2, 3) is a solution to the equation y = 5x - 7. Now let’s take a look at (1, 5). Which number is the x value and which one is the y value? If you said x = 1 and y = 5, you are right! Let’s plug (1, 5) into the equation and see what we get:
*Plug in 1 for x and 5 for y
Whoops, it looks like we have ourselves a FALSE statement. This means that (1, 5) is NOT a solution to the equation 5x - 7. Now let’s look at (-1, -12). Which number is the x value and which one is the y value? If you said x = -1 and y = -12, you are right! Let’s plug (-1, -12) into the equation and see what we get:
*Plug in -1 for x and -12 for y
We have another TRUE statement. This means (-1, -12) is another solution to the equation y = 5x - 7. Note that you were only given three ordered pairs to check, however, there are an infinite number of solutions to this equation. It would very cumbersome to find them all.
Example 4: Determine whether each ordered pair is a solution of the given equation. x = 3; (3, 5), (2, 3), (3, 4)
This equation looks a little different than the one on example 3. In this equation, we only have an x value to plug in. So as long as the x value is 3, then we have a solution to the equation. It doesn’t matter what y’s value is.
Let’s start with the ordered pair (3, 5). Which number is the x value and which one is the y value? If you said x = 3 and y = 5, you are correct! Let’s plug (3, 5) into the equation and see what we get:
*Plug in 3 for x
This is a TRUE statement, so (3, 5) is a solution to the equation x = 3. Now let’s take a look at (2, 3). Which number is the x value and which one is the y value? If you said x = 2 and y = 3, you are right! Let’s plug (2, 3) into the equation and see what we get:
*Plug in 2 for x
Whoops, it looks like we have ourselves a FALSE statement. This means that (2, 3) is NOT a solution to the equation x = 3. Now let’s look at (3, 4). Which number is the x value and which one is the y value? If you said x = 3 and y = 4, you are right! Let’s plug (3, 4) into the equation and see what we get:
*Plug in 3 for x
We have another TRUE statement. This means (3, 4) is another solution to the equation x = 3. Note that you were only given three ordered pairs to check, however, there are an infinite number of solutions to this equation. It would very cumbersome to find them all.
Finding the Corresponding Value in an Ordered Pair Given One Variable’s Value
Again, the solutions to equations in two variables consist of two values that when substituted into their corresponding variables in the equation, make a true statement. Sometimes you are given a value of one of the variables and you need to find the corresponding value of the other variable. The steps involved in doing that are: Step 1: Plug given value for variable into equation. Step 2: Solve the equation for the remaining variable.
Example 5: Complete each ordered pair so that it is a solution of the equation . (1, ) and ( , -1).
In the ordered pair (1, ), is 1 that is given the x or the y value? If you said x, you are correct. Plugging in 1 for x into the given equation and solving for y we get:
*Plug in 1 for x *Solve for y
So, the ordered pair (1, 1) would be a solution to the given equation. In the ordered pair ( , -1), is the -1 that is given the x or the y value? If you said y, you are correct. Plugging in -1 for y into the given equation and solving for x we get:
*Plug in -1 for y *Solve for x
So, the ordered pair (4, -1) would be another solution to the given equation.
Example 6: Complete the table of values for the equation .
x y 0 -1 1
The only difference between this one and example 5 above is that we are using a table to match up our values of our variables instead of writing it in an ordered pair. The concept is still the same, we need to find the corresponding values of our variables that are solutions to the given equation. Plugging in 0 for y into the given equation and solving for x we get:
So, the ordered pair (-1/2, 0) would be a solution to the given equation. Plugging in -1 for y into the given equation and solving for x we get:
So, the ordered pair (-1/2, -1) would be another solution to the given equation. Plugging in 1 for y into the given equation and solving for x we get:
So, the ordered pair (-1/2, 1) would be another solution to the given equation.
Filling in the table we get:
x y -1/2 0 -1/2 -1 -1/2 1
Practice Problems
These are practice problems to help bring you to the next level. It will allow you to check and see if you have an understanding of these types of problems. Math works just like anything else, if you want to get good at it, then you need to practice it. Even the best athletes and musicians had help along the way and lots of practice, practice, practice, to get good at their sport or instrument. In fact there is no such thing as too much practice. To get the most out of these, you should work the problem out on your own and then check your answer by clicking on the link for the answer/discussion for that problem. At the link you will find the answer as well as any steps that went into finding that answer.
Practice Problem 1a: Plot each point and name the quadrant or axis in which the point lies.
1a. A(3, 1), B(-2, -1/2), C(2, -2), and D(0,1) (answer/discussion to 1a)
Practice Problem 2a: Find the x- and y- coordinates of the following labeled points.
Practice Problems 3a - 3b:Determine if each ordered pair is a solution of the given equation.
3a. y = 4x - 10 ; (0, -10), (1, -14), (-1, -14) (answer/discussion to 3a)
3b. y = -5 ; (2, -5), (-5, 1), (0, -5) (answer/discussion to 3b)
Practice Problem 4a:Complete each ordered pair so that it is a solution of the equation .
4a. (0, ) and ( , 1). (answer/discussion to 4a)
Practice Problem 5a: Complete the table of values for the equation .
5a.
x y 0 -1 1
Need Extra Help on these Topics?
The following is a webpage that can assist you in the topics that were covered on this page:
http://www.purplemath.com/modules/plane.htm This webpage helps you with plotting points.
Go to Get Help Outside the Classroom found in Tutorial 1: How to Succeed in a Math Class for some more suggestions.
Last revised on July 29, 2011 by Kim Seward.<|endoftext|>
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## Trigonometric Ratios
Pythagoras' Theorem links the lengths of sides of right angled-triangles.
This section of trigonometry makes connections between the lengths of sides and angles in right-angled triangles.
### Right-angled Triangles
Given a right-angled triangle with an angle marked a as shown: In the diagram: y is called the opposite side (to the angle α ) x is called the adjacent side (to the angle α) r is called the hypotenuse side Greek letters, such as α are often used in trigonometry.
There are several methods used for finding angles and sides in right-angled triangles. You may have been taught and use a different one to that shown below. They all produce the same answers if done correctly!
For example, some people call the opposite side, the separated side and the adjacent side, the connected side.
Examples Answers In the triangle shown, how long is: (a) The side opposite to θ ? (b) The side adjacent to θ ? (c) The hypotenuse? (a) The opposite side is 5 cm long. (b) The adjacent side is 6 cm long. (c) The hypotenuse is 8 cm long.
### Trigonometric Ratios
For a right-angled triangle:
REMEMBER Sine of angle α = SOH Cosine of angle α = CAH Tangent of angle α = TOA
These can be rearranged to:
y = r sin α x = r cos α y = x tan α
### Circular Functions
The trigonometric ratios are also known as circular functions and the sine, cosine and tangent of any angle, positive or negative can be found.
Click here for an activity showing the sine as a circular function.
Click here for an activity showing the cosine as a circular function.
Click here for an activity showing the tangent as a circular function.
### Finding Ratios
The sine, cosine and tangent ratios are the same for a particular angle regardless of the size of the triangle.
The ratios can be found using a calculator or from a book of trigonometric tables.
Calculators.
Most calculators have trigonometric function keys. These will give the sine, cosine, and tangent of an angle as well as the inverse of these functions. These decimals will be given to a large number of significant figures, which will often need to be rounded off (4 significant figures is usually accurate enough).
e.g To find sine 53° press 0.798635510 which could then be rounded as necessary.
The other trigonometric buttons are and .
Care must be taken to ensure that the calculator is set to work in values in degrees (DEG), as there are other ways of measuring angles such as radians (RAD) and gradians (GRAD). Use the mode button to change these settings.
Tables.
Before the days of calculators, everyone used printed tables giving the trigonometric ratios and these can be used if you do not have a calculator available. These tables give the ratios for angles from 0° to 90° to four or five significant figures, with angles being given to 1 decimal place.<|endoftext|>
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Children learn important character lessons best when taught by example. All children are faced with situations where they need to have courage and bravery. Outside of situations that present physical danger, children need to learn courage and bravery in the social situations they will face in everyday life. They need the courage to stand up for what is right and bravery to stand up for those being mistreated. Most importantly they must learn to hold to their standards when faced with peer pressure. You can help your grandchildren learn these important character traits by sharing and reading books like these that explore different types of courage and bravery in engaging and powerful stories.
This post contains affiliate links to take you directly to the products listed.
Sheila Rae, the Brave by Kevin Henkes
Big sister Sheila Rae is not afraid of anything – She growls at stray dogs, and bares her teeth at stray cats. But it’s hard demonstrating courage without new and terrifying challenges. When Sheila Rae decides to go home from school a new way she gets lost and becomes lonely and….well, scared. Her younger sister Louise courageously helps her find her way home. The trip home is a triumph for both girls as they learn the value of courage and sisterly support. Written and Illustrated By Kevin Henkes.
Wildest Brother by Cornelia Funke Illustrated by Kerstin Meyer
Ben is a fearless young boy, Brave as a lion, strong as an elephant. When it comes to protecting his big sister, Ann, nothing can stand in his way! Gallantly he spends his day battling monsters and all sorts of ferocious beasts. Ben is a fearless young boy, Brave as a lion, strong as an elephant. When it comes to protecting his big sister, Ann, nothing can stand in his way! Gallantly he spends his day battling monsters and all sorts of ferocious beasts.
By Maria Dismondy Illustrations by Kimberly Shaw-Peterson
How can Ralph be so mean? Lucy is one of a kind and Ralph loves to point that out. Lucy’s defining moment comes when Ralph truly needs help. Because she knows what she stands for, Lucy has the courage to make a good choice. This charming story empowers children to always do the right thing and be proud of themselves, even when they are faced with someone as challenging as Ralph.
The Bravest of Us All By Marsha Diane Illustrated by Brad Sneed
By Marsha Diane Illustrated by Brad SneedDaring ten-year-old Velma Jean walks barefoot over sandburs, swims in the new horse tank, even stands up to Alfred the Bull. Every day Velma Jean does something that amazes her siblings. To her sister Ruby Jane, she is the bravest of them all. But when a tornado sets down near the edge of their farm, Velma Jean is afraid to seek shelter in the dark storm cellar. It is Ruby Jane who stands up to the weather and brings her sister to safety.
The Story Of Ruby Bridges: Special Anniversary Edition By Robert Coles, Illustrated by George Ford
This is the true story of an extraordinary 6-year-old who helped shape history when she became the first African-American sent to first grade in an all white school. This moving book captures the courage of a little girl standing alone in the face of racism.
Thank You, Mr. Falker By Patricia Polacco
Patricia Polacco is now one of America’s most loved children’s book creators, but once upon a time, she was a little girl named Trisha starting school. Trisha could paint and draw beautifully, but when she looked at words on a page, all she could see was jumble. It took a very special teacher to recognize little Trisha’s dyslexia: Mr. Falker, who encouraged her to overcome her reading disability.
Stuart’s Cape (pb) Illustrated by Martin Matje
A quirky, inventive chapter book featuring an unusual hero–an 8-year-old worrier. Now in paperback! Stuart’s got problems. It’s raining. He’s bored. And worst of all, he’s new in town, so he’s got a lot to worry about. What does a kid like Stuart need in order to have an adventure? A cape, of course!
Mirette on the High Wire By Emily Arnold McCully
Mirette on the High Wire By Emily Arnold McCullyMirette was always fascinated by the strange and interesting people who stayed in her mother’s boardinghouse. But no one excited her as much as Bellini, who walks the clothesline with the grace and ease of a bird. When Mirette discovers that fear has kept him from performing for years, she knows she must repay him for the kindness he has shown her — and show him that sometimes a student can be the greatest teacher of all.
Not Afraid of Dogs by Susanna Pitzer Illustrated by Lary Day
Daniel is the bravest boy of all! Daniel isn’t afraid of spiders. He isn’t afraid of snakes. He isn’t even afraid of thunderstorms. And no matter what his sister says, he’s certainly not afraid of dogs ― he just doesn’t like them. But there’s no avoiding them when he comes home and his mother is babysitting his aunt’s dog. Susanna Pitzer’s humorous look into the nature of courage, fear, and friendship has a touching outcome for both the brave and the frail of heart.
Illustrated by Gerald Kruglik, Olof Landström
Wallace, a mouse, could do almost anything. Anything that is, as long as he had a list. Wallace is a shy mouse. He writes lists. Lists of recipes, funny words, and frightening experiences. Wallace meets his lively neighbor named Albert. His world is swiftly opened to new delights, such as painting and music. Wallace and Albert experience the excitement of an adventure, and Wallace discovers a new joy. Friendship.
The Invisible Boy by Trudy Ludwig Illustrated by Patrice Barton
Meet Brian, the invisible boy. Nobody ever seems to notice him or think to include him in their group, game, or birthday party . . . until, that is, a new kid comes to class. When Justin, the new boy, arrives, Brian is the first to make him feel welcome. And when Brian and Justin team up to work on a class project together, Brian finds a way to shine.
Elmer by David McKee
Elmer the elephant is bright-colored patchwork all over. No wonder the other elephants laugh at him! If he were ordinary elephant color, the others might stop laughing. That would make Elmer feel better, wouldn’t it? The surprising conclusion of David McKee’s comical fable is a celebration of individuality and the power of laughter.
Hilda Hen’s Scary Night by Mary Wormell
Night has fallen and Hilda is late getting back to the henhouse. On her way she sees strange, mysterious shapes-a snake, a monster-lurking in the shadows. What are these creatures? Where do they go during the day? Children will soon identify the troublesome shapes as everyday objects found in the farmyard-things that can look a lot spookier at night.
Pete & Pickles by Berkeley Breathed
Pete is a perfectly predictable, practical, uncomplicated pig. At least, he was . . . before a runaway circus elephant named Pickles stampeded into his life, needing a friend. Pickles is larger than life and overflowing with imagination. She takes Pete swandiving off Niagara Falls. (Sort of.) And sledding down the Matterhorn. (Sort of.) Pete goes along for the wild ride and actually begins to enjoy himself . . . until Pickles goes too far. And Pete tells her she must leave. Yet sometimes the simple life isn?t all it?s cracked up to be.
Willow Finds a Way by Lana Button Illustrated by Tania Howells
In this simple but substantial picture book by Lana Button, shy, quiet Willow silently wishes she could find a way to say no to her bossy classmate Kristabelle’s demands, but the words never seem to come when she needs them.Surprising everyone, even herself, Willow steps up and bravely does something shocking, and it changes the entire dynamic of the classroom.
The Story of Fish and Snail by Deborah Freedman
Every day, Snail waits for Fish to come home with a new story. Today, Fish’s story (about pirates!) is too grand to simply be told: Fish wants to show Snail. But that would mean leaving the familiar world of their book—a scary prospect for Snail, who would rather stay safely at home and pretend to be kittens. Fish scoffs that cats are boring; Snail snaps back. Is this book too small for the two feuding friends? Could this be THE END of The Story of Fish and Snail?
Brave Irene by William Steig
Brave Irene is Irene Bobbin, the dressmaker’s daughter. Her mother, Mrs. Bobbin, isn’t feeling so well and can’t possibly deliver the beautiful ball gown she’s made for the duchess to wear that very evening. So plucky Irene volunteers to get the gown to the palace on time, in spite of the fierce snowstorm that’s brewing– quite an errand for a little girl.
The Empty Pot (An Owlet Book) by Demi
A long time ago in China there was a boy named Ping who loved flowers. Anything he planted burst into bloom. The Emperor loved flowers too. When it was time to choose an heir, he gave a flower seed to each child in the kingdom. “Whoever can show me their best in a year’s time,” he proclaimed, “shall succeed me to the throne!” Ping plants his seed and tends it every day. But month after month passes, and nothing grows. When spring comes, Ping must go to the Emperor with nothing but an empty pot. Demi’s exquisite art and beautifully simple text show how Ping’s embarrassing failure is turned triumphant in this satisfying tale of honesty rewarded.
Rotten Teeth by Laura Simms, David Catrow
Speaking in front of the class isn’t easy for small people like Melissa Herman. Especially when there’s nothing very special to say about her house or her family or herself. But with the help of her older brother, Melissa borrows a bottle from her father’s dental office to take to show and tell. The teacher is appalled, but the children are intrigued.
The Princess Knight by Cornelia Funker, Illustrator Kerstin Meyer
Violetta is a princess. But she wants to be a knight. At night, she practices at becoming the best knight in the land. When her father, the king, stages a tournament for Violetta’s hand in marriage, she knows she must win the greatest battle yet, for the most important prize of all – herself.
The Kissing Hand by Audrey Penn Illustrator Ruth E. Harper & Nancy M. Leak
School is starting in the forest, but Chester Raccoon does not want to go. To help ease Chester’s fears, Mrs. Raccoon shares a family secret called the Kissing Hand to give him the reassurance of her love any time his world feels a little scary. This heartwarming book has become a children’s classic that has touched the lives of millions of children and their parents, especially at times of separation, whether starting school, entering daycare, or going to camp.
One quiet day at the North Pole, Lars, the Little Polar Bear, hears a cry coming from a deep hole in the ice. It‘s Hugo, a scared little hare, who is trapped and needs to be rescued. The two fast become friends, but Lars teases Hugo for being timid, and Hugo wishes Lars would be just a little more careful! Then Lars lands himself in trouble, and Hugo has to show just how brave he can be in an emergency.
by Bernard Waber
What is courage? Certainly it takes courage for a firefighter to rescue someone trapped in a burning building, but there are many other kinds of courage too. Everyday kinds that normal, ordinary people exhibit all the time, like “being the first to make up after an argument,” or “going to bed without a nightlight.” Bernard Waber explores the many varied kinds of courage and celebrates the moments, big and small, that bring out the hero in each of us.
Mystery of the Spooky Junkyard – A Tale of Courage (Auto-B-Good) by Phillip Walton
Mystery of the Spooky Junkyard – A Tale of Courage
A terrifying encounter with the spooky thing that lurks in the junkyard leaves EJ shaken up. But when a fast-talking ghost hunter shows up in town and promises to catch it for him — for a small fee, of course — EJ would do anything to avoid his fear. Back in the spooky junkyard, they all discover things are not as they seem and EJ finds the source of true courage.
Rainbow Fish to the Rescue by Marcus Pfister Illustrator Alison James
Santosh and the Little Elephant Santosh the little elephant has a problem. A BIG, HUMONGOUS problem. His family has to move. Not just to another neighborhood, but across the ocean to another continent.
YES, ACROSS THE OCEAN!
That though isn’t the biggest problem he has. There is a SUPER-HUGE, GINOMOROUS problem on top of that. His dog, Cooper, isn’t able to go with the family to their new home.
What is Santosh to do? How can he convince his parents to let Cooper go with them?
Santosh has an idea! He has a great idea! But, will it work? And, if it doesn’t, then what? Will he accept his fate?
Being a Nana is the BEST!<|endoftext|>
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Mechanical dust collectors have three categories: settling chamber, inertial dust collector and cyclone. The work of the settling chamber uses gravity, and the so-called gravity is the attraction of the earth to objects. The dust in the dust-containing gas is separated in the settling chamber by gravity. Inertial dust collectors use inertial forces to separate dust. The inertial force is the force that reflects the state of motion of the material itself, and changes the state of motion when the external force is applied.
Under the same force, an object with small inertia is more likely to change its motion state than an object with large inertia, that is, the obtained acceleration is relatively large, which is advantageous for dust separation with small inertia. The cyclone uses centrifugal force. The so-called centrifugal force refers to the centripetal separation force applied to an object that makes a circular motion. It is based on the reaction force in the rotating body, and the separation process using the centrifugal force to separate the heterogeneous system is generally called centrifugal separation.
It works according to the principle that the centrifugal force generated by the material with high mass and high rotation speed during the rotation process is also large.<|endoftext|>
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The long-tailed marmot or golden marmot (Marmota caudata) is a species of marmot in the Sciuridae family. It is found in high mountain areas of Pakistan above 3000 meters.
Marmots are large ground squirrels in the genus Marmota, of which there are 15 species. Those most often referred to as marmots tend to live in mountainous areas. Marmots typically live in burrows and hibernate there through the winter. Most marmots are highly social and use loud whistles to communicate with one another, especially when alarmed.
Marmots mainly eat greens and many types of grasses, berries, lichens, mosses, roots and flowers.
Marmots have been known since antiquity. Research by the French ethnologist Michel Peissel claimed the story of “gold-digging ants” reported by the Ancient Greek historian Herodotus, who lived in the 5th century BC, was founded on the golden Himalayan marmot of the Deosai Plateau and the habit of local tribes such as the Minaro to collect the gold dust excavated from their burrows.<|endoftext|>
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ZingPath: Ratio, Rate, and Proportion
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Ratio, Rate, and Proportion
Learn in a way your textbook can't show you.
Explore the full path to learning Ratio, Rate, and Proportion
Lesson Focus
Proportion and Its Properties
Pre-Algebra
Students determine if two ratios form a proportion, and solve for the unknown value of a proportion.
Now You Know
After completing this tutorial, you will be able to complete the following:
• Determine if two ratios form a proportion.
• Determine if a given relationship is proportional.
• Use the properties of proportions to solve problems involving proportional relationships.
• Solve for the unknown value of a proportion in mathematical statements and real-life situations.
Everything You'll Have Covered
Proportionality is a type of relation between quantities. Two quantities are proportional if they are constant multiples of each other. More specifically, two variables x and y vary directly if there is a nonzero constant k such that y = k . x. The constant k is called the constant of proportionality.
There is a constant ratio between proportional quantities, which can be seen by manipulating the equation y = k . x.
This fact is the basis for proportional reasoning questions, such as the one below.
The cost of purchasing coffee is proportional to the amount purchased. If five pounds of coffee cost \$7.00, how much can be purchased with \$21.00?
The quantities are proportional, which implies that the following ratio is constant for any amount of coffee purchased.
In particular, the constant ratio can be determined by using the information given in the problem: five pounds of coffee cost \$7.00.
Therefore, if x is the number of pounds of coffee that can be purchased for \$21.00, then the ratio must equal the ratio above. This fact can be expressed in an equation, from which it follows that x equals 15 pounds.
In order to facilitate discussions and justify solution methods, there are a handful of terms referring to the parts and properties of a proportional relationship. Suppose and that and d are nonzero. The quantities b and c are called the means, whereas the quantities a and d are called the extremes. Simple arithmetic yields the means-extremes, or cross-product, property of proportions.
Cross-product property
The majority of proportional reasoning problems can be solved by using some variation of this property.
Tutorial Details
Approximate Time 10 Minutes Pre-requisite Concepts Students should know the concept of division and be able to evaluate expressions using operations with fractions. Course Pre-Algebra Type of Tutorial Concept Development Key Vocabulary cross-product, equivalent ratios, extremes<|endoftext|>
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# solve the inequality
• Nov 5th 2008, 04:44 PM
hoger
solve the inequality
1/x+1/x+2≤1/x+1
• Nov 5th 2008, 05:10 PM
Plato
Solve this inequally $\frac{1}
{x} + \frac{1}
{{x + 2}} - \frac{1}
{{x + 1}} \leqslant 0
$
• Nov 7th 2008, 11:02 AM
HallsofIvy
Geherally the best way to solve a complicated inequality, like $\frac{1}{x}+ \frac{1}{x+2}\le \frac{1}{x+1}$ or, equivalently $\frac{1}{x}+ \frac{1}{x-2}-\frac{1}{x+1}\le 0$, is to solve the corresponding equation: $\frac{1}{x}+ \frac{1}{x+2}= \frac{1}{x+1}$.
Multiply the entire equation by x(x+1)(x+2): (x+1)(x+2)+ x(x+1)= x(x+2). Multiplying that out, $x^2+ 3x+ 2+ x^2+ x= x^2+ 2x$ which reduces to $x^2+ x+ 2= 0$. The discriminant for that is [tex]2^2- 4(1)(2)= -4 so there are NO real number roots.
A function can change from ">" to "<" or vice-versa only at points where it is "=" or where it is discontinuous. Since there are no points where it is "=", it can only change at points where it is not continuous: where one of the denominators is 0, that is at x= -1, x= -2, and x= 0.
You can check a single value in each interval having those endpoints to determine whether every point in that interval satisfies the inequality or not.
For example, -3 is in the interval of all numbers less than -2 and [tex]\frac{1}{-3}+ \frac{1}{-3+ 2}= -\frac{1}{3}-1= -\frac{4}{3} math which < is than [tex]\frac{1}{-3+1}= -\frac{1}{2}[tex] so the inequality is satisified for all x< -2. Try, say, x= -3/2, which is between -2 and -1 to check if that interval works, x= -1/2 for the interval (-1, 0) and x= 1 for the interval of numbers larger than 1.<|endoftext|>
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Cleft lip and cleft palate are openings or splits in the upper lip, the roof of the mouth (palate) or both. Cleft lip and cleft palate result when facial structures that are developing in an unborn baby don't close completely.
Cleft lip and cleft palate are among the most common birth defects. They most commonly occur as isolated birth defects but are also associated with many inherited genetic conditions or syndromes.
Having a baby born with a cleft can be upsetting, but cleft lip and cleft palate can be corrected. In most babies, a series of surgeries can restore normal function and achieve a more normal appearance with minimal scarring.
Usually, a split (cleft) in the lip or palate is immediately identifiable at birth. Cleft lip and cleft palate may appear as:
- A split in the lip and roof of the mouth (palate) that affects one or both sides of the face
- A split in the lip that appears as only a small notch in the lip or extends from the lip through the upper gum and palate into the bottom of the nose
- A split in the roof of the mouth that doesn't affect the appearance of the face
Less commonly, a cleft occurs only in the muscles of the soft palate (submucous cleft palate), which are at the back of the mouth and covered by the mouth's lining. This type of cleft often goes unnoticed at birth and may not be diagnosed until later when signs develop. Signs and symptoms of submucous cleft palate may include:
- Difficulty with feedings
- Difficulty swallowing, with potential for liquids or foods to come out the nose
- Nasal speaking voice
- Chronic ear infections
When to see a doctor
A cleft lip and cleft palate are usually noticed at birth, and your doctor may start coordinating care at that time. If your baby has signs and symptoms of a submucous cleft palate, make an appointment with your child's doctor.
Cleft lip and cleft palate occur when tissues in the baby's face and mouth don't fuse properly. Normally, the tissues that make up the lip and palate fuse together in the second and third months of pregnancy. But in babies with cleft lip and cleft palate, the fusion never takes place or occurs only part way, leaving an opening (cleft).
Researchers believe that most cases of cleft lip and cleft palate are caused by an interaction of genetic and environmental factors. In many babies, a definite cause isn't discovered.
The mother or the father can pass on genes that cause clefting, either alone or as part of a genetic syndrome that includes a cleft lip or cleft palate as one of its signs. In some cases, babies inherit a gene that makes them more likely to develop a cleft, and then an environmental trigger actually causes the cleft to occur.
Several factors may increase the likelihood of a baby developing a cleft lip and cleft palate, including:
- Family history. Parents with a family history of cleft lip or cleft palate face a higher risk of having a baby with a cleft.
- Exposure to certain substances during pregnancy. Cleft lip and cleft palate may be more likely to occur in pregnant women who smoke cigarettes, drink alcohol or take certain medications.
- Having diabetes. There is some evidence that women diagnosed with diabetes before pregnancy may have an increased risk of having a baby with a cleft lip with or without a cleft palate.
- Being obese during pregnancy. There is some evidence that babies born to obese women may have increased risk of cleft lip and palate.
Males are more likely to have a cleft lip with or without cleft palate. Cleft palate without cleft lip is more common in females. In the United States, cleft lip and palate are reportedly most common in Native Americans and least common in African-Americans.
Children with cleft lip with or without cleft palate face a variety of challenges, depending on the type and severity of the cleft.
- Difficulty feeding. One of the most immediate concerns after birth is feeding. While most babies with cleft lip can breast-feed, a cleft palate may make sucking difficult.
- Ear infections and hearing loss. Babies with cleft palate are especially at risk of developing middle ear fluid and hearing loss.
- Dental problems. If the cleft extends through the upper gum, tooth development may be affected.
- Speech difficulties. Because the palate is used in forming sounds, the development of normal speech can be affected by a cleft palate. Speech may sound too nasal.
- Challenges of coping with a medical condition. Children with clefts may face social, emotional and behavioral problems due to differences in appearance and the stress of intensive medical care.
After a baby is born with a cleft, parents are understandably concerned about the possibility of having another child with the same condition. While many cases of cleft lip and cleft palate can't be prevented, consider these steps to increase your understanding or lower your risk:
- Consider genetic counseling. If you have a family history of cleft lip and cleft palate, tell your doctor before you become pregnant. Your doctor may refer you to a genetic counselor who can help determine your risk of having children with cleft lip and cleft palate.
- Take prenatal vitamins. If you're planning to get pregnant soon, ask your doctor if you should take prenatal vitamins.
- Don't use tobacco or alcohol. Use of alcohol or tobacco during pregnancy increases the risk of having a baby with a birth defect.<|endoftext|>
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# Ratios Unit 1 Lesson 1 Math 6 Ratios
• Slides: 18
Ratios Unit 1 Lesson 1 Math 6
Ratios Students will be able to: Determine the comparison between or relationship of two things using ratio. Solve word problems involving ratio.
Ratios Key Vocabulary: Ratio Equal Ratios Reduced Ratio Fraction GCF
Ratios Ratio is a comparison between, or a relationship of two things. Example: There is 1 ice cream cone to 3 cookies.
Ratios Example: There are 4 boys to 2 girls.
Ratios can be shown in different ways! There is 1 ice cream cone to 3 cookies.
Ratios Sample Problem 1: Write in three different ways the ratio of the given figure. The ratio of 3 blue rectangles to 1 yellow rectangle.
Ratios Sample Problem 2: Answer the following questions given the picture below. a. What is the ratio of apples to bananas? Solution: 5 : 2 a. What is the ratio of bananas to apples? Solution: 2 : 5
Ratios Equal Ratios To find an equal ratio, you can either multiply or divide each term in the ratio by the same number (but not zero).
Ratios Equal Ratios
Ratios Equal Ratios or
Ratios
Ratios
Ratios Reducing ratios is similar to reducing a fraction in lowest terms since ratios can be expressed as fractions. Example: Reduce 12: 16 in lowest terms. Step 1: Find the GCF of the numbers in the ratio. GCF is 4
Ratios
Ratios
Ratios
Ratios<|endoftext|>
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In 1849, E. G. Squier negotiated a treaty for the United States to build a canal across Honduras from the Caribbean Sea to the Gulf. Frederick Chatfield, the British commander in Central America, was afraid the American presence in Honduras would destabilize the British Mosquito Coast, and sent his fleet to occupy El Tigre Island at the entrance to the Gulf. Shortly thereafter, however, Squier demanded the British leave, since he had anticipated the occupation and negotiated the island's temporary cession to the United States. Chatfield could only comply.
All three countries—Honduras, El Salvador, and Nicaragua—with coastline along the Gulf have been involved in a lengthy dispute over the rights to the Gulf and the islands located within.
In 1917, the Central American Court of Justice ruled in a trial which became known as the Fonseca case. It arose out of a controversy between El Salvador and Nicaragua. The latter had entered the Bryan–Chamorro Treaty which granted a portion of the bay to the United States for the establishment of a naval base. El Salvador argued that this violated its right to common ownership in the bay. The court sided with El Salvador, but the US decided to ignore the decision.
In 1992, a chamber of the International Court of Justice (ICJ) decided the Land, Island and Maritime Frontier Dispute, of which the Gulf dispute was a part. The ICJ determined that El Salvador, Honduras, and Nicaragua were to share control of the Gulf of Fonseca. El Salvador was awarded the islands of Meanguera and Meanguerita, while Honduras was awarded El Tigre Island.
The Gulf of Fonseca covers an area of about 3,200 km2 (1,200 sq mi), with a coastline that extends for 261 km (162 mi), of which 185 km (115 mi) are in Honduras, 40 km (25 mi) in Nicaragua, and 29 km (18 mi) in El Salvador.
The climate in the Gulf is typical of tropical and subtropical regions, with two distinct seasons, the rainy and the dry. The Gulf receives nearly 80% of its total yearly rainfall of 1,400–1,600 mm (55–63 in) during the rainy season from May to November. The dry season occurs between December and May and contributes to an annual evaporation rate of 2,800 mm (110 in). As a result of less water flowing into the Gulf, the currents tend to flow inward from the Pacific Ocean, and levels of salinity in the estuaries increase, and seasonal drought occurs.
Temperatures in the Gulf average between 25 and 30 °C (77–86 °F); March and April are the warmest months and November and December the coolest. Relative humidity varies between 65 and 86% depending on location. In contrast, the interior of the country is semitropical and cooler with an average temperature of 26 °C (79 °F).
The vegetation of the wetland ecosystem is dominated by species of mangroves. Of the six species of mangrove identified in the Gulf, red mangrove (Rhizophora mangle) is the most common, mostly occupying the areas permanently inundated by the tides. Black mangrove (Bruguiera gymnorhiza) is the second-most pervasive species and is generally found around the rivers where sediments are deposited along the shoreline. White mangrove (Laguncularia racemosa) is the third-most dominant, followed by botoncillo (Conocarpus erectus); both are generally found further inland and are inundated by the tide less frequently. The dominance of different species over others correlates with the frequency of floods, water quality, and levels of salinity.
The cycle of tides is 2.3 m (7.5 ft) on average per day in the Gulf. During low tides, the soils are inhabited by crabs, conch, and other species. During the high tide, the mangrove forests serve as a feeding ground and habitat for fish, shrimp, and other species, as the root structure of mangroves provides a refuge from larger predators.
A number of volcanoes lie within and around the gulf.
Amapala is a municipality in the Honduran department of Valle.
It is formed by El Tigre Island and its satellite islets and rocks in the Gulf of Fonseca. It has an area of 75.2 km² and a population of 2,482 as of the census of 2001 (of which 4 people were living on Isla Comandante). Thanks to a natural deep channel, and despite lacking modern infrastructure, Amapala long served as the main Honduran port in the Pacific Ocean.Bryan–Chamorro Treaty
The Bryan–Chamorro Treaty was signed between Nicaragua and The United States on August 5, 1914. The Wilson administration changed the treaty by adding a provision similar in language to that of the Platt Amendment, which would have authorized United States military intervention in Nicaragua. The United States Senate opposed the new provision; in response, it was dropped and the treaty was formally ratified on June 19, 1916.
From 1912 to 1925, the United States had amicable relations with the Nicaraguan government because of friendly conservative party presidents Adolfo Diaz, Emiliano Chamorro, and Diego Manuel Chamorro. In exchange for political concessions from the presidents, the United States provided the military strength to ensure the Nicaraguan government internal stability.
The Treaty was named after the principal negotiators: William Jennings Bryan, U. S. Secretary of State; and then General Emiliano Chamorro, representing the Nicaraguan government. By the terms of the treaty, the United States acquired the rights to any canal built in Nicaragua in perpetuity, a renewable 99 year option to establish a naval base in the Gulf of Fonseca and a renewable 99-year lease to the Great and Little Corn Islands in the Caribbean. For those concessions, Nicaragua received three million dollars.
Most of the three million dollars was paid back to foreign creditors by the United States officials in charge of Nicaraguan financial affairs, which allowed the Nicaraguan government to avoid having to pay from its internal revenue the loans it acquired from foreign banks. The debt was amassed by the Nicaraguan government for internal development due to the devastation inflicted from several civil wars waged years prior.
At the request of Nicaragua, the United States under Richard Nixon and Nicaragua under Anastasio Somoza Debayle, held a convention, on July 14, 1970, which officially abolished the treaty and all its provisions.Choluteca River
The Choluteca River (Spanish: Río Grande o Choluteca) is a river in southern Honduras. Its source is in the Department of Francisco Morazán, near Lepaterique (south-west Tegucigalpa), and from there it flows north through the city of Tegucigalpa, then south through the department of El Paraíso, and the department and city of Choluteca. The mouth of the river—located among wetland—is near the coastal town of Cedeño, on the Gulf of Fonseca.
According to FAO, the Choluteca River is 349 kilometres (217 mi) long from source to mouth. Its hydrographic basin has an area of 7,681 square kilometres (2,966 sq mi). It increases its volume between May and October, together with the rainy season. Its basin is affected by severe drought together with the El Niño phenomenon, and this is usually associated with severe bush fires.
There are no dams built along the main course of the river to leave it to its natural health.
The flooding of this river was a major source of destruction during Hurricane Mitch in 1998. It washed out entire neighborhoods in Tegucigalpa, and eventually swelled to six times its normal size in Choluteca. There it destroyed neighborhoods and part of the commercial center. Further down it also devastated the tiny Morolica, where it not only destroyed the entire hamlet but nearly all its inhabitants died or disappeared.Conchagua (volcano)
Conchagua (also known as Cochague) is a stratovolcano in southeastern El Salvador, overlooking the Gulf of Fonseca. Cerro del Ocote and Cerro de la Bandera are the two main summits, with Bandera appearing younger and more conical (see photo). There are active fumarolic areas on both peaks, but no confirmed historical eruptions. It is surrounded by forest called Bosque Conchagua.Conchagüita
Conchagüita is a volcanic island in Gulf of Fonseca, eastern El Salvador.
In October 1892, an earthquake triggered a large landslide at the volcano, and the resulting dust cloud was first thought to be new volcanic ash. The event was discredited as volcanic eruption by the Smithsonian Institution.Conejo Island
Conejo Island, in Spanish Isla Conejo, meaning "rabbit island", is a disputed island between El Salvador and Honduras located in the Gulf of Fonseca.Cosigüina
Cosigüina (also spelt Cosegüina) is a stratovolcano located in the western part of Nicaragua. It forms a large peninsula extending into the Gulf of Fonseca. The summit is truncated by a large caldera, 2 x 2.4 km in diameter and 500 m deep, holding a substantial crater lake (Laguna Cosigüina). This cone has grown within an earlier caldera, forming a somma volcano. The earlier caldera rim is still exposed on the north side, but has been buried by the younger cone elsewhere.El Tamarindo Airport
El Tamarindo Airport (ICAO: MSET) is an airport serving El Tamarindo, a coastal town in the La Unión Department of El Salvador.
The runway is crossways on a point (Punta de Amapala) at the entrance to the Gulf of Fonseca, and approaches to either end are over the water.Geography of Honduras
Honduras is a country in Central America. Honduras borders the Caribbean Sea and the North Pacific Ocean. Guatemala lies to the west, Nicaragua south east and El Salvador to the south west. Honduras is the second largest Central American republic, with a total area of 112,890 square kilometres (43,590 sq mi).
Honduras has a 700-kilometer (430-mile) Caribbean coastline extending from the mouth of the Río Motagua in the west to the mouth of the Río Coco in the east, at Cape Gracias a Dios. The 922 km (573 mi) southeastern side of the triangle is a land border with Nicaragua. It follows the Río Coco near the Caribbean Sea and then extends southwestward through mountainous terrain to the Gulf of Fonseca on the Pacific Ocean. The southern apex of the triangle is a 153 km (95 mi) coastline on the Gulf Fonseca, which opens onto the Pacific Ocean. In the west there are two land borders: with El Salvador as 342 km long (213 mi) and with Guatemala as 256 km long (159 mi).Greater Republic of Central America
The Greater Republic of Central America was a short-lived political union between Honduras, Nicaragua, and El Salvador, lasting from 1896 to 1898. It was an attempt to revive the failed Federal Republic of Central America from earlier in the century.
The three countries agreed to establish a union with the signing of the Treaty of Amapala on 20 June 1895. On 15 September 1896, after the countries had all ratified the treaty individually, the union was formally confirmed. The republic was rechristened the "United States of Central America" when its constitution came into effect on 1 November 1898.
The capital was to be located at the Honduran town of Amapala on the Gulf of Fonseca. The union was dissolved after General Tomás Regalado seized power in El Salvador on 21 November.
Before its dissolution, the Greater Republic established diplomatic relationships with the United States. Guatemala and Costa Rica both considered joining the union, but neither of them eventually did.Honduras–Nicaragua border
The Honduras–Nicaragua border is the roughly 950 kilometres (590 mi) long international boundary between Honduras and Nicaragua, running from the Gulf of Fonseca on the Pacific Ocean to the Caribbean Sea. The Coco River, which flows generally northeast to the Caribbean, forms more than half of the border.
The border passes between the following departments, from west to east:
Honduras – Choluteca, Colón, Olancho, Gracias a Dios.
Nicaragua – Chinandega, Madriz, Nueva Segovia, Jinotega and North Caribbean Coast Autonomous Region.Honduras and Nicaragua, respectively, were part of the Central American Federation and the United Provinces of Central America. Between 1823 and 1838, these federations fell apart and both nations gained their independence and defined their border.In 1937, the issuance of a stamp from Nicaragua with a sticker on part of Honduran territory indicating "territory in dispute" almost caused a war between the two countries. The territory had been claimed by Nicaragua, but Honduras thought the matter closed in 1906 when an arbitration by King Alfonso XIII of Spain gave it the area.Isla Zacate Grande
Isla Zacate Grande is a stratovolcano in Honduras. The volcano forms a 7 by 10 km (4 by 6 mi) island in the Gulf of Fonseca and has seven satellite cones, including Guegensi Island located 3 km (2 mi) from Zacate Grande.Jorge Varela
Jorge Varela is an environmentalist from Honduras. He received the Goldman Environmental Prize in 1999, for his contribution to marine conservation in the Gulf of Fonseca.List of airports in Honduras
This is a list of airports in Honduras, sorted by location.
Honduras, officially the Republic of Honduras (Spanish: República de Honduras), is a republic in Central America. It was formerly known as Spanish Honduras to differentiate it from British Honduras (now Belize). The country is bordered to the west by Guatemala, to the southwest by El Salvador, to the southeast by Nicaragua, to the south by the Pacific Ocean at the Gulf of Fonseca, and to the north by the Gulf of Honduras, a large inlet of the Caribbean Sea. Its area is just over 112,000 square kilometres (43,000 sq mi) with an estimated population of almost 8 million inhabitants. The nation is currently divided into 18 departments (departamentos). The capital city of Honduras is Tegucigalpa.Meanguera del Golfo
Meanguera del Golfo is a municipality in the La Unión department of El Salvador. Located 30 kilometres (19 mi) from department of La Unión and 213 km (132 mi) from San Salvador on the island of Meanguera in the Gulf of Fonseca. It has an area of 23.6 km2 (9.1 sq mi) with a population of 2,398 inhabitants (2007).
Three countries - Honduras, El Salvador, and Nicaragua - have coastline along the gulf, and all three have been involved in a lengthy dispute over the rights to the gulf and the islands located there within. In 1992, a chamber of the International Court of Justice (ICJ) decided the Land, Island and Maritime Frontier Dispute, of which the gulf dispute was a part. The ICJ determined that El Salvador, Honduras, and Nicaragua were to share control of the Gulf of Fonseca. El Salvador was awarded the islands of Meanguera and Meanguerita, and Honduras was awarded El Tigre Island.Current Mayor: Since 2012-2015 Luis Dheming-AlmendarezOutline of Honduras
The following outline is provided as an overview of and topical guide to Honduras:
Honduras – sovereign country located in Central America. Honduras was formerly known as Spanish Honduras to differentiate it from British Honduras (now Belize). The country is bordered to the west by Guatemala, to the southwest by El Salvador, to the southeast by Nicaragua, to the south by the Pacific Ocean at the Gulf of Fonseca, and to the north by the Gulf of Honduras, a large inlet of the Caribbean Sea.Territorial disputes of Nicaragua
Territorial disputes of Nicaragua include the territorial dispute with Colombia over the Archipelago de San Andres y Providencia and Quita Sueno Bank. Nicaragua also has a maritime boundary dispute with Honduras in the Caribbean Sea and a boundary dispute over the Rio San Juan with Costa Rica.Tiger Island
El Tigre is an island located in the Gulf of Fonseca, a body of water on the Pacific coast of Central America. The island is a conical basaltic stratovolcano and the southernmost volcano in Honduras. It belongs to Valle department. Together with Isla Zacate Grande, Isla Comandante and a few tiny satellite islets and rocks, it forms the municipality of Amapala, with an area of 75.2 km2 (29.0 sq mi) and a population of 9,687 as of the census of 2001 (of which 4 were living on Isla Comandante).
Three countries, Honduras, El Salvador, and Nicaragua, have a coastline along the Gulf of Fonseca, and all three have been involved in a lengthy dispute over the rights to the gulf and the islands located therewithin. In 1992, a chamber of the International Court of Justice (ICJ) decided the Land, Island and Maritime Frontier Dispute, of which the gulf dispute was a part. The ICJ determined that El Salvador, Honduras, and Nicaragua were to share control of the Gulf of Fonseca. El Salvador was awarded the islands of Meanguera and Meanguerita, and Honduras was awarded the island of El Tigre.Valle Department
Valle is one of the 18 departments into which Honduras is divided.
The departmental capital is Nacaome. The department faces the Gulf of Fonseca and contains mangrove swamps; inland, it is very hot and dry.
The department covers a total surface area of 1,665 km² and, in 2015, had an estimated population of 178,561 people.
Valle Department was organized in 1893.<|endoftext|>
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History of Grenada
The recorded history of the Caribbean island of Grenada begins in the early 17th century. First settled by indigenous peoples, by the time of European contact it was inhabited by the Caribs. French colonists drove most of the Caribs off the island and established plantations on the island, eventually importing African slaves to work on the sugar plantations.
Control of the island was disputed by Great Britain and France in the 18th century, with the British ultimately prevailing. In 1795, Fédon's Rebellion, inspired by the Haitian Revolution, very nearly succeeded, and was crushed with significant military intervention. Slavery was abolished in the 1830s. In 1885, the island became the capital of the British Windward Islands.
Grenada achieved independence from Britain in 1974. Following a leftist coup in 1983, the island was invaded by U. S. troops and a democratic government was reinstated. The island's major crop, nutmeg, was significantly damaged by Hurricane Ivan in 2004.
About 2 million years ago, Grenada was formed as an underwater volcano. Before the arrival of Europeans, Grenada was inhabited by Caribs who had driven the more peaceful Arawaks from the island. Christopher Columbus sighted Grenada in 1498 during his third voyage to the new world. He named the island "Concepción." The origin of the name "Grenada" is obscure, but it is likely that Spanish sailors renamed the island for the city of Granada. By the beginning of the 18th century, the name "Grenada", or "la Grenade" in French, was in common use. Partly because of the Caribs, Grenada remained uncolonized for more than one hundred years after its discovery.
English attempted settlement
In June 1609, the first attempt at settlement by Europeans was made by an English expedition of 24 adventurers led by Mossis Goldfry, Hall, Lull, and Robincon, who arrived in the ships Diana, the Penelope, and the Endeavour. The settlement was attacked and destroyed by the indigenous islanders and many killed and tortured. The few survivors were evacuated when the ships returned on 15 December 1609.
French settlement and conquest
On 17 March 1649, a French expedition of 203 men from Martinique, led by Jacques Dyel du Parquet who had been the Governor of Martinique on behalf of the Compagnie des Iles de l'Amerique (Company of the Isles of America) since 1637, landed at St. Georges Harbour and constructed a fortified settlement, which they named Fort Annunciation. A treaty was swiftly agreed between du Parquet and the indigenous Chief Kairouane to peacefully partition the island between the two communities. Du Parquet returned to Martinique leaving his cousin Jean Le Comte as Governor of Grenada. Conflict broke out between the French and the indigenous islanders in November 1649 and fighting lasted for five years until 1654, when the last opposition to the French on Grenada was crushed. Rather than surrender, Kairouane and his followers chose to throw themselves off a cliff, a fact celebrated in the poetry of Jan Carew. The island continued for some time after to suffer raids by war canoe parties from St. Vincent, whose inhabitants had aided the local Grenadian islanders in their struggle and continued to oppose the French.
On 27th Sep 1650, du Parquet bought Grenada, Martinique, and St. Lucia from the Compagnie des Iles de l'Amerique, which was dissolved, for the equivalent of £1160. In 1657 du Parquet sold Grenada to the Comte de Cerrillac for the equivalent of £1890. In 1664, King Louis XIV bought out the independent island owners and established the French West India Company. In 1674 the French West India Company was dissolved. Proprietary rule ended in Grenada, which became a French colony as a dependency of Martinique. In 1675, Dutch privateers captured Grenada, but a French man-of-war arrived unexpectedly and recaptured the island.
In 1700, Grenada had a population of 257 whites, 53 coloureds, and 525 slaves. There were 3 sugar estates, 52 indigo plantations, 64 horses, and 569 head of cattle. Between 1705 and 1710 the French built Fort Royal at St. George's which is now known as Fort George. The collapse of the sugar estates and the introduction of cocoa and coffee in 1714 encouraged the development of smaller land holdings, and the island developed a land-owning yeoman farmer class. In 1738 the first hospital was constructed.
Grenada was captured by the British during the Seven Years' War on 4 March 1762 by Commodore Swanton without a shot being fired. Grenada was formally ceded to Britain by the Treaty of Paris on 10 February 1763. In 1766 the island was rocked by a severe earthquake. In 1767 a slave uprising was put down. In 1771 and again in 1775 the town of St. George, which was constructed solely of wood, was burnt to the ground - after which it was sensibly rebuilt using stone and brick. France recaptured Grenada between 2–4 July 1779 during the American War of Independence, after Comte d'Estaing stormed Hospital Hill. A British relief force was defeated in the naval Battle of Grenada on 6 July 1779. However the island was restored to Britain with the Treaty of Versailles four years later on 3 September 1783. In 1784 the first newspaper, the Grenada Chronicle, began publication.
Julien Fédon, a mixed race owner of the Belvedere estate in the St. John Parish, launched a rebellion against British rule on the night of 2 March 1795, with coordinated attacks on the towns of Grenville, La Baye and Gouyave. Fédon was clearly influenced by the ideas emerging from the French Revolution, especially the Convention's abolition of slavery in 1794: he stated that he intended to make Grenada a "Black Republic just like Haiti". Fédon and his troops controlled all of Grenada except the parish of St George's, the seat of government, between March 1795 and June 1796. During those insurgent months 14,000 of Grenada's 28,000 slaves joined the revolutionary forces in order to write their own emancipation and transform themselves into "citizens"; some 7,000 of these self-liberated slaves would perish in the name of freedom. The British defeated Fédon's forces in late 1796, but they never caught Fédon himself, and his fate is unknown.
Early 19th century
In 1833, Grenada became part of the British Windward Islands Administration and remained so until 1958. Slavery was abolished in 1834. Nutmeg was introduced in 1843, when a merchant ship called in on its way to England from the East Indies.
Late 19th century
In 1857, the first East Indian immigrants arrived. In 1871 Grenada was connected to the telegraph. In 1872 the first secondary school was built. On 3 December 1877 the pure Crown colony model replaced Grenada's old representative system of government. On 3 December 1882, the largest wooden jetty ever built in Grenada was opened in Gouyave. In 1885, after Barbados left the British Windward Islands, the capital of the colonial confederation was moved from Bridgetown to St. George on Grenada. From 1889-1894 the 340 foot Sendall Tunnel was built for horse carriages.
Last colonial years 1900–1974
Early 20th century
The 1901 census showed that the population of the colony was 63,438. In 1917 Theophilus A. Marryshow founded the Representative Government Association (RGA) to agitate for a new and participative constitutional dispensation for the Grenadian people. Partly as a result of Marryshow's lobbying the Wood Commission of 1921-1922 concluded that Grenada was ready for constitutional reform in the form of a 'modified' Crown Colony government. This modification granted Grenadians from 1925 the right to elect 5 of the 15 members of the Legislative Council, on a restricted property franchise enabling the wealthiest 4% of Grenadian adults to vote. In 1928 electricity was installed in St. George's. In 1943 Pearls Airport was opened. On 5 August 1944 the Island Queen schooner disappeared with the loss of all 56 passengers and 11 crew.
In 1950, Grenada had its constitution amended to increase the number of elected seats on the Legislative Council from 5 to 8, to be elected by full adult franchise at the 1951 election. In 1950 Eric Gairy founded the Grenada United Labour Party, initially as a trades union, which led the 1951 general strike for better working conditions. This sparked great unrest - so many buildings were set ablaze that the disturbances became known as the 'red sky' days - and the British authorities had to call in military reinforcements to help regain control of the situation. On 10 October 1951 Grenada held its first general elections on the basis of universal adult suffrage. United Labour won 6 of the 8 elected seats on the Legislative Council in both the 1951 and 1954 elections. However the Legislative Council had few powers at this time, with government remaining fully in the hands of the colonial authorities.
On 22 September 1955, Hurricane Janet hit Grenada, killing 500 people and destroying 75% of the nutmeg trees. A new political party, the Grenada National Party led by Herbert Blaize, contested the 1957 general election and with the cooperation of elected independent members took control of the Legislative Council from the Grenada United Labour Party. In 1958, the Windward Islands Administration was dissolved, and Grenada joined the Federation of the West Indies.
In 1960, another constitutional evolution established the post of Chief Minister, making the leader of the majority party in the Legislative Council, which at that time was Herbert Blaize, effective head of government. In March 1961 the Grenada United Labour Party won the general election and George E.D. Clyne became chief minister until Eric Gairy was elected in a by-election and took the role in August 1961. Also in 1961 the cruise liner MV Bianca C (2) sank off Point Salines, although thankfully there was only a single fatality. In April 1962 Grenada's Administrator, the Queens representative on the island, James Lloyd suspended the constitution, dissolved the Legislative Council, and removed Eric Gairy as Chief Minister, following allegations concerning the Gairy's financial impropriety. At the 1962 general election the Grenada National Party won a majority and Herbert Blaize became Chief Minister for the second time.
After the Federation of the West Indies collapsed in 1962, the British government tried to form a small federation out of its remaining dependencies in the Eastern Caribbean. Following the failure of this second effort, the British and the islanders developed the concept of "associated statehood". Under the Associated Statehood Act on 3 March 1967 Grenada was granted full autonomy over its internal affairs. Herbert Blaize was the first Premier of the Associated State of Grenada from March to August 1967. Eric Gairy served as Premier from August 1967 until February 1974, as the Grenada United Labour Party won majorities in both the 1967 and 1972 general elections.
Independence, Revolution and US invasion: 1974–1983
On 7 February 1974, Grenada became a fully independent state. Grenada continued to practise a modified Westminster parliamentary system based on the British model with a governor general appointed by and representing the British monarch (head of state) and a prime minister who is both leader of the majority party and the head of government. Eric Gairy was independent Grenada's first prime minister serving from 1974 until his overthrow in 1979. Gairy won re-election in Grenada's first general election as an independent state in 1976; however, the opposition New Jewel Movement refused to recognize the result, claiming the poll was fraudulent, and so began working towards the overthrow of the Gairy regime by revolutionary means. In 1976 St. George's University was established.
The 1979 coup and revolutionary government
On March 13, 1979, the New Jewel Movement launched an armed revolution which removed Gairy, suspended the constitution, and established a People's Revolutionary Government (PRG), headed by Maurice Bishop who declared himself prime minister. His Marxist-Leninist government established close ties with Cuba, Nicaragua, and other communist bloc countries. All political parties except for the New Jewel Movement were banned and no elections were held during the four years of PRG rule.
The 1983 coups
On 14 October 1983, a power struggle within the government resulted in the house arrest of Bishop at the order of his Deputy Prime Minister, Bernard Coard who became Head of Government. This coup resulted in demonstrations in various parts of the island which eventually led to Bishop being freed from arrest briefly, before being recaptured by the army and executed along with seven others, including members of the cabinet on 19 October 1983.
On 19 October 1983, the military under Hudson Austin took power in a second coup and formed a military government to run the country. A four-day total curfew was declared under which any civilian outside their home was subject to summary execution.
A U.S.–Caribbean force invaded Grenada on October 25, 1983, in an action called Operation Urgent Fury, and swiftly defeated the Grenadan forces and their Cuban allies. During the fighting 45 Grenadians, 25 Cubans, and 19 Americans were killed. This action was taken in response to an appeal obtained from the governor general and to a request for assistance from the Organization of Eastern Caribbean States, without consulting the island's head of state, Queen Elizabeth II, Commonwealth institutions or other usual diplomatic channels (as had been done in Anguilla). Furthermore, United States government military strategists feared that Soviet use of the island would enable the Soviet Union to project tactical power over the entire Caribbean region. U.S. citizens were evacuated, and constitutional government was resumed.
Seventeen members of the PRG and the PRA were convicted by a court. Fourteen were sentenced to death for actions related to the overthrow of the Bishop government and the murder of several people including Maurice Bishop. The sentences were eventually commuted to life imprisonment after an international campaign. Another three were sentenced to forty five years in prison. These seventeen have become known as the Grenada 17, and are the subject of an ongoing international campaign for their release. In October 2003 Amnesty International issued a report which stated that their trial had been a miscarriage of justice. The seventeen have protested their sentences consistently since 1983. The United States gave $48.4 million in economic assistance to Grenada in 1984.
Democracy restored: 1983 to present day
Post liberation politics
When US troops withdrew from Grenada in December 1983, Nicholas Braithwaite was appointed Prime Minister of an interim administration by the Governor General Sir Paul Scoon until elections could be organized.
On 28 October 1984, the new Point Salines International Airport was opened, which enabled Grenada to receive large commercial jets for the first time.
The first democratic elections since 1976 were held in December 1984 and were won by the Grenada National Party under Herbert Blaize who won 14 out of 15 seats in elections and served as Prime Minister until his death in December 1989. The NNP continued in power until 1989 but with a reduced majority. Five NNP parliamentary members, including two cabinet ministers, left the party in 1986–87 and formed the National Democratic Congress (NDC) which became the official opposition. In August 1989, Prime Minister Blaize broke with the GNP to form another new party, The National Party (TNP), from the ranks of the NNP. This split in the NNP resulted in the formation of a minority government until constitutionally scheduled elections in March 1990. Prime Minister Blaize died in December 1989 and was succeeded as prime minister by Ben Jones until after the 1990 elections.
The National Democratic Congress emerged from the 1990 elections as the strongest party, winning 7 of the fifteen available seats. Nicholas Brathwaite added 2 TNP members and 1 member of the Grenada United Labor Party (GULP) to create a 10-seat majority coalition. The governor general appointed him to be prime minister for a second time. Braithwaite resigned in Feb 1995 and was succeeded as Prime Minister by George Brizan who served until the Jun 1995 election.
In parliamentary elections on 20 June 1995, the NNP won 8 of the 15 seats and formed a government headed by Keith Mitchell. The NNP maintained and affirmed its hold on power when it took all 15 parliamentary seats in the January 1999 elections. Mitchell went on to win the 2003 elections with a reduced majority of 8 of the 15 seats and served as Prime Minister for a record 13 years until his defeat in 2008.
The 2001 census showed that the population of Grenada was 100,895.
In 2009, Point Salines International Airport was renamed Maurice Bishop International Airport in tribute to the former Prime Minister.
Truth and reconciliation commission
In 2000–02, much of the controversy of the late 1970s and early 1980s was once again brought into the public consciousness with the opening of the truth and reconciliation commission. The commission was chaired by a Catholic priest, Father Mark Haynes, and was tasked with uncovering injustices arising from the PRA, Bishop's regime, and before. It held a number of hearings around the country. The commission was formed because of a school project. Brother Robert Fanovich, head of Presentation Brothers' College (PBC) in St. George's tasked some of his senior students with conducting a research project into the era and specifically into the fact that Maurice Bishop's body was never discovered. Their project attracted a great deal of attention, including from the Miami Herald and the final report was published in a book written by the boys called Big Sky, Little Bullet. It also uncovered that there was still a lot of resentment in Grenadian society resulting from the era, and a feeling that there were many injustices still unaddressed. The commission began shortly after the boys concluded their project.
On September 7, 2004, Grenada was hit directly by category four Hurricane Ivan. The hurricane destroyed about 85% of the structures on the island, including the prison and the prime minister's residence, killed thirty-nine people, and destroyed most of the nutmeg crop, Grenada's economic mainstay. Grenada's economy was set back several years by Hurricane Ivan's impact. Hurricane Emily ravaged the island's north end in June 2005.
- British colonization of the Americas
- French colonization of the Americas
- History of the Americas
- History of the British West Indies
- History of the Caribbean
- History of North America
- List of Governors of the British Windward Islands
- List of heads of government of Grenada
- Politics of Grenada
- Spanish colonization of the Americas
- West Indies Federation
- Steele, pp. 35–36
- Steele, page 38
- Steele, page 39
- Steele, page 40
- Return to Streets of Eternity, Carew, Smokestack Books, 2015
- Steele, p. 44
- Steele, page 52
- Steele, page 54
- Steele, page 55
- Steele, p. 59
- Archived October 22, 2014, at the Wayback Machine.
- "About Grenada: Historical Events". GOV.gd. 2013-05-07. Retrieved 2015-03-16.
- Steele, p. 72
- "The Fedon Rebellion". BigDrumNation.org. Retrieved 2015-03-16.
- "Grenada Restaurant | Local Restaurants & Dining Guide Reviews". Travelgrenada.com. Retrieved 2015-03-16.
- "From Old Representative System to Crown Colony". Bigdrumnation.org. 2008-07-01. Retrieved 2015-03-16.
- "1951 and Coming of General Elections". BigDrumNation.org. Retrieved 2015-03-16.
- "New Grenada prime minister vows to boost economy, lower cost of living". Associated Press via International Herald Tribune. July 9, 2008. Archived from the original on 2008-08-04. Retrieved 2011-07-31.
- Grenade, Wendy C. ed. The Grenada Revolution: Reflections and Lessons (University Press of Mississippi; 2015) 320 pages; $political history of the 1970s and 1980s
- Kurlansky, Mark. 1992. A Continent of Islands: Searching for the Caribbean Destiny. Addison-Wesley Publishing. ISBN 0-201-52396-5.
- Steele, Beverley A. (2003). Grenada. A History of its People. Macmillan. ISBN 0-201-52396-5.
- Background Note: Grenada
- History of the Invasion of Grenada from the Dean Peter Krogh Foreign Affairs Digital Archives<|endoftext|>
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Celebrating Black History Month and the Pivotal Role of African-Americans in the Making of America
In 1924, Jim Crow laws were still enforced in many parts of the United States and the Ku Klux Klan was experiencing resurgence. Martin Luther King Jr. had not yet been born, and the Civil Rights Act would not be enacted for another 40 years. Nonetheless, it was the year in which the Knights of Columbus commissioned and published a landmark history of black Americans: The Gift of Black Folk: The Negroes in the Making of America, by civil rights pioneer W.E.B. Du Bois.
The Gift of Black Folk, which received critical acclaim, presented the contributions of black Americans from the earliest colonial settlements through World War I and the early 1920s. It was recently republished by the Knights of Columbus. The new edition features an introduction by Carl A. Anderson, who, prior to becoming Supreme Knight of the Knights of Columbus, spent nearly a decade working on issues of racial equality as a member of the U.S. Commission on Civil Rights.
“A hundred years after W.E.B. Du Bois helped cofound the NAACP, the United States can view its civil rights achievements with pride,” Anderson wrote in the introduction. “African-Americans have served on the Supreme Court, in the Cabinet, and, finally, as President of the United States. The Gift of Black Folk allows us to fully appreciate these monumental achievements. It is our belief that Du Bois’ classic work will continue to inform and inspire for many generations to come.”
The book is available through KnightsGear.
Three years earlier, against the same backdrop of widespread bigotry, the Order established the Knights of Columbus Historical Commission to combat the revisionist history of the time, which tended to exclude minority groups from the record of historical achievement. The project was overseen by Edward McSweeney, who served as assistant U.S. Commissioner of Immigration at Ellis Island from 1893-1902.
As early as the 1890s African-Americans were members, and officers, of the Knights of Columbus. In 1895 - just 13 years after the Order's founding - the Philip Sheridan Council was formed in Southboro, MA; Samuel Williams, an African-American, was one of the four organizers of the council and became the council's first Chancellor. A year later, Williams also assumed a special role at the Massachusetts State Convention as one of the concluding speakers, along with the State Chaplain.<|endoftext|>
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The complement system is part of your body’s immune system.
It consists of a group of proteins circulating in the body working to protect you from threats like bacteria and viruses.
There are 3 distinct parts (pathways) of the complement system, known as the classical, lectin, and alternative pathways, each with their own roles and responsibilities.
The classical or lectin pathways are turned "on" or "off," as needed. They help the body fight a threat like an infection, either directly, or by recruiting other parts of the immune system.
By contrast, the alternative pathway is always on and helping to deal with potential threats, but the body controls it to keep it running at a healthy level. Loss of control and overactivity of the alternative pathway can damage healthy cells in your body.
This is believed to be the key problem in patients with C3G.
It is important to know how the complement system may be impacting your kidneys and overall health.<|endoftext|>
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Find the area of the shaded region in the following diagram
Last updated date: 17th Jun 2024
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Hint: Formula for area of intersection of two circle is $A=r_{1}^{2}{{\cos }^{-1}}\left( \dfrac{{{d}_{1}}}{{{r}_{1}}} \right)-{{d}_{1}}\sqrt{r_{1}^{2}-d_{1}^{2}}+r_{2}^{2}{{\cos }^{-1}}\left( \dfrac{{{d}_{2}}}{{{r}_{2}}} \right)+{{d}_{2}}\sqrt{r_{2}^{2}-d_{2}^{2}}$
Here ${{r}_{1}}$ and ${{r}_{2}}$ are the radius of the first and second circle.
And ${{d}_{1}}$ , ${{d}_{2}}$ are the distance of radius from the line that pass-through intersection of two circles.
In the above diagram there are two semicircles and the semicircles are inside a rectangle.
So, we have two similar semicircles. The radius of the semi-circle is 2 centimetres. Hence here ${{r}_{1}}=2$ and ${{r}_{2}}=2$. As the distance from the line intersecting two circles is one centimetre that is ${{d}_{1}}={{d}_{2}}=1$.
Now using it in the formula for area
$A=r_{1}^{2}{{\cos }^{-1}}\left( \dfrac{{{d}_{1}}}{{{r}_{1}}} \right)-{{d}_{1}}\sqrt{r_{1}^{2}-d_{1}^{2}}+r_{2}^{2}{{\cos }^{-1}}\left( \dfrac{{{d}_{2}}}{{{r}_{2}}} \right)+{{d}_{2}}\sqrt{r_{2}^{2}-d_{2}^{2}}$
$\Rightarrow A={{2}^{2}}{{\cos }^{-1}}\left( \dfrac{1}{2} \right)-1\sqrt{{{2}^{2}}-{{1}^{2}}}+{{2}^{2}}{{\cos }^{-1}}\left( \dfrac{1}{2} \right)+1\sqrt{{{2}^{2}}-{{1}^{2}}}$
$A=4{{\cos }^{-1}}\left( \dfrac{1}{2} \right)-\sqrt{3}+4{{\cos }^{-1}}\left( \dfrac{1}{2} \right)+\sqrt{3}$
As we know ${{\cos }^{-1}}\left( \dfrac{1}{2} \right)$is $\dfrac{\pi }{3}$ using this in the equation
$\Rightarrow A=4\dfrac{\pi }{3}-\sqrt{3}+4\dfrac{\pi }{3}+\sqrt{3}=8\dfrac{\pi }{3}-0\sqrt{3}$
Hence, the area of the shaded region is $\left( 8\dfrac{\pi }{3} \right)c{{m}^{2}}$.
Note: Consider the following diagram
Here we have two circle with centre ${{c}_{1}}$ and ${{c}_{2}}$ and radius ${{r}_{1}}$ and ${{r}_{2}}$ and ${{d}_{1}}$ and ${{d}_{2}}$ are distance from the line that pass through intersection point of two circle .
And the formula for the area is
$A=r_{1}^{2}{{\cos }^{-1}}\left( \dfrac{{{d}_{1}}}{{{r}_{1}}} \right)-{{d}_{1}}\sqrt{r_{1}^{2}-d_{1}^{2}}+r_{2}^{2}{{\cos }^{-1}}\left( \dfrac{{{d}_{2}}}{{{r}_{2}}} \right)+{{d}_{2}}\sqrt{r_{2}^{2}-d_{2}^{2}}$
This formula can be used to find the intersecting area of any two circles.<|endoftext|>
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# Understanding What is 12 Percent – Simple Guide
Percentages are a fundamental concept in mathematics and everyday life. Many of us come across percentages regularly, whether it’s calculating discounts while shopping or understanding the proportion of a certain quantity in relation to a whole. In this guide, we’ll explore the concept of percentages, specifically focusing on what is 12 percent and how it is calculated.
When we say 12 percent, we are referring to twelve out of every hundred. It is a way of expressing a fraction or decimal as a proportion of a hundred. To convert a decimal to a percentage, you simply multiply it by 100. For example, to convert the decimal 0.12 to a percentage, we multiply it by 100, resulting in 12 percent. Similarly, to convert a fraction to a percentage, divide the numerator by the denominator and then multiply by 100.
In our daily lives, we encounter different scenarios where percentages play a significant role. Whether it’s analyzing data, calculating interest rates, or understanding proportions, having a solid understanding of percentages is essential. In the following sections, we will dive deeper into percentage calculations, converting between decimals and percentages, and solving percentage problems.
### Key Takeaways:
• Percentages represent parts of a whole and are expressed as a proportion out of 100.
• To convert a decimal to a percentage, multiply it by 100.
• To convert a fraction to a percentage, divide the numerator by the denominator and multiply by 100.
• Understanding percentages is crucial for various calculations and real-life applications.
## What is Percentage?
The word percentage is derived from “percent,” which means “per hundred.” Percentages are a way of representing parts of a whole based on a hundred units. For example, if you have 87 percent, it means you have 87 per 100. Percentages can be understood as fractions or decimals, and they are used to describe the proportion of a specific quantity in relation to the total. Whether you’re talking about students in a class or dollars in your bank account, percentages help us understand the distribution and representation of different parts.
Percentages are often used to compare and analyze data, providing a clear understanding of the relative size or value of different components. They allow us to break down a whole into meaningful parts and make it easier to comprehend numerical relationships. From calculating discounts during a sale to determining tax amounts, percentages play a crucial role in everyday life. Understanding the concept of percentage is essential for making informed decisions and interpreting statistical information accurately.
### Examples of using percentages:
1. The physician’s assistant recommends that patients follow a diet consisting of 30% protein, 40% carbohydrates, and 30% fats.
2. A sales report shows that Lisa achieved a 25% increase in sales compared to the previous quarter.
3. The pie chart represents the distribution of households in a neighborhood, with 45% being rented and 55% being owned.
Percentages can be converted to fractions and decimals to express relationships more precisely. By using percentages, we can effectively communicate proportions, allocations, and growth rates in a standardized format that is easily understood.
## Percentage Formula
The percentage formula is an essential tool for calculating the percentage of a specific value in relation to a total value. By using this formula, you can easily determine the proportion or share of a particular quantity in terms of 100. The formula itself is quite simple: divide the value by the total value and then multiply the result by 100.
This formula can be expressed as:
Percentage = (Value/Total Value) x 100
Let’s say you have a situation where there are 10 dogs out of a total of 40 animals. To find the percentage of dogs, you would use the percentage formula:
Percentage of dogs = (10/40) x 100 = 25%
The result shows that 25% of the animals in this scenario are dogs. This formula is applicable in various situations. For example, you can use it to calculate the percentage of sales, taxes, or any other value in relation to a total value.
To better understand the concept, here’s an example:
Value Total Value Percentage
500 1000 50%
75 150 50%
30 60 50%
As shown in the table above, regardless of the specific values, the percentage formula remains consistent. It is a reliable method for accurately determining the percentage of a value in relation to a total value.
This formula provides a straightforward and efficient way to calculate percentages, allowing you to analyze and interpret data effectively in a variety of contexts.
## Converting Decimals and Fractions to Percentages
Converting decimals and fractions to percentages is a simple process that allows you to express numbers in different forms and make calculations involving percentages. Let’s take a look at how to convert decimals and fractions to percentages.
### Converting Decimals to Percentages
To convert a decimal to a percentage, you multiply it by 100. For example, to convert the decimal 0.87 to a percentage:
0.87 x 100 = 87%
So, 0.87 is equivalent to 87 percent.
Percentages are often represented using the % symbol. In the case of our example, 0.87 can be written as 87%.
### Converting Fractions to Percentages
Converting fractions to percentages involves two steps. First, divide the numerator by the denominator. Then, multiply the result by 100. Let’s convert the fraction 13/100 to a percentage:
(13 ÷ 100) x 100 = 13%
Therefore, 13/100 is equal to 13 percent.
Converting fractions to percentages is particularly useful in situations where you want to express a fraction as a proportion of 100.
### Example Conversion Table
Here’s a conversion table that can help you convert common decimals and fractions to percentages:
Decimal Percentage
0.1 10%
0.25 25%
0.5 50%
0.75 75%
1 100%
1.5 150%
2 200%
This table provides a quick reference for converting common decimals to percentages.
By converting decimals and fractions to percentages, you can express numbers in a different form and easily incorporate percentages into your calculations. Understanding this conversion allows for clearer communication and simplified mathematical operations.
## Calculating Percentages of a Specific Number
Calculating the percentage of a specific number is a reverse process of finding a percentage. First, convert the percentage to a decimal by dividing it by 100. Then, multiply the decimal by the specific number to determine the percentage value.
To illustrate, let’s say you need to find 40 percent of a paycheck that is \$750.
“The percentage formula allows you to find the share of a whole in terms of 100.”
To begin, convert 40 percent to decimal form by dividing it by 100: 40/100 = 0.40.
Next, multiply the decimal by the specific number, which in this case is \$750: 0.40 × 750 = \$300.
Therefore, 40 percent of a \$750 paycheck is \$300.
Percentage Specific Number Calculated Value
40% \$750 \$300
Visualizing the concept of percentages greater than 100 percent can help in understanding their magnitude and impact. It showcases the scale of growth or increase beyond the original value and enables a better grasp of the significance of such percentages.
### Example: Sales Growth
Let’s consider an example to further illustrate the concept of percentages greater than 100 percent. Imagine a small retail store that had sales of \$10,000 in the previous year. This year, they experienced significant growth and generated \$25,000 in sales. To calculate the percentage increase, we can use the following formula:
Percent Increase = ((New Value – Old Value) / Old Value) x 100
By substituting the values into the formula, we get:
Percent Increase = ((\$25,000 – \$10,000) / \$10,000) x 100 = 150%
Thus, the sales growth of the retail store is 150 percent, indicating a significant improvement and an increase of 150 percent compared to the previous year’s sales.
Percentages greater than 100 percent are powerful indicators of progress, growth, and remarkable achievements. They highlight the magnitude of improvement, expansion, or multiples beyond the initial measurement, and can serve as motivating benchmarks for individuals and businesses striving for exceptional results.
## Solving Percent Problems
Solving percent problems requires a strong understanding of the relationship between percentages and fractions. By connecting these concepts, you can utilize simple techniques to solve a wide range of percent problems. Recognizing patterns and employing problem-solving strategies can greatly simplify calculations and make them easier to tackle.
Let’s explore some problem-solving techniques for working with percentages and fractions:
### 1. Converting Percentages to Fractions
Converting percentages to fractions is a useful skill when solving percent problems. To convert a percentage to a fraction, divide the percentage by 100 and simplify the resulting fraction, if possible. Here’s an example:
“Convert 25% to a fraction.”
To convert 25% to a fraction, divide 25 by 100:
25 ÷ 100 = 1/4
Therefore, 25% can be represented as the fraction 1/4.
### 2. Converting Fractions to Percentages
Converting fractions to percentages is another essential technique. To convert a fraction to a percentage, divide the numerator by the denominator, then multiply by 100. Let’s look at an example:
“Convert 3/5 to a percentage.”
To convert 3/5 to a percentage, divide 3 by 5 and multiply by 100:
(3 ÷ 5) × 100 = 60%
Therefore, 3/5 is equivalent to 60%.
### 3. Finding a Percentage of a Number
When you need to find a specific percentage of a number, you can use a quick mental calculation technique. Here are a few examples:
“What is 35% of 80?”
To find 35% of 80, multiply 80 by 35% (or 0.35):
80 × 0.35 = 28
Therefore, 35% of 80 is 28.
“What is 75% of 120?”
To find 75% of 120, multiply 120 by 75% (or 0.75):
120 × 0.75 = 90
Therefore, 75% of 120 is 90.
### 4. Solving Percent Increase and Decrease Problems
Percent increase and decrease problems involve finding the final value after a percentage change. The formula for calculating percent increase or decrease is:
Final Value = Initial Value +/- (Percentage Change × Initial Value)
Here’s an example:
“If the original price of a product was \$50 and it increased by 20%, what is the final price?”
To find the final price, first calculate the increase:
(20% × \$50) = \$10
Next, add the increase to the initial price:
\$50 + \$10 = \$60
Therefore, the final price is \$60.
### 5. Using Proportions to Solve Percent Problems
In some cases, using proportions can be an effective approach to solving percent problems. Here’s an example:
“If a car travels 180 miles on 9 gallons of gas, how far can it travel on 15 gallons? Assume gas mileage remains constant.”
To solve this problem, set up a proportion:
Miles Gallons
180 9
x 15
Next, cross-multiply and solve for x:
180 × 15 = 9 × x
2700 = 9x
x = 2700/9
x = 300
Therefore, the car can travel 300 miles on 15 gallons of gas.
Solving percent problems involves understanding the relationships between percentages, fractions, and various problem-solving techniques. By applying these strategies, you can confidently solve a wide range of percent problems and enhance your mathematical skills.
## Quick Guide to Percentages and Decimals
A quick guide to percentages and decimals can simplify calculations and conversions. Understanding the relationship between percentages and decimals enables efficient calculations and accurate representations of numerical values.
### Percentages
Percentages are a way to express parts of a whole. They are represented by the % symbol and are often used to describe proportions or ratios.
Percentages represent a certain number out of 100. For example, 50 percent is the same as saying 50 out of 100, or 1/2.
To convert a percentage to a decimal, divide it by 100. For instance, 25% is equal to 0.25 when written as a decimal.
### Decimals
Decimals are numerical representations of fractions or parts of a whole. They are used in mathematical calculations.
Decimals can be converted to percentages by multiplying them by 100. For example, 0.75 is equal to 75% when expressed as a percentage.
When working with decimals, rounding to a certain accuracy or number of decimal places can be useful for practical purposes.
### Rounding Decimals
Rounding decimals allows for simpler and more concise representation of values. When rounding decimals, look at the digit to the right of the desired place value.
If the digit is 5 or greater, round up. If the digit is less than 5, round down.
Rounding decimals is especially useful when dealing with measurements, currency, or any other context where precision is important.
Here is an example of rounding decimals:
Original Decimal Rounded Decimal
2.345 2.35
5.674 5.67
8.912 8.91
Understanding percentages and decimals allows for accurate calculations and clear representation of numerical values. Whether you are converting between percentages and decimals, rounding decimals, or performing other calculations, this quick guide provides a solid foundation for working with percentages and decimals effectively.
## Visualizing Percentages
Understanding percentages can be easier when they are visually represented. One effective way to visualize percentages is by using a percentage grid. The grid consists of 100 cells, where each cell represents 1 percent of the whole. This grid allows you to have a clear visual representation of proportions and calculations related to percentages.
To illustrate, imagine shading a certain number of cells on the grid. Each shaded cell represents a specific percentage of the whole. By visually representing percentages in this way, you can easily grasp the relationship between different parts and wholes and understand how percentages are applied in various contexts. It provides a tangible and intuitive way to perceive the concept of percentages.
Visualizing percentages through a percentage grid is a valuable tool for students, professionals, and anyone working with data analysis or financial calculations. It helps in developing a solid understanding of percentages and enhances problem-solving skills related to percentages. Using visual representations allows for a more engaging and comprehensive learning experience, making the concept of percentages easier to grasp.
## FAQ
### What is 12 percent?
12 percent is a way of expressing a fraction or portion of a whole, where 12 represents 12 out of 100. It is equivalent to saying 12 per 100 or 0.12 as a decimal.
### How do I calculate a percentage?
To calculate a percentage, you can use the following formula: Percentage = (Value/Total Value) x 100. Divide the value by the total value, multiply the result by 100, and you will get the percentage.
### How do I convert a decimal to a percent?
To convert a decimal to a percent, you can multiply the decimal by 100. For example, 0.87 multiplied by 100 equals 87 percent.
### How do I convert a fraction to a percent?
To convert a fraction to a percent, divide the numerator by the denominator and then multiply by 100. For example, 13/100 divided by 100 equals 0.13, which is 13 percent.
### How do I calculate the percentage of a specific number?
To calculate the percentage of a specific number, convert the percentage to a decimal (by dividing it by 100) and then multiply the decimal by the specific number. For example, to find 40 percent of a paycheck that is \$750, you would convert 40 percent to the decimal 0.40. Then, multiply 0.40 by \$750 to get \$300, which represents 40 percent of the paycheck.
### Can percentages be greater than 100 percent?
Yes, percentages can be greater than 100 percent. Percentages greater than 100 percent indicate an increase or multiple of the original value. For example, if you sell ten hot dogs in the morning and thirty hot dogs in the afternoon, the number of hot dogs sold in the afternoon is 300 percent of the number sold in the morning, or three times as many.
### How can I solve percent problems?
Percent problems can often be solved by understanding the relationship between percentages and fractions. By recognizing patterns, such as converting between percentages and fractions, you can simplify calculations and problem-solving techniques.
### What is a quick guide to percentages and decimals?
A quick guide to percentages and decimals involves understanding that percentages are represented by the % symbol and can describe parts of a whole, while decimals are numerical representations of fractions or parts of a whole. Conversions between percentages and decimals can be done by dividing or multiplying by 100, and rounding decimals is a useful skill for accuracy.
### How can visualizing percentages help with understanding?
Visualizing percentages can aid in understanding their meaning and representation. Using a percentage grid, which consists of 100 cells, each representing 1 percent, can help visualize proportions and calculations related to percentages. By visually representing percentages, it becomes easier to grasp the relationship between parts and wholes and how percentages are applied in various contexts.<|endoftext|>
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# Perimeter and Area Class 7 Notes: Chapter 11
### Perimeter
• Perimeter is the total length or total distance covered along the boundary of a closed shape.
To know more about Perimeter, visit here.
### Area
• The area is the total amount of surface enclosed by a closed figure.
### The perimeter of Square and Rectangle
• Perimeter of a square = a + a + a + a = 4a, where a is the length of each side.
• Perimeter of a rectangle = l + l + b + b = 2(l + b), where l and b are length and breadth, respectively.
To know more about Perimeter Formula’s of All geometrical Figures, visit here.
### Area of Square & Rectangle
Area of square = 4a2
Here a is the length of each side
Area of rectangle = Length(l) × Breadth(b) = l×b
### Area of a Parallelogram
• Area of parallelogram ABCD = (base×height)
Area of parallelogram ABCD  = (b×h)
### Triangle as Part of Rectangle
• The rectangle can be considered as a combination of two congruent triangles.
• Consider a rectangle ABCD, it is divided into 2 triangles ACDÂ and ABD.
• Area of each triangle = 12 (Area of the rectangle).
= 12(10cm×5cm)
=Â 25cm2
### Area of a Triangle
• Consider a parallelogram ABCD.
• Draw a diagonal BD to divide the parallelogram into two congruent triangles.
• Area of triangle ABD = 1/2Â (Area of parallelogram ABCD)
Area of triangle ABD  = 1/2 (b×h)
To know more about Area and Perimeter, visit here.
### Conversion of Units
• Kilometres, metres, centimetres, millimetres are units of length.
• 10 millimetres = 1Â centimetre
• 100 centimetres =Â 1 metre
• 1000 metres = 1 kilometre
### Terms Related to Circle
• A circle is a simple closed curve which is not a polygon.
• A circle is a collection of points which are equidistant from a fixed point.
• The fixed point in the middle is called the centre.
• The fixed distance is known as radius.
• The perimeter of a circle is also called as the circumference of the circle.
### Circumference of a Circle
• The circumference of a circle ( C )Â is the total path or total distance covered by the circle. It is also called a perimeter of the circle.
Circumference of a circle = 2×π×r,
where r is the radius of the circle.
## Visualising Area of a Circle
### Area of Circle
• Area of a circle is the total region enclosed by the circle.
Area of a circle = π×r2, where r is the radius of the circle.
#### For More Information On Area Of Circle, Watch The Below Video.
To know more about Circles, visit here.
### Introduction and Value of Pi
• Pi (Ï€)  is the constant which is defined as the ratio of a circle’s circumference (2Ï€r) to its diameter(2r).
Ï€= Circumference (2Ï€r)/Diameter (2r)
• The value of pi is approximately equal to 3.14159 or 22/7.
#### For More Information On The Value Of Pi, Watch The Below Video.
To know more about Value of Pi, visit here.
## Problem Solving
### Cost of Framing, Fencing
• Cost of framing or fencing a land is calculated by finding its perimeter.
• Example: A square-shaped land has length of its side 10m.
Perimeter of the land = 4 × 10 = 40m
Cost of fencing 1m = Rs 10
Cost of fencing the land = 40 m × Rs 10 = Rs 400
### Cost of Painting, Laminating
• Cost of painting a surface depends on the area of the surface.
• Example: A wall has dimensions 5m×4m.
Area of the wall = 5m×4m=20m2
Cost of painting 1m2 of area is Rs 20.
Cost of painting the wall =20m2×Rs 20=Rs 400
### Area of Mixed Shapes
• Find the area of the shaded portion using the given information.
Solution: Diameter of the semicircle = 10cm
Area of the shaded portion = Area of rectangle ABCD – Area of semicircle
Area of the shaded portion  = (l×b) − (πr2/2)
= 30×10 − (π×52/2)
= 300 − (π×25/2)
= (600 – 25Ï€)/2
= (600 – 78.5)/2
= 260.7Â cm2
## Frequently Asked Questions on CBSE Class 7 Maths Notes Chapter 1: Perimeter and Area
### What is value of ‘pi’?
The value of ‘pi’ is 3.14159.
### What is meant by area of a substance?
The amount of space taken up by any 2D shape is known to be the area covered by that substance.
### What is the purpose of Unit conversion?
Unit conversion helps in the expression of the same property in different units of measurement. For ex. time can be expressed in hours, minutes or seconds.
#### 1 Comment
1. Every useful
Thank you byjus
Love you<|endoftext|>
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What to do with this activity?
Finding and understanding patterns is what maths is all about. When we discover the pattern of a series of numbers or items, we can predict what comes next.
For instance, if a series goes like this ( 3, 5, 7, 9, 11 ) we might notice that each number in the series is 2 larger than the previous number. If the pattern continues, we can predict that the next number in the series is the number 13. A maths formula or rule is simply a way of describing a pattern that has been discovered. The formula or rule for this pattern is "the previous number plus 2".
Here's an online game from IXL predicting the next in a series with Increasing numbers. If you get the wrong answer it explains clearly how to work it out correctly next time.
This game from SoftSchools uses animal pictures to create a series. Get your child to explain to you how they made their choice. Often they will know the answer instinctively, but it's good to be able to say out loud the formula or rule that they have discovered.
If your child needs a more challenging learning game, have a go at cracking codes to a Locked Safe (from Top Marks).
Our brains are usually pretty good at noticing and remembering patterns instinctively. This is a great Pattern Memory Game from Cool Math for a bit more fun.
Everyday activities, like shopping and taking journeys provide a great opportunity for your child to practise maths skills by recognising patterns, counting out amounts, working out the best value, weighing and understanding money or understanding timetables and estimating your time of arrival!
Estimating is a very useful maths skill for everyday life – helping you decide if you have enough money to pay for a number of items or enough paint to paint a room. Encourage your child to estimate, for example, how many potatoes you will need for dinner or how much money to buy the shopping.
Rate this activity
Based on 9 reviews
How would you rate it?
1 = Poor, 5 = Great.<|endoftext|>
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The term Bluetooth refers to an open specification for a technology to enable short-range wireless voice and data communications anywhere in the world. This simple and straightforward description of the Bluetooth technology includes several points that are key to its understanding:
Open specificationThe Bluetooth Special Interest Group (SIG) has produced a specification for Bluetooth wireless communication that is publicly available and royalty-free. To help foster widespread acceptance of the technology, a truly open specification has been a fundamental objective of the SIG since its formation.
Short-range wirelessThere are many instances of short-range digital communication among computing and communications devices; today, much of that communication takes place over cables. These cables connect to a multitude of devices using a wide variety of connectors with many combinations of shapes, sizes, and number of pins; this plethora of cables can become quite burdensome to users. With Bluetooth technology, these devices can communicate without wires over a single air interface, using radio waves to transmit and receive data. Bluetooth wireless technology is specifically designed for short-range (nominally 10 meters) communications; one result of this design is very low power consumption, making the technology well suited for use with small, portable personal devices that typically are powered by batteries.
Voice and dataTraditional lines between computing and communications environments are continually becoming less distinct. Voice is now commonly transmitted and stored in digital formats. Voice appliances such as mobile telephones are also used for data applications such as information access or browsing. Through voice recognition, computers can be controlled by voice and through voice synthesis, and computers can produce audio output in addition to visual output. Some wireless communication technologies are designed to carry only voice, while others handle only data traffic. Bluetooth wireless communication makes provisions for both voice and data, so it is an ideal technology for unifying these worlds by enabling all sorts of devices to communicate using either or both of these content types.
Anywhere in the worldThe telecommunications industry is highly regulated in many parts of the world. Telephone systems, for example, must comply with many governmental restrictions, and telephony standards vary by country. Many forms of wireless communications are also regulated; radio frequency spectrum usage often requires a license with strict transmission power obligations. However, some portions of the available radio frequency spectrum may be used without license, and Bluetooth wireless communications operate within a chosen frequency spectrum that is unlicensed throughout the world (with certain limitations and restrictions that are discussed later in the book). Thus, devices that employ Bluetooth wireless communication can be used unmodified, no matter where a person might be.
The Bluetooth short range wireless technology is ideally suited for replacing the many cables that are associated with today's pervasive devices. The Bluetooth specification (see http://www.bluetooth.com/, hereafter referred to as "the specification") explicitly defines a means for wireless transports to replace serial cables, such as those used with modems, digital cameras, and personal digital assistants; the technology could also be used to replace other cables, such as those associated with computer peripherals (including printers, scanners, keyboards, mouse devices, and others). Moreover, wireless connectivity among a plethora of fixed and mobile devices can enable many other new and exciting usage scenarios beyond simple cable replacement. In this book, we explore various applications of the technology.
Important characteristics and applications of Bluetooth wireless communications are examined in detail in this book. The Bluetooth specification is explained in easy-to-understand terms with the benefit of the authors' experiences gained while participating in its development. If Bluetooth wireless technology succeeds in the marketplace to the extent predicted by many analysts, it has the potential to change people's lives and the way that people think about and interact with computing and communication devices. Understanding this emerging technology can benefit not only industry professionals, but also consumers who can use and obtain value from it.<|endoftext|>
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Fun and informative activities encourage kids to get outside, play with objects found in nature and learn about math along the way. By measuring worms, building snowmen and splashing in puddles, for example, kids ages 5 to 8 will learn about basic mathematic operations, shapes, time and more. All activities promote active living and an understanding of the natural world, while developing important character skills, such as teamwork and cooperation. Cross-curricular applications make Outdoor Math a strong institutional choice. Fun, quirky illustrations demonstrate each activity and show kids that learning about math can be all fun and games!
Emma lives in Sm?land, SwedenEmma lives in Sm?land, Sweden<|endoftext|>
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One of the two events must happen. Given that the chance of one is two-third of the other, find the odds in favour of the other.
Asked by Aaryan | 1 year ago | 36
##### Solution :-
Let A and B are two events.
As, out of 2 events A and B only one can happen at a time which means no event have anything common.
We can say that A and B are mutually exclusive events.
So, by definition of mutually exclusive events we know that:
P (A ∪ B) = P (A) + P (B)
According to question one event must happen.
A or B is a sure event.
So, P (A ∪ B) = P (A) + P (B) = 1 … Equation (1)
Given: P (A) = ($$\dfrac{2}{3}$$) P (B)
We have to find the odds in favour of B.
P (B) = $$\dfrac{3}{5}$$
So, P (B′) = 1 – $$\dfrac{3}{5}$$
=$$\dfrac{2}{5}$$
Odd in favour of B: $$\dfrac{3}{2}$$
Answered by Aaryan | 1 year ago
### Related Questions
#### One number is chosen from numbers 1 to 100. Find the probability that it is divisible by 4 or 6?
One number is chosen from numbers 1 to 100. Find the probability that it is divisible by 4 or 6?
#### The probability that a student will pass the final examination in both English and Hindi is 0.5
The probability that a student will pass the final examination in both English and Hindi is 0.5 and the probability of passing neither is 0.1. If the probability of passing the English examination is 0.75. What is the probability of passing the Hindi examination?
#### A card is drawn from a deck of 52 cards. Find the probability of getting an ace or a spade card.
A card is drawn from a deck of 52 cards. Find the probability of getting an ace or a spade card.<|endoftext|>
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Snowflake chemistry could give clues about ozone depletion
The unique shapes of snow crystals and the complex chemical reactions that occur on their surface could give clues about ground-level ozone loss. (Purdue University photo/Shepson Lab)
WEST LAFAYETTE, Ind. - There is more to the snowflake than its ability to delight schoolchildren and snarl traffic.
The structure of the frosty flakes also fascinate ice chemists like Purdue University's Travis Knepp, a doctoral candidate in analytical chemistry who studies the basics of snowflake structure to gain more insight into the dynamics of ground-level, or "tropospheric," ozone depletion in the Arctic.
"A lot of chemistry occurs on ice surfaces," Knepp said. "By better understanding the physical structure of the snow crystal - how it grows and why it takes a certain shape - we can get a better idea of the chemistry that occurs on that surface."
His work on snowflake shape and how temperature and humidity affect it takes place in a special laboratory chamber no larger than a small refrigerator. Knepp can "grow" snow crystals year-round on a string inside this chamber. The chamber's temperature ranges from 100-110 degrees Fahrenheit down to minus 50 degrees Fahrenheit.
Knepp, under the direction of Paul Shepson, professor and head of Purdue's Department of Chemistry, is studying snow crystals and why sharp transitions in shape occur at different temperatures. The differences he sees not only explain why no two snowflakes are identical, but also hold implications for his ozone research in the Arctic Ocean region.
"On the surface of all ice is a very thin layer of liquid water," Knepp said. "Even if you're well below the freezing point of water, you'll have this very thin layer of water that exists as a liquid form. That's why ice is slippery. Whenever you slip, you're not slipping on ice, you're slipping on that thin layer of water."
This thin, or quasi-liquid, layer of water exists on the top and sides of a snow crystal. Its presence causes the crystal to take on different forms as temperature and humidity change.
For example, the sides of a crystal growing in a warmer range of 27-32 degrees Fahrenheit expand much faster than the top or bottom, causing it to take on a platelike structure. Between 14 and 27 degrees Fahrenheit, crystals look like tall, solid prisms or needles.
"As you increase the humidity, you'll get more branching," Knepp said.
Snow crystals transition to other shapes, and sometimes even back and forth, as the temperature and humidity change.
"The bottom line is that the thickness or the presence of this really thin layer of water is what dictates the general shape that the snow crystal takes," Knepp said. "By altering the quasi-liquid layer's thickness, we changed the temperature at which the snow crystal changes shape.
"Until now, nobody knew that the quasi-liquid layer had such a significant role in determining the shape of snow crystals. Our research clearly shows this to be the case."
This knowledge has application for Knepp and his colleagues in their ozone work.
"Most people have probably heard of ozone depletion in the North and South Poles. This occurs in the stratosphere, about 15 miles up," Knepp said. "What people don't know is that we also see ozone levels decrease significantly at ground level."
Ground-level ozone is very important. It gives the atmosphere the ability to clean itself. However, it also is toxic to humans and vegetation at high concentrations, like those found in smog, Shepson said.
Complex chemical reactions regularly take place on the snow's surface. These reactions, which involve the thin layer of water found on the surface of snow crystals, cause the release of certain chemicals that reduce ozone at ground level.
"How fast these reactions occur is partially limited by the snow crystals' surface area," Knepp said. "Snow crystals with more branching will have higher surface areas than non-branched snow crystals, which will allow the rate of reaction to increase."
The need to understand these intricate chemical reactions and their implications for ozone reduction drive the researchers to continue studying snow.
"As the impact of emissions from human activities continues to grow, we need to be able to understand the impact of global average ozone," Shepson said. "Understanding ice and snow is part of that."
Knepp's research was published Oct. 16 in the online journal Atmospheric Chemistry and Physics. A downloadable version of the article is available at https://www.atmos-chem-phys.net/9/7679/2009/acp-9-7679-2009.html
Writer: Kim Schoonmaker, 765-494-2081, [email protected]
Sources: Travis Knepp, 765-496-2404, [email protected]
Paul Shepson, 765-494-7441, [email protected]<|endoftext|>
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Caries is derived from a Latin Word which means “Rot” or “Decay” and in Greek it means “Ker” for “Death”.
According to Ostrom (1980) has defined as a process of Enamel or Dentin dissolution which is caused by microbial action at the tooth surface and is mediated by physiochemical flow of water dissolved ions.
According to Hume (1993) Dental caries is essentially a progressive loss by acid dissolution of the apetite (mineral) component of the enamel then the dentin or of the cementum and then dentin.
Root Caries is a type of Dental caries which is seen apical to the cement enamel junction (CEJ), this type of lesions have a distinct outline in contrast to the sound tooth structure or the non carious portion of the tooth.
Causes or Aetiology of Toot Caries:
These are the most common associated factors which can be seen with Root caries which can be the primary factor playing a major role in leading to root caries or can be a contributing factor.
- Gingival Recession which can be due to Periodontitis or with Age
- Radiation Therapy
- Primary toot caries
- Recurrent Caries
- Removable Partial Dentures or Over dentures
- Malocclusion of teeth which are tipped and increases food lodgement and decreased accessibility for cleaning
- Diabetes and in disabilities physical and psychological which decreases cleaning efficiency
The Micro organisms responsible for Root Caries are Streptococcus Mutans, Lactobacillus and Actinobacillus. The rate of progression or demineralization of tooth structure is much higher in Root caries compared to Enamel Caries because Root has less Mineral content when compared to Enamel.
Important Features of Root Caries:
Sex Predilection: Male > Females
Root caries is mostly seen in cases where there is periodontal attachment loss exposing the root surface to the oral environment which leads to initiation of caries.
Root caries appears as a white or discoloured soft irregular and progressive lesion which occurs at or apical to the CEJ.
Shape of Root caries is Round or Oval in shape and is highly demarcated from the surrounding non carious tooth.
But the Root caries progresses rapidly and may join adjoining Root carious lesions
Incidence of Root Caries in Maxilla and Mandibular Teeth:
Maxilla: More common in the following order Incissors > Canines > Pre Molars > Molars
Mandible: More common in Molars > Premolars > Canines > Incissors
Root Caries Classification based on Extent of Lesion:
Grade 1 or Initial Root Caries:
- Light Brown to Tan in color on visual inspection
- No surface defect seen
- Surface Texture is Soft and the surface of Caries can be disrupted with the pointed tip of Dental Explorer
Grade 2 or Shallow Root Caries:
- Dark Brown to variable Tan in Color
- Surface defect is seen which can be less than 0.5 mm in depth
- Surface texture is Soft, irregular, rough which can be penetrated with the pointed tip of Dental Explorer
Grade 3 or Cavitation Root Caries:
- Light Brown to Dark Brown in color which is variable
- Surface texture is similar to Grade 1 which is soft and penetrated with a dental explorer
- The lesion is penetrating and cavitation is more than 0.5mm without pulpal involvement
Grade 4 or Pulpal Root Caries:
- It is similar in color to Grade 3 type root caries which is Dark Brown
- The Surface of Lesion is cavitated and the lesion has pulpal involvement extending upto the Root canal.
Treatment of Root caries:
Treatment of Root Caries is similar to Dental Caries depending on the extent of the lesion into the tooth structure the mode of treatment is planned.
Excavation of the Infected tooth structure and replacement with the help of Restorations like Composite, GIC etc
In some cases where the caries is deep but not extending till Pulp can be treated with Indirect Pulp Capping and then Restoration
In case of Grade 4 types Root caries – Root canal Treatment is the ideal form of treatment indicated along with excavation and restoration of the structure.<|endoftext|>
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# Section 2.3 Question 2
## How do you solve a system of three equations in two variables?
To solve a system of three equations in two variables, we extend the Substitution and Elimination Methods introduced earlier. A third equation in two variables simply adds a third line to the system. A solution to the system is an ordered pair that solves all of the equations in the system.
Figure 3 – Two systems of three equations in two variables. In Figure 4a, the solution to the system is (4,1). In Figure 4b, there is no solution since all three lines do not intersect at a single point.
Graphically, this is a point of intersection where all of the lines intersect. In Figure 3a, three lines are graphed corresponding to the three lines in a linear system. All of the lines intersect at the point (4, 1) which means it satisfies each of the equations in the system. If you consider only two of the lines in the system and use the Substitution Method or the Elimination Method, the resulting solution will also satisfy the third line in the system.
The system in Figure 3b has several points, such as (2, 3), where two of the lines in the system intersect. If you use the Substitution Method or the Elimination Method on these two lines, you would find a solution of x = 2 and y = 3. However, if this ordered pair is substituted in the other equation in the system, it will not be satisfied. This means that there is no ordered pair that satisfies all three equations simultaneously so the system is inconsistent.
### Example 3 Find the Solution to the System
Solve the system
Solution Although we could use the Substitution Method to solve this system, the Elimination Method will be used in this example since it generalizes to larger systems much more easily. The leading coefficient of the first equation is already a 1, so we need to eliminate x from the other two equations.
Replace the second and third equations in the original system of equations with these new equations to give
Multiply the second equation by 1/12 to give the equivalent system of equations,
To complete the Elimination Method, we need to eliminate y from the first and third equations:
This helps us to write the equivalent system of equations,
The last equation is an identity which means it is always true. The first two equations indicate that the solution to two of the equations is (x, y) = (4,1). This and the identity indicate that this ordered pair also solves the third equation. We can check this by substituting into each equation:
Since (x, y) = (4,1) satisfies each equation in the system, it is the solution to the system of equations. Furthermore, since the first two equation specify a unique solution and not a relationship between the variables, this is the only solution to the original system of equations.
### Example 4 Find the Solution to the System
Solve the system
Solution Start by solving any two of the equations for a solution. The Elimination Method provides a systematic approach for solving this system. To make the leading coefficient on the first equation a 1, interchange the first and third equation to yield
Now eliminate x from the second and third equations:
Replace the second and third equations with these new equations to give an equivalent system of equations,
Multiply the second equation by 1/2 to change the leading coefficient of the second equation to a 1. This leaves us with the equivalent system of equations,
Finally, eliminate x in the first and third equations:
Use these new equations to write the equivalent system of equations,
This indicates that (x,y) = (2,3) satisfies two of the equations, but not the third. The third equation is a contradiction. So the system is inconsistent and has no solutions. If we substitute into the original system of equations, we can discover which equations are satisfied and which are not:
The strategies in Example 3 and 4 can be applied to a system of any number of equations in two variables. If you use the Substitution Method, find the solution to two of the equations and then check it in each of the other equations. A solution to the system will satisfy all of the equations in the system. If the solution from any two equations does not work in all of the other equations in the system, the system does not have any solutions. If you use the Elimination Method, follow the strategy and look for the transformations to yield new equations that are contradictions (the original system has no solutions) or identities (the original system has many solutions). Remember, contradictions are equations like 0 = 27 that are never true and identities are equations like that are always true.<|endoftext|>
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# HOW TO CHECK WHETHER THE GIVEN NUMBER IS PERFECT SQUARE OR NOT
## About "How to check whether the given number is perfect square or not"
How to check whether the given number is perfect square or not ?
Here we are going to see How to check whether the given number is perfect square or not.
Perfect Square :
The numbers 1, 4, 9, 16, 25, g are called perfect squares or square numbers as
1 = 12, 4 = 22, 9 = 32, 16 = 42 and so on.
A number is called a perfect square if it is expressed as the square of a number.
We may observe the following properties through the patterns of square numbers.
Property 1 :
In square numbers, the digits at the unit’s place are always 0, 1, 4, 5, 6 or 9. The numbers having 2, 3, 7 or 8 at its units' place are not perfect square numbers.
Property 2 :
(i) If a number has 1 or 9 in the unit's place then its square ends in 1.
Number1911 Square181121
(ii) If a number has 2 or 8 in the unit's place then its square ends in 4.
Number2812 Square464144
(iii) If a number has 3 or 7 in the unit's place then its square ends in 9.
Number3713 Square949169
(iv) If a number has 4 or 6 in the unit's place then its square ends in 6.
Number4614 Square1636196
(v) If a number has 5 in the unit's place then its square ends in 5.
Number51525 Square25225625
(v) If a number has 5 in the unit's place then its square ends in 5.
Number51525 Square25225625
Property 3 :
When a number ends with ‘0’ , its square ends with double zeros.
Let us consider the following examples,
102 = 100, 202 = 400
1002 = 10000, 2002 = 40000
Property 4 :
If a number ends with odd number of zeros then it is not a perfect square.
Let us consider the examples,
Check if 100 is a perfect square.
100 is a perfect square. Because it has even number of zeroes.
100 = 10 ⋅ 10 = 102
(ii) 81000 = 81 ⋅ 10 ⋅ 100
= 92⋅ 10 ⋅ 102
Hence 81000 is not a perfect square. Because it has odd number of zeroes.
Property 5 :
(i) Squares of even numbers are even.
(ii) Squares of odd numbers are odd.
Let us look into some example problems to understand the above concepts.
Example 1 :
By observing the unit’s digits, which of the numbers 3136, 867 and 4413 can not be perfect squares?
Solution :
Since 6 is in units place of 3136, there is a chance that it is a perfect square.
867 and 4413 are surely not perfect squares as 7 and 3 are the unit digit of these numbers.
Example 2 :
Just observe the unit digit and state if the given number is perfect square or not.
9348
Solution :
In square numbers, the digits at the unit’s place are always 0, 1, 4, 5, 6 or 9.
Since the unit digit is 8, it is not a perfect square.
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WORD PROBLEMS
Word problems on simple equations
Word problems on linear equations
Algebra word problems
Word problems on trains
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on unit price
Word problems on unit rate
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Double facts word problems
Trigonometry word problems
Percentage word problems
Profit and loss word problems
Markup and markdown word problems
Decimal word problems
Word problems on fractions
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Time and work word problems
Word problems on sets and venn diagrams
Word problems on ages
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Profit and loss shortcuts
Percentage shortcuts
Times table shortcuts
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
Sum of all three four digit numbers formed using 0, 1, 2, 3
Sum of all three four digit numbers formed using 1, 2, 5, 6<|endoftext|>
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Constantine the Great and Christianity
|Constantine the Great|
|Born||Feb 27, 272 in Naissus, Roman Empire (now Niš, Serbia)|
|Died||May 22, 337 in Nicomedia, Byzantine Empire (now İzmit, Turkey)|
Eastern Orthodox Church
Oriental Orthodox Church
Eastern Catholic Church
|Major shrine||Church of the Holy Apostles|
|Attributes||In hoc signo vinces, Labarum|
While the Roman Emperor Constantine the Great (reigned 306–337) ruled, Christianity began to transition to the dominant religion of the Roman Empire. Historians remain uncertain about Constantine's reasons for favoring Christianity, and theologians and historians have argued about which form of Early Christianity he subscribed to. Although Constantine had been exposed to Christianity by his mother Helena, there is no consensus among scholars as to whether he adopted his mother's Christianity in his youth, or gradually over the course of his life, and he did not receive baptism until shortly before his death.
Constantine's decision to cease the persecution of Christians in the Roman Empire was a turning point for Early Christianity, sometimes referred to as the Triumph of the Church, the Peace of the Church or the Constantinian shift. In 313, Constantine and Licinius issued the Edict of Milan decriminalizing Christian worship. The emperor became a great patron of the Church and set a precedent for the position of the Christian emperor within the Church and the notion of orthodoxy, Christendom, ecumenical councils and the state church of the Roman Empire declared by edict in 380. He is revered as a saint and isapostolos in the Eastern Orthodox Church and Oriental Orthodox Church for his example as a "Christian monarch."
- 1 Before Constantine
- 2 Conversion
- 3 Patronage of the Church
- 4 Christian emperorship
- 5 Constantinian shift
- 6 See also
- 7 Notes and references
- 8 Further reading
- 9 External links
The first recorded official persecution of Christians on behalf of the Roman Empire was in AD 64, when, as reported by the Roman historian Tacitus, Emperor Nero attempted to blame Christians for the Great Fire of Rome. According to Church tradition, it was during the reign of Nero that Peter and Paul were martyred in Rome. However, modern historians debate whether the Roman government distinguished between Christians and Jews prior to Nerva's modification of the Fiscus Judaicus in 96, from which point practicing Jews paid the tax and Christians did not.
Christians suffered from sporadic and localized persecutions over a period of two and a half centuries. Their refusal to participate in Imperial cult was considered an act of treason and was thus punishable by execution. The most widespread official persecution was carried out by Diocletian. During the Great Persecution (303–311), the emperor ordered Christian buildings and the homes of Christians torn down and their sacred books collected and burned. Christians were arrested, tortured, mutilated, burned, starved, and condemned to gladiatorial contests to amuse spectators. The Great Persecution officially ended in April 311, when Galerius, senior emperor of the Tetrarchy, issued an edict of toleration, which granted Christians the right to practice their religion, though it did not restore any property to them. Constantine, Caesar in the Western empire and Licinius, Caesar in the East, also were signatories to the edict of toleration. It has been speculated that Galerius' reversal of his long-standing policy of Christian persecution has been attributable to one or both of these co-Caesars.
Constantine was exposed to Christianity by his mother, Helena, but he was over 42 when he finally declared himself a Christian. Writing to Christians, Constantine made clear that he believed his successes were owed to the protection of that High God alone.
Battle of Milvian Bridge
Eusebius of Caesarea and other Christian sources record that Constantine experienced a dramatic event in 312 at the Battle of the Milvian Bridge, after which Constantine claimed the emperorship in the West. According to these sources, Constantine looked up to the sun before the battle and saw a cross of light above it, and with it the Greek words "Ἐν Τούτῳ Νίκα" (~in this sign, conquer!), often rendered in a Latin version, "in hoc signo vinces"(–in this sign, you will conquer). Constantine commanded his troops to adorn their shields with a Christian symbol (the Chi-Rho), and thereafter they were victorious.
Following the battle, the new emperor ignored the altars to the gods prepared on the Capitoline and did not carry out the customary sacrifices to celebrate a general's victorious entry into Rome, instead heading directly to the imperial palace. Most influential people in the empire, however, especially high military officials, had not been converted to Christianity and still participated in the traditional religions of Rome; Constantine's rule exhibited at least a willingness to appease these factions. The Roman coins minted up to eight years after the battle still bore the images of Roman gods. The monuments he first commissioned, such as the Arch of Constantine, contained no reference to Christianity.
Edict of Milan
In 313 Constantine and Licinius announced "that it was proper that the Christians and all others should have liberty to follow that mode of religion which to each of them appeared best", thereby granting tolerance to all religions, including Christianity. The Edict of Milan went a step further than the earlier Edict of Toleration by Galerius in 311, returning confiscated Church property. This edict made the empire officially neutral with regard to religious worship; it neither made the traditional religions illegal nor made Christianity the state religion, as occurred later with the Edict of Thessalonica. The Edict of Milan did, however, raise the stock of Christianity within the empire and it reaffirmed the importance of religious worship to the welfare of the state.
Patronage of the Church
The accession of Constantine was a turning point for early Christianity. After his victory, Constantine took over the role of patron of the Christian faith. He supported the Church financially, had an extraordinary number of basilicas built, granted privileges (e.g., exemption from certain taxes) to clergy, promoted Christians to high-ranking offices, returned property confiscated during the Great Persecution of Diocletian, and endowed the church with land and other wealth. Between 324 and 330, Constantine built a new imperial capital at Byzantium on the Bosporos, which would be named Constantinople for him. Unlike "old" Rome, the city began to employ overtly Christian architecture, contained churches within the city walls and had no pre-existing temples from other religions.
In doing this, however, Constantine required those who had not converted to Christianity to pay for the new city. Christian chroniclers tell that it appeared necessary to Constantine "to teach his subjects to give up their rites (...) and to accustom them to despise their temples and the images contained therein," This led to the closure of temples because of a lack of support, their wealth flowing to the imperial treasure; Constantine did not need to use force to implement this. Only the chronicler Theophanes has added that temples "were annihilated", but this was considered "not true" by contemporary historians.
Many times imperial favor was granted to Christianity by the Edict; new avenues were opened to Christians, including the right to compete with other Romans in the traditional cursus honorum for high government positions, and greater acceptance into general civil society. Constantine respected cultivated persons, and his court was composed of older, respected, and honored men. Men from leading Roman families who declined to convert to Christianity were denied positions of power yet still received appointments, even up to the end of his life, and two-thirds of his top government were non-Christian.
Constantine's laws enforced and reflected his Christian reforms. Crucifixion was abolished for reasons of Christian piety, but was replaced with hanging, to demonstrate the preservation of Roman supremacy. On March 7, 321, Sunday, the Day of the Sun, was declared an official day of rest, on which markets were banned and public offices were closed, except for the purpose of freeing slaves. The Christians reacted to this by moving their Sabbath from the tradition Jewish day to Sunday. There were, however, no restrictions on performing farming work, which was the work of the great majority of the population, on Sundays.
Some laws made during his reign were even humane in the modern sense, possibly inspired by his Christianity: a prisoner was no longer to be kept in total darkness but must be given the outdoors and daylight; a condemned man was allowed to die in the arena, but he could not be branded on his "heavenly beautified" face, since God was supposed to have made man in his image, but only on the feet. Publicly displayed Gladiatorial games were ordered to be eliminated in 325.
Early Christian Bibles
In 331, Constantine commissioned Eusebius to deliver fifty Bibles for the Church of Constantinople. Athanasius (Apol. Const. 4) recorded around 340 Alexandrian scribes preparing Bibles for Constans. Little else is known. It has been speculated that this may have provided motivation for canon lists, and that Codex Vaticanus and Codex Sinaiticus are examples of these Bibles. Together with the Peshitta and Codex Alexandrinus, these are the earliest extant Christian Bibles.
Enforcement of Church policy
The reign of Constantine established a precedent for the position of the Christian emperor in the Church. Emperors considered themselves responsible to God for the spiritual health of their subjects, and thus they had a duty to maintain orthodoxy. The emperor did not decide doctrine — that was the responsibility of the bishops — rather his role was to enforce doctrine, root out heresy, and uphold ecclesiastical unity. The emperor ensured that God was properly worshiped in his empire; what proper worship (orthodoxy) and doctrines and dogma consisted of was for the Church to determine.
In 316, Constantine acted as a judge in a North African dispute concerning the Donatist controversy. More significantly, in 325 he summoned the First Council of Nicaea, effectively the first Ecumenical Council (unless the Council of Jerusalem is so classified). Nicaea however was to deal mostly with the Arian controversy. Constantine was torn between the Arian and Trinitarian camps. After the Nicene council and against its conclusions, he eventually recalled Arius from exile and banished Athanasius of Alexandria to Trier.
Just before his death in May 337, Constantine was baptised into the Arian version of Christianity by his distant relative Arian Bishop Eusebius of Nicomedia. During Eusebius of Nicomedia's time in the Imperial court, the Eastern court and the major positions in the Eastern Church were held by Arians or Arian sympathizers. With the exception of a short period of eclipse, Eusebius enjoyed the complete confidence both of Constantine and Constantius II and was the tutor of Emperor Julian the Apostate. After Constantine's death, his son and successor Constantius II was an Arian, as was Emperor Valens.
Suppression of other religions
Constantine's position on the religions traditionally practiced in Rome evolved during his reign. In fact, his coinage and other official motifs, until 325, had affiliated him with the pagan cult of Sol Invictus. At first, Constantine prohibited the construction of new temples and tolerated traditional sacrifices; by the end of his reign, he had begun to order the pillaging and tearing down of Roman temples.
Beyond the limes, east of the Euphrates, the Sassanid rulers of the Persian Empire, perennially at war with Rome, had usually tolerated Christianity. Constantine is said to have written to Shapur II in 324 and urged him to protect Christians under his rule. With the establishment of Christianity as the state religion of the Roman Empire, Christians in Persia would be regarded as allies of Persia's ancient enemy. According to an anonymous Christian account, Shapur II wrote to his generals:
You will arrest Simon, chief of the Christians. You will keep him until he signs this document and consents to collect for us a double tax and double tribute from the Christians … for Our Godhead have all the trials of war and they have nothing but repose and pleasure. They inhabit our territory and agree with Caesar, our enemy.—Shapur II, A History of Christianity in Asia: Beginnings to 1500
The "Great Persecution" of the Persian Christian churches occurred between 340-363 CE, after the Persian Wars that reopened upon Constantine's death.
Constantinian shift is a term used by Anabaptist and Post-Christendom theologians to describe the political and theological aspects of Constantine's legalization of Christianity in the 4th century. The term was popularized by the Mennonite theologian John H. Yoder.
- Constantine I and the bishops of Rome
- Christian pacifism
- Philip the Arab and Christianity
- List of rulers who converted to Christianity
Notes and references
- R. Gerberding and J. H. Moran Cruz, Medieval Worlds (New York: Houghton Mifflin Company, 2004) p. 55.
- About.com retrieved 19 September 2011
- Roman-Empire.net retrieved 19 September 2011
- Wylen, Stephen M., The Jews in the Time of Jesus: An Introduction, Paulist Press (1995), ISBN 0-8091-3610-4, Pp 190-192.; Dunn, James D.G., Jews and Christians: The Parting of the Ways, A.D. 70 to 135, Wm. B. Eerdmans Publishing (1999), ISBN 0-8028-4498-7, Pp 33-34.; Boatwright, Mary Taliaferro & Gargola, Daniel J & Talbert, Richard John Alexander, The Romans: From Village to Empire, Oxford University Press (2004), ISBN 0-19-511875-8, p. 426.;
- Bomgardner, D. L. The Story of the Roman Amphitheatre. New York: Routledge, 2000. p. 142.
- Lactantius, De Mortibus Persecutorum ("On the Deaths of the Persecutors") ch. 35–34.
- Galerius, "Edict of Toleration," in Documents of the Christian Church, trans. and ed. Henry Bettenson (London: Oxford University Press, 1963), 21.
- H. A. Drake, Constantine and the Bishops: The Politics of Intolerance (Baltimore: Johns Hopkins University Press, 2000), 149.
- Peter Brown, The Rise of Christendom 2nd edition (Oxford, Blackwell Publishing, 2003) p. 61.
- Peter Brown, The Rise of Christendom 2nd edition (Oxford, Blackwell Publishing, 2003) p. 60.
- Eusebius, Life of Constantine.
- J.R. Curran, Pagan City and Christian Capital. Rome in the Fourth Century (Oxford, 2000) pp. 70–90.
- Lactantius, De Mortibus Persecutorum ("On the Deaths of the Persecutors") ch. 48.
- Constantine and Licinius, "The 'Edict of Milan'," in Documents of the Christian Church, trans. and ed. Henry Bettenson (London: Oxford University Press, 1963), 22.
- R. Gerberding and J. H. Moran Cruz, Medieval Worlds (New York: Houghton Mifflin Company, 2004) pp. 55-56
- MacMullan 1984:49.
- R. Gerberding and J. H. Moran Cruz, Medieval Worlds (New York: Houghton Mifflin Company, 2004) p. 56
- quoted after MacMullan 1984:49.
- MacMullan 1984:50.
- MacMullan 1984: 141, Note 35 to Chapter V; Theophanes, Chron. a. 322 (PG 108.117)
- Corpus Juris Civilis 3.12.2
- MacMullen 1969; New Catholic Encyclopedia, 1908; Theodosian Code.
- Norwich, John Julius, A Short History of Byzantium. Alfred A. Knopf, 1997, p. 8. ISBN 0-679-77269-3.
- Miles, Margaret Ruth, The Word Made Flesh: A History of Christian Thought. Blackwell Publishing, 2004, p. 70, ISBN 1-4051-0846-0.
- The Canon Debate, McDonald & Sanders editors, 2002, pages 414-415, for the entire paragraph
- Richards, Jeffrey. The Popes and the Papacy in the Early Middle Ages 476–752 (London: Routledge & Kegan Paul, 1979) pp. 14–15.
- Richards, Jeffrey. The Popes and the Papacy in the Early Middle Ages 476–752 (London: Routledge & Kegan Paul, 1979) p. 15.
- Richards, Jeffrey. The Popes and the Papacy in the Early Middle Ages 476–752 (London: Routledge & Kegan Paul, 1979) p. 16.
- Pre-Ecumenical councils include the Council of Rome 155 AD, Second Council of Rome 193 AD, Council of Ephesus 193 AD, Council of Carthage 251 AD, Council of Iconium 258 AD, Councils of Antioch, 264 AD, Council of Elvira 306 AD, Council of Carthage 311 AD, Council of Ancyra 314 AD, Council of Arles 314 AD and the Council of Neo-Caesarea 315 AD).
- (ABC-CLIO 2012 ISBN 978-0-31338359-5), p. 113Early Controversies and the Growth of ChristianityKevin Kaatz,
- Drake, "Constantine and the Bishops", pp.395.
- Gerberding, R. and J. H. Moran Cruz, Medieval Worlds (New York: Houghton Mifflin Company, 2004) p. 28.
- R. MacMullen, "Christianizing The Roman Empire A.D.100-400, Yale University Press, 1984, ISBN 0-300-03642-6
- "A History of the Church", Philip Hughes, Sheed & Ward, rev ed 1949, vol I chapter 6.
- Eusebius Pamphilius and Schaff, Philip (Editor) and McGiffert, Rev. Arthur Cushman, Ph.D. (Translator) NPNF2-01. Eusebius Pamphilius: Church History, Life of Constantine, Oration in Praise of Constantine quote: "he razed to their foundations those of them which had been the chief objects of superstitious reverence".
- Eusebius, vita Constantini IV, 8-13
- Moffett, Samuel H. (1992). A History of Christianity in Asia: Beginnings to 1500. p. 140.
- In general, there is a "silence of the Perso-Arab and classical historians on any claim by Iranian kings to divinity". The Cambridge history of Iran: The Seleucid, Parthian and Sasanian ...: Volume 1 - Page xxxiii.
Clapp, Rodney (1996). A Peculiar People. InterVarsity Press. p. 23.
What might be called the Constantinian shift began around the year 200 and took more than two hundred years to grow and unfold to full bloom.
Yoder, John H. (1996). "Is There Such a Thing as Being Ready for Another Millennium?". In Miroslav Volf, Carmen Krieg, Thomas Kucharz (ed.). The Future of Theology: Essays in Honor of Jurgen Moltmann. Eerdmanns. p. 65.
The most impressive transitory change underlying our common experience, one that some thought was a permanent lunge forward in salvation history, was the so-called Constantinian shift.
- Ramsay MacMullen, "Christianizing The Roman Empire A.D. 100-400, Yale University Press, 1984, ISBN 0-300-03642-6
- The Full Text of the "Edict of Milan"
- OrthodoxWiki:Constantine the Great
- The First Missionary War - a non-Christian perspective aftermath of Constantinian's actions<|endoftext|>
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In this lesson, we're just introducing the nonfiction structures to the kids to help prepare for CCSS.ELA-Literacy.RI.5.5 which is comparing and contrasting the structures. They should have learned these in 4th grade common core, but if this is your first year of implementation, a good overview will let the kids know where they're heading specifically over the next few weeks. This serves as a way to activate previous knowledge, as they are introduced to this information in 4th grade. When I pre-assessed my students, I found this skill is still shaky, so I am planning to fully teach the structures before comparing structures of two different texts.
A really helpful resource I found is this document. There are sample paragraphs to use here as well. They'll be especially helpful when we get into the guided practice. I use something I purchased, but there are some great alternatives included in this document.
How does an author organize nonfiction texts? Do they just start writing?
Students can discuss in pairs at their table or with their neighbor. I tend to use numbered heads (one student is 3 1 and the other is #2) so that I can make sure each student gets to chat. You could say something like, 1s tell 2s how you think an author organizes nonfiction texts. 2s tell ones if you agree and why.
Once you've heard some thoughts (And I usually make my kiddos tell what their partner said to make sure they are working on active listening), discuss
just as fiction has a plot structure, nonfiction also has structures. We're going to refresh our memories about the nonfiction text structures by completing a matching activity.
Hand out the text structure scramble N sort activity. I will let the students work with their table groups, but you could also have them paired strategically based on reading level as well. I provided the resource, but here is the link to the blog as well. She has some other great ideas listed there.
With your partners, work to match the structure with the definitions. When you're finished, we'll share ideas. Don’t discuss right or wrong with the students. Ask students: who is ready to find out who is right?!
During this lesson, I will refer to slides and notes featured in this TeachingTextStructure powerpoint. I will also refer to my interactive notebook throughout all of my lessons. The use of these notebooks is not necessary to use the lessons. I hope this Interactive Notebook Overview is helpful if you'd like to try them out!
This power point is attached, but this teacher has other great free resources for nonfiction.
We're going to use the Text Structure notes to review the basic attributes of each structure. This is just a general overview of the structures. Students will keep these in their notebook or binder as you go through the powerpoint. These notes help students connect the knowledge of structure to things like buildings and bridges. Students need to understand what a structure is before knowing the different types of text structures. This is important to help students connect the new knowledge learned in the next few lessons. We'll be digging deep into the structures to look for the specific attributes and analyzing the author's use of those structures, so I like to give the kids a big idea of it all before we dig in.
While going through the notes in the slides, ask students to mark their text with the following symbols:
* I didn’t know that
? I don’t understand
+ I knew that.
This interactive note-taking is something I use to be sure the students are constantly interacting with the text. It's also helpful when starting close reading. This common core shift has probably been practiced by teachers for a long time, but the common core now shows how important it is for all students to dig into the text. Have discussions with students about the information presented and encourage students to make connections to the notes. I draw in the text. For example, where it says a text structure refers to how a text is built, I draw a wooden framework of a house next to that note. Modeling how good readers think is so important for this age as they have already learned the basics of reading. At this point they are learning how to dig deep into text and how to interact with what they are reading. I have attached an example.
*Some teachers like to have students copy all notes at this age. That is also a possibility. I have found that interactive note-taking on printed notes while reading is wonderful for my students, but these notes can be written in by the students just the same.
Now that we've interacted with the notes, we will create a word splash for Text Structure. A word splash is placing the word "text structure" in the middle of a box, circle, etc. and then you write any words that come to mind that connect to text structure. You can write these all around the center box.
My kids do this in color. All of our processing is done in color as this leaves more of an imprint on the brain. This activity is summarizing the concept reviewed before moving on to the overview of specific nonfiction text structures. I like to use this because it's quick and gets the students to start synthesizing ideas. Allow students about 5 minutes for this processing activity. Here a two examples of my kids working on these. Student Word Splash 1 and Student Word Splash 2. When they finish or after a few minutes let them share.
To wrap up this section, we'll look at a graphic organizer.
Think about the scramble and sort activity we did earlier and discuss with a partner what you remember. Read through each definition, word clues, and visuals.
Allow students time to discuss what they know about these structures and to mark when they remember with a + sign. I purchased my notes from teachers pay teachers. There are lots of other free resources as well. This one is almost identical to the one I use:
Students will create a foldable to work with these terms in the next section.
Students will create a structure foldable to work with the overview knowledge of the text structures. Foldables help organize knowledge and appeal to the kinesthetic learners.This is also a helpful way for students to start thinking about the 5th grade common core standard of comparing the text structures. When all of the structures are together on one foldable, it lets the students see the similarities and differences between them all. This will also help scaffold learning for the students when it comes time to read different texts and compare the structures.
Before students start working, I go through all directions with them first. See the picture for a better idea of how this should look.
Once I pass out the foldable, cut this out. This organizer is divided in thirds. On the front of the organizer should be the structures, the definition of the structure, and the clue words that go with the structure. The far right column will be folded in to create the visual column. You must write the information from the graphic organizer in your own words. You may include other word clues if you think of some and you may also include other graphic organizers if you feel that they truly fit. You will complete this organizer in color.
I have my students glue the very back of the organizer into their interactive notebooks so it is there as a reference. Here is a shot of a student completing a foldable. Again, if you'd rather have the students create their own, this is simple to recreate on white paper or lined paper instead of making copies.
Every year my group is different, so I use my knowledge of their collective learning styles to decide what I will do while they are working. Some of my usual strategies are:
1. Circulate the room and sit with individual students that need my help while the other students are working in table groups. Some of my individuals usually struggle with reading the attributes of the structures and putting that information into their own words on the graphic organizer. I know they get the big idea of each structure if they can paraphrase the information.
2. Pull a small group and work with them while the rest of the class works in groups. I do this if I know more than 1 or 2 students struggle with paraphrasing the information in the graphic organizer.
3. Complete 1 or 2 structures with the class and then let the students work on them one at a time. Call students to fill in their thoughts on the board as we continue to work on this step-by-step together.
If you have a group ready for a challenge, you could let them fill in as much as they can remember without using the structures graphic organizer.
Now you will return to the scramble and sort cards and try to match the words and definitions again in groups.
Here are my kids with the scramble and sort in action. You could do pairs as well. During this time I like to walk around to check for understanding. When I do this, I write down a few names of students who still appear to be struggling with matching the correct definitions. I prompt students to join in discussion if they are waiting for others to complete the task. "Laura, how can you find the definition of a descriptive structure?" This closure summarizes everything we just learned and will give a quick check of whether students get the overall definitions of each structure. This will be helpful as we move through the analysis of each structure in subsequent lessons.
You could turn this into an exit ticket and pass out the scramble sheets pre-cut for each student to complete. They can glue these on a sheet of paper to turn in. You could also create a matching sheet based on the scramble and sort organizer. This Exit Ticket is something you could use if you wish. When I do this, I can make piles of students who know it well and students who are still struggling.
In the next lesson we will break down the structures more in depth and you will get to practice interacting with the different types of texts one at a time.<|endoftext|>
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# How do you write an equation of a line parallel to the graph of 2x+5y=3 and the x-intercept is -2?
Apr 9, 2016
$2 x + 5 y = - 4$
#### Explanation:
Any equation of the form $A x + B y = C$ has a slope of $m = - \frac{A}{B}$
Therefore $2 x + 5 y = 3$ has a slope of$\left(- \frac{2}{5}\right)$
All parallel lines have the same slope.
If a line has an x-intercept of $\left(- 2\right)$
then $\left(x , y\right) = \left(- 2 , 0\right)$ is a point on the line.
Using the slope definition:
$\textcolor{w h i t e}{\text{XXX}} \frac{y - 0}{x - \left(- 2\right)} = \left(- \frac{2}{5}\right)$
$\textcolor{w h i t e}{\text{XXX}} y = \left(- \frac{2}{5}\right) \left(x + 2\right)$
$\textcolor{w h i t e}{\text{XXX}} 5 y = - 2 x - 4$
$\textcolor{w h i t e}{\text{XXX}} 2 x + 5 y = - 4$ (standard linear form)<|endoftext|>
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On November 28, 1520, Ferdinand Magellan and three of his ships finally entered the Pacific Ocean after a horrendous thirty-eight days of trying to sail through the South American strait that eventually bore his name. Two researchers, Scott M. Fitzpatrick and Richard Callaghan, put forth a study showing that the favorable winds of an El Niño year charted the course of Magellan’s ships and may have allowed Magellan to operate his ships with fewer crew members. The researchers used computer models to study the wind and weather conditions, as well as information from Magellan’s writings. This site has an animation of the route of the Victoria, the ship that circumnavigated the globe, as well as illustrations of the behavior of trade winds in normal years and in El Niño years.
courtesy of Knovation<|endoftext|>
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Wildfire across a Kansas grassland. (Credit: U.S. Fish and Wildlife Service)
Global warming tends to increase the risk of wildfires by drying the things that fuel them like trees, grasses and other vegetation. The role of carbon dioxide actually helps to decrease that risk, largely because the gas is used by plants to grow. But what parts do humans play in ramping up or stomping out the risk of wildfires?
An investigation completed by researchers at European universities and the National Center for Atmospheric Research has found that it’s complicated. This is owed to the fact that humans can serve as both igniters and extinguishers of out-of-control forest fires.
To better pinpoint the effects that people have on fire risk, scientists incorporated changes in population size and distribution into a model. This helped to reveal that population growth and its hotspots will have a greater impact on future fire risk than just population increases alone.
That finding, combined with the fact that people put out more fires than they start, helps to explain why global burned area has gone down over the past century. For other results, find the full study published in the journal Nature Climate Change.
Top image: Wildfire across a Kansas grassland. (Credit: U.S. Fish and Wildlife Service)<|endoftext|>
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Statistics
# 1.1Definitions of Statistics, Probability, and Key Terms
Statistics1.1 Definitions of Statistics, Probability, and Key Terms
The science of statistics deals with the collection, analysis, interpretation, and presentation of data. We see and use data in our everyday lives.
## Collaborative Exercise
In your classroom, try this exercise. Have class members write down the average time—in hours, to the nearest half-hour—they sleep per night. Your instructor will record the data. Then create a simple graph, called a dot plot, of the data. A dot plot consists of a number line and dots, or points, positioned above the number line. For example, consider the following data:
5, 5.5, 6, 6, 6, 6.5, 6.5, 6.5, 6.5, 7, 7, 8, 8, 9.
The dot plot for this data would be as follows:
Figure 1.2
Does your dot plot look the same as or different from the example? Why? If you did the same example in an English class with the same number of students, do you think the results would be the same? Why or why not?
Where do your data appear to cluster? How might you interpret the clustering?
The questions above ask you to analyze and interpret your data. With this example, you have begun your study of statistics.
In this course, you will learn how to organize and summarize data. Organizing and summarizing data is called descriptive statistics. Two ways to summarize data are by graphing and by using numbers, for example, finding an average. After you have studied probability and probability distributions, you will use formal methods for drawing conclusions from good data. The formal methods are called inferential statistics. Statistical inference uses probability to determine how confident we can be that our conclusions are correct.
Effective interpretation of data, or inference, is based on good procedures for producing data and thoughtful examination of the data. You will encounter what will seem to be too many mathematical formulas for interpreting data. The goal of statistics is not to perform numerous calculations using the formulas, but to gain an understanding of your data. The calculations can be done using a calculator or a computer. The understanding must come from you. If you can thoroughly grasp the basics of statistics, you can be more confident in the decisions you make in life.
## Statistical Models
Statistics, like all other branches of mathematics, uses mathematical models to describe phenomena that occur in the real world. Some mathematical models are deterministic. These models can be used when one value is precisely determined from another value. Examples of deterministic models are the quadratic equations that describe the acceleration of a car from rest or the differential equations that describe the transfer of heat from a stove to a pot. These models are quite accurate and can be used to answer questions and make predictions with a high degree of precision. Space agencies, for example, use deterministic models to predict the exact amount of thrust that a rocket needs to break away from Earth’s gravity and achieve orbit.
However, life is not always precise. While scientists can predict to the minute the time that the sun will rise, they cannot say precisely where a hurricane will make landfall. Statistical models can be used to predict life’s more uncertain situations. These special forms of mathematical models or functions are based on the idea that one value affects another value. Some statistical models are mathematical functions that are more precise—one set of values can predict or determine another set of values. Or some statistical models are mathematical functions in which a set of values do not precisely determine other values. Statistical models are very useful because they can describe the probability or likelihood of an event occurring and provide alternative outcomes if the event does not occur. For example, weather forecasts are examples of statistical models. Meteorologists cannot predict tomorrow’s weather with certainty. However, they often use statistical models to tell you how likely it is to rain at any given time, and you can prepare yourself based on this probability.
## Probability
Probability is a mathematical tool used to study randomness. It deals with the chance of an event occurring. For example, if you toss a fair coin four times, the outcomes may not be two heads and two tails. However, if you toss the same coin 4,000 times, the outcomes will be close to half heads and half tails. The expected theoretical probability of heads in any one toss is $1 2 1 2$ or .5. Even though the outcomes of a few repetitions are uncertain, there is a regular pattern of outcomes when there are many repetitions. After reading about the English statistician Karl Pearson who tossed a coin 24,000 times with a result of 12,012 heads, one of the authors tossed a coin 2,000 times. The results were 996 heads. The fraction $996 2,000 996 2,000$ is equal to .498 which is very close to .5, the expected probability.
The theory of probability began with the study of games of chance such as poker. Predictions take the form of probabilities. To predict the likelihood of an earthquake, of rain, or whether you will get an A in this course, we use probabilities. Doctors use probability to determine the chance of a vaccination causing the disease the vaccination is supposed to prevent. A stockbroker uses probability to determine the rate of return on a client's investments.
## Key Terms
In statistics, we generally want to study a population. You can think of a population as a collection of persons, things, or objects under study. To study the population, we select a sample. The idea of sampling is to select a portion, or subset, of the larger population and study that portion—the sample—to gain information about the population. Data are the result of sampling from a population.
Because it takes a lot of time and money to examine an entire population, sampling is a very practical technique. If you wished to compute the overall grade point average at your school, it would make sense to select a sample of students who attend the school. The data collected from the sample would be the students' grade point averages. In presidential elections, opinion poll samples of 1,000–2,000 people are taken. The opinion poll is supposed to represent the views of the people in the entire country. Manufacturers of canned carbonated drinks take samples to determine if a 16-ounce can contains 16 ounces of carbonated drink.
From the sample data, we can calculate a statistic. A statistic is a number that represents a property of the sample. For example, if we consider one math class as a sample of the population of all math classes, then the average number of points earned by students in that one math class at the end of the term is an example of a statistic. Since we do not have the data for all math classes, that statistic is our best estimate of the average for the entire population of math classes. If we happen to have data for all math classes, we can find the population parameter. A parameter is a numerical characteristic of the whole population that can be estimated by a statistic. Since we considered all math classes to be the population, then the average number of points earned per student over all the math classes is an example of a parameter.
One of the main concerns in the field of statistics is how accurately a statistic estimates a parameter. In order to have an accurate sample, it must contain the characteristics of the population in order to be a representative sample. We are interested in both the sample statistic and the population parameter in inferential statistics. In a later chapter, we will use the sample statistic to test the validity of the established population parameter.
A variable, usually notated by capital letters such as X and Y, is a characteristic or measurement that can be determined for each member of a population. Variables may describe values like weight in pounds or favorite subject in school. Numerical variables take on values with equal units such as weight in pounds and time in hours. Categorical variables place the person or thing into a category. If we let X equal the number of points earned by one math student at the end of a term, then X is a numerical variable. If we let Y be a person's party affiliation, then some examples of Y include Republican, Democrat, and Independent. Y is a categorical variable. We could do some math with values of X—calculate the average number of points earned, for example—but it makes no sense to do math with values of Y—calculating an average party affiliation makes no sense.
Data are the actual values of the variable. They may be numbers or they may be words. Datum is a single value.
Two words that come up often in statistics are mean and proportion. If you were to take three exams in your math classes and obtain scores of 86, 75, and 92, you would calculate your mean score by adding the three exam scores and dividing by three. Your mean score would be 84.3 to one decimal place. If, in your math class, there are 40 students and 22 are males and 18 females, then the proportion of men students is $22402240$ and the proportion of women students is $18401840$. Mean and proportion are discussed in more detail in later chapters.
## NOTE
The words mean and average are often used interchangeably. In this book, we use the term arithmetic mean for mean.
## Example 1.1
### Problem
Determine what the population, sample, parameter, statistic, variable, and data referred to in the following study.
We want to know the mean amount of extracurricular activities in which high school students participate. We randomly surveyed 100 high school students. Three of those students were in 2, 5, and 7 extracurricular activities, respectively.
## Try It 1.1
Find an article online or in a newspaper or magazine that refers to a statistical study or poll. Identify what each of the key terms—population, sample, parameter, statistic, variable, and data—refers to in the study mentioned in the article. Does the article use the key terms correctly?
## Example 1.2
### Problem
Determine what the key terms refer to in the following study.
A study was conducted at a local high school to analyze the average cumulative GPAs of students who graduated last year. Fill in the letter of the phrase that best describes each of the items below.
1. Population ____ 2. Statistic ____ 3. Parameter ____ 4. Sample ____ 5. Variable ____ 6. Data ____
• a) all students who attended the high school last year
• b) the cumulative GPA of one student who graduated from the high school last year
• c) 3.65, 2.80, 1.50, 3.90
• d) a group of students who graduated from the high school last year, randomly selected
• e) the average cumulative GPA of students who graduated from the high school last year
• f) all students who graduated from the high school last year
• g) the average cumulative GPA of students in the study who graduated from the high school last year
## Example 1.3
### Problem
Determine what the population, sample, parameter, statistic, variable, and data referred to in the following study.
As part of a study designed to test the safety of automobiles, the National Transportation Safety Board collected and reviewed data about the effects of an automobile crash on test dummies (The Data and Story Library, n.d.). Here is the criterion they used.
Speed at which Cars Crashed Location of Driver (i.e., dummies) 35 miles/hour Front seat
Table 1.1
Cars with dummies in the front seats were crashed into a wall at a speed of 35 miles per hour. We want to know the proportion of dummies in the driver’s seat that would have had head injuries, if they had been actual drivers. We start with a simple random sample of 75 cars.
## Example 1.4
### Problem
Determine what the population, sample, parameter, statistic, variable, and data referred to in the following study.
An insurance company would like to determine the proportion of all medical doctors who have been involved in one or more malpractice lawsuits. The company selects 500 doctors at random from a professional directory and determines the number in the sample who have been involved in a malpractice lawsuit.
## Collaborative Exercise
Do the following exercise collaboratively with up to four people per group. Find a population, a sample, the parameter, the statistic, a variable, and data for the following study: You want to determine the average—mean—number of glasses of milk college students drink per day. Suppose yesterday, in your English class, you asked five students how many glasses of milk they drank the day before. The answers were 1, 0, 1, 3, and 4 glasses of milk.
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A dam presents an obvious obstacle to migrating fish. Dams block the downstream movement of juvenile fish to the waters where they will spend their adult lives — the ocean for salmon and steelhead, or a lake or river for resident fish like trout, bull trout, or sturgeon. With more than 400 dams in the Columbia River Basin, and more than half of them dedicated fully or partly to generating hydropower, the region’s primary source of electricity, fish passage at dams has been a major problem for nearly as long as dams have been built in the basin.
Juvenile salmon and steelhead are sluiced over dam spillways, collected and transported around dams in barges and tank trucks, diverted past dams in fish bypass systems and even, in one brief-lived experiment in the 1970s, flown down the lower Snake and Columbia rivers and dropped from an airplane, giving new meaning to the term “flying fish.”
Fish ladders and even water-filled fish elevators have been built to try to improve the survival of adult salmon and steelhead as they return upriver. At some dams there is no fish passage for either juvenile or adult fish. These dams block access to more than 40 percent of the habitat once available to salmon and steelhead in the Columbia River Basin.
The problem of getting juvenile fish safely past dams on their downstream journeys and adult fish safely past dams when they return to spawn was recognized even before the end of the 19th century. In 1890, Washington’s Legislature passed a law requiring fishways to be built at dams “wherever food fish are wont to ascend.” The law authorized the state commissioner of fisheries to levy fines for violations and ask courts to order the removal of illegal dams, but the law was not well-enforced. By 1922 it was off the books. In 1931, the Oregon Fish Commission adopted a policy to protest applications for new dams or irrigation projects filed with the state if they did not include provisions for protecting the upstream and downstream migration of salmon. Irrigation diversions began to be screened in the 1930s, but the progress was slow. The commission estimated that 50 percent of the prime spawning and rearing habitat in the Columbia Basin had been lost, although surveys would not begin to assess actual losses until 1938. The Commission commented:
“Knowing further that each race [stock] is self-propagating, it becomes perfectly apparent that all parts of the salmon run in the Columbia River must be given adequate protection if the run as a whole is to be maintained. The protection of only one or two portions of the run will not be sufficient, inasmuch as certain races will be left entirely unprotected.”
Fish passage at the big dams on the Columbia always has been problematic. Fish passage ends at Chief Joseph Dam at River Mile 545 on the Columbia. Before that dam was completed, fish passage ended at Grand Coulee Dam, 51 miles upriver. In the Snake River system, fish passage ends at Hells Canyon Dam, at River Mile 247, and, on the North Fork Clearwater River, at Dworshak Dam, which is about three miles from the confluence of the North Fork with the mainstem of the Clearwater. The Idaho Power Company attempted fish passage at its complex of three dams on the Snake — Hells Canyon, Oxbow and Brownlee — in the late 1950s, but these were unsuccessful. Subsequently, the company reached agreement with the Federal Power Commission to compensate for the loss of salmon and steelhead spawning habitat upstream of the three-dam complex by producing fish at hatcheries downstream of the dams. Similarly, the Army Corps of Engineers built a fish hatchery a short distance downstream from Dworshak Dam to compensate for the lack of salmon and steelhead passage.
The first dam completed on the mainstem Columbia, Rock Island in 1933, included a gently inclining fish ladder. The dam was built by Northwestern Power Company, which later became part of Puget Sound Power and Light Company (Puget Sound Energy today). The same year Rock Island was completed, the Bureau of Reclamation began construction of Grand Coulee Dam 143 miles upstream, and the Army Corps of Engineers began work at Bonneville Dam 320 miles downstream. Passage facilities for salmon and steelhead were under consideration at both dams.
In 1933, the Bureau recommended a flume and an elevator to collect and carry fish over or around Grand Coulee. But the United States Commissioner of Fisheries, Frank Bell, studied the plans and determined they would not work because the dam was too high — about 350 feet from the downstream side to the usual level of the reservoir behind the dam. Subsequently the Bureau considered trapping juvenile fish above the dam and hauling them in trucks to a release point below the dam, and also trapping adult fish below the dam and hauling them to a release point above the dam. These ideas, too, were rejected because of their potential complexity, uncertainty and cost. Ultimately, a complex of hatcheries was constructed in Columbia tributaries downstream of the dam in an attempt to relocate and rebuild the runs that would be lost to the dam.
Meanwhile, salmon and steelhead passage at Bonneville Dam presented its own challenges. To this day some people believe — it is in the realm of an urban myth — that the Corps of Engineers never intended to provide fish passage facilities at the dam and that the agency was pressured into providing them. In a word, that is untrue. The Corps was well aware of the importance of providing fish passage at dams and, besides, the Federal Power Act of 1920 required the builders of dams on public waterways to provide either fish passage or hatcheries in compensation for the loss of passage.
While the Bureau chose hatcheries to compensate for the losses that would be caused by Grand Coulee, the Corps always intended to provide passage at Bonneville. The written record is clear on that point. For example, in a March 8, 1929, letter to the Corps’ Chief of Engineers in Washington, D.C., Portland Division Engineer Gustave Lukesh wrote: “In connection with tentative design of dams for [the] Columbia River and certain tributaries it appears that provision should be made for the passage upstream of fish, especially salmon, migrating to breeding places.” The Corps already had installed fish passage facilities at dams on the Willamette River and at the Ballard Locks in Seattle.
In 1933, Portland District Engineer Major Oscar Kuentz wrote about the planning for Bonneville Dam in the January-February issue of Military Engineer magazine. He wrote that “. . .studies must be made to determine the best method of passing the salmon over the [proposed] high structure . . . ” of the dam. Written before construction of the dam began, Lukesh’s letter and Kuentz’ comments in his article show that the Corps was planning to build fish passage facilities at the dam and was not forced to do so.
However, the facilities that eventually were built were more complex and expensive than originally planned. The Corps’ original budget for fishways at the dam was $640,000. The eventual cost was more than $7 million after numerous additions to the original plan were made, many in response to public concerns. But the fishway worked. In 1937, the annual report of the U.S. Commissioner of Fisheries commented, “Salmon are climbing the fish ladder at Bonneville Dam with “. . .far less effort than their forebears that fought upstream through the swirling rapids that are now buried beneath fifty feet of water.”
And as a matter of historical trivia, Grand Coulee Dam did have a fish ladder for a short time during construction. The ladder was completed in 1937 to allow salmon and steelhead to cross the foundation of the dam. At the time, the river was flowing through 25-foot-wide slots in the concrete foundation. The ladder was considered temporary. It was built from logs and formed seven pools, or steps, for the fish to climb over the foundation.
While fishways, or fish ladders, were for adult fish, dam passage was considered problematic for juvenile fish, and research steadily would prove the assumption. In 1942, Ivan Donaldson, who was hired the previous year as the Corps of Engineers’ first biologist on the Columbia River, suggested various measures to protect what he called his “beloved fish” from the turbines at Bonneville Dam, including experiments to determine juvenile fish mortality, fish screens at the power house, Bradford Island fish ladders and removing predatory fish below the dam. In a memo to Captain R.B. Cochrane on September 17, 1942, Donaldson wrote that initially some engineers at Bonneville Dam did not “want to be bothered with the concerns of a scientist” and that an engineer “in a high place” told him, “I don’t know anything about fish except that they are a damn nuisance.” In the memo, Donaldson described the attitude of the engineers as, “to hell with the fish, I’m here to build a dam.”
Soon fish advocates took up the cause, badgering the Corps to pay attention to the impacts on juvenile fish. In 1937, at a public hearing in Lewiston where the Corps took testimony on whether to build dams on the lower Snake River, V.E. Bennington remarked that the Corps did not propose enough money for fish passage. He warned the Inland Empire Waterways Association (IEWA), which represented barge lines and ports and was the chief advocate of the dams, that it could expect a “considerable fight” from sport and commercial fishing interests unless the association supported more money for fish passage. The IEWA promptly wrote a supportive letter to Congress. Others, however, were less willing to openly support expenditures for fish passage. In 1945, The Dalles Chamber of Commerce, which was a member of the IEWA, urged the association to “adopt measures to effectively combat” the “highly organized” opposition to Snake River dams by fish and wildlife agencies. According to the Chamber, “these agencies are going out of bounds, and we contend that in some activities [they are] are exceeding their authority.”
Fish advocates entered the battle too late to effectively derail dam advocates like the IEWA, which had been working for years to win congressional authorization of McNary Dam and the Snake River dams. The Corps seemed convinced, too, that dams were not dangerous to juvenile salmon and steelhead. In 1955, the Walla Walla District of the Corps announced that a year of studying juvenile fish passage at McNary Dam yielded results that “. . .discount considerably the claims of the fish industries that dams on the river are a hindrance to the anadromous hordes” and that the real culprit in the salmon decline is the “... commercial fishermen’s nets and sportsmen’s lures.” Oregon’s director of fisheries denounced these statements as “propaganda.” It was the same word that dam advocates had been using since the early 1940s to define the concerns of fish advocates.
Over time, the four Snake River dams were built, despite opposition from fish advocates. The dams have fish ladders for adult fish, and each is capable of passing fish through spillways. Over time, collection facilities for juvenile fish were installed at three of the four dams. But when the dams were built, the primary passage method for juveniles was through turbines. The first dam, Ice Harbor, was completed in 1962 and the last, Lower Granite, in 1975.
Congress long had recognized that dams kill fish. The Fish and Wildlife Coordination Act of 1934, amended in 1946 and 1958, required that potential impacts on fish and wildlife be addressed in planning and building federal dams. At Ice Harbor, the Corps quickly recognized that juvenile fish were dying or being injured in the turbines. Tests at McNary Dam using marked smolts demonstrated the danger, and the Corps responded with studies of alternative turbine designs. But then research showed that juvenile fish actually sought out the bulkhead slots above the turbine entrances, apparently to avoid going through turbines. There was no escape from the bulkhead slots, but with a little innovation there could be.
In 1967, the Corps of Engineers created a juvenile fish bypass system at Ice Harbor by drilling six-inch holes between the bulkhead slots and the ice/trash sluiceway on the other side. Once in the sluiceway, the fish could pass the dam — literally with the floating debris and trash in the river, but it was a much safer passage route than through the turbines. In 1969 the Corps and the National Marine Fisheries Service tested the first submerged traveling fish screen, a device installed in front of a turbine entrance at Ice Harbor that would deflect juvenile fish up to the gatewells and into the bypass system.
The traveling screens look a bit like railroad flat cars wrapped lengthwise with a nylon mesh that moves constantly upward on rollers. The screens are angled into the water from the face of the dam above the turbine entrances, and the fish ride upward on a cushion of water. Once in the bulkhead slots, the fish are attracted to lights that mark the entrances to the bypass system.
Further research and refinements over the years improved the fish-passage efficiency of the screens and bypass systems, and ultimately the Corps installed screens and bypass systems at all Columbia and Snake river mainstem dams where salmon and steelhead pass. Only The Dalles Dam does not have a bypass system, but that is because the ice and trash sluiceway always provides effective passage for juvenile fish.
There have been problems at some dams, however. The second powerhouse at Bonneville Dam, for example, is a notorious fish killer. Ironically, it is the newest powerhouse on the mainstem river, completed in 1982. For reasons that never were completely clear, but apparently had something to do with the shape of the river bed in front of the dam, juvenile fish were swept by the current almost directly into the turbines. The problem became so bad that the Corps had to shut down the powerhouse during the juvenile salmon migration period for most of the 1990s while an effective bypass system was designed and tested. A juvenile fish collection device, installed in 2003, appeared to solve the problem, finally.
Predation on juvenile fish as they emerge from bypass systems or turbines, sometimes stunned or dead, also has been a problem. Piscivorous birds and fish — Caspian terns, gulls, northern pikeminnow, walleye and bass — prey on juvenile salmon and steelhead, and the federal river management agencies have gone to great lengths to protect the fish. The Bonneville Power Administration finances a bounty reward fishery for pikeminnow (267,213 fish were turned in at receiving stations in 2004, a record for the program to that point), and the Corps has remodeled bypass system outfalls to carry the juvenile fish to release points in swift-moving water away from predator fish. It is an ongoing battle.
Meanwhile, research by NOAA Fisheries shows that survival of juvenile fish through the eight dams of the lower Snake and Columbia rivers in the first few years of the 21st century is as good as or better than survival before the Snake River dams were built. Federal research on fish passage survival and potential passage improvements at the dams is continuing. This research is reported on the website of the NOAA’s Northwest Fisheries Science Center (external link).
Fish in a tube
If fish passage at hydroelectric dams can kill juvenile salmon and steelhead migrating to the ocean, why not devise a means of keeping the fish away from the dams? It’s a simple proposition, and it is at the heart of various fish-passage techniques that have been tried with varying degrees of success at the big dams on the lower Snake and Columbia rivers.
One idea that never caught on despite repeated proposals in various configurations, was to build a migratory channel around the dams for the fish. One variation was to build a canal along the shoreline; another was to install a floating tube in the river, presumably connecting to the bypass systems at each dam. Each proposal suffered the same flaws — how to get salmon into the tube or canal and keep them there; how to keep water moving through the devices and keep predators out of them; how to create a “natural” migration experience for the tiny fish, which tend to rest and feed during daylight hours and migrate primarily at night; and how to ensure the fish obtain nutrients and other ecological cues and services that are fundamental to the salmon life cycle. The U.S. Army Corps of Engineers studied various options and, in the Columbia River System Configuration Study Phase 1 Report, issued in 1994, determined that all such migratory canal and pipeline proposals would be eliminated from further consideration because of the concerns and uncertainties about biological impacts.<|endoftext|>
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At stake: two free tickets to the All-Star Game. And all you have to do is guess the correct number of jelly beans in a jar at the Planet Toys store. One particularly smart boy has an idea: Why guess when you can estimate? He plays a game with his buddy as they head over to the store on the bus. With four people per row, 10 rows, and a few folks standing in the aisle, he estimates that there are 43 people on the bus. "I didn't even need a pencil," he boasts.
Knowing how to estimate is an essential skill that helps children determine approximate totals as well as check the reasonableness of their solutions to problems.
Illustrated by S.D. Schindler.
Place a handful of coins on the table and talk about the value of each. Ask questions such as: "Which coin is a dime?" "How many pennies equal a dime?" "How many nickels?" "Can you combine pennies and nickels to make a dime?"
Reread the story with your child (or class) and identify the different coins in the story. How much each is worth?
Practice using coins in everyday situations: Help your child (or students) choose the coins needed to buy a magazine or a healthy snack. What is the correct change needed to ride the bus? Or buy a stamp?
Teacher Idea: Before we read "The Penny Pot," I ask my kids, “How many different combinations can you make using 25 cents?” The answer is 13 different ways. The kids can use money to help them figure it out and can write out how they came to the answer. A lot of them can do it in their heads! When I read the book, they can see the computations. —Richard Callan, Bunker Hill Elementary School, Indianapolis, IN<|endoftext|>
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In the last program, we learned how we can arrange an array of 8-bit hexadecimal numbers in ascending, now in this program, we are going to arrange the same 8-bit hexadecimal numbers in descending order.
For this program also we are going to use five 8-bit hexadecimal numbers, hence, we will be requiring five memory locations; 2000H – 2004H.
The 8-bit hexadecimal numbers which we are going to use are C2H, ABH, 1DH, F9H, and 9BH.
MVI C, 05H // C register will be used as the main counter which we will keep decrementing as we compare one 8-bit number after another
Label3 MVI B, 04H // B register will also be used as another counter which we will need for comparison
LXI H, 2000H // HL register pair will be loaded and will point to the content of 2000H memory location
Label2 MOV A, M // the content of 2000H ML pointed by HL register will be copied to the accumulator
INX H// HL register pair will get incremented by one
CMP M// the content of accumulator will be compared with the content of memory location pointed by HL register pair
JNC Label1 // JNC will jump if the content of ML pointed by HL register pair is smaller than the content of accumulator
MOV D, M // the content which is pointed by HL register will be moved to D register
MOV M, A // the content of accumulator will be moved to the memory location pointed by HL register
DCX H // using DCX we decremented the HL register pair by 1
MOV M, D // now the 8-bit number stored in D register will be moved to the memory location pointed by HL register
INX H // HL register pair will be incremented by 1
Label1 DCR B // the content of B register pair will be decremented by 1
JNZ Label2 // JNZ will keep on working unless the content of ML doesn’t become null
DCR C // the content of C register pair will be decremented by 1
JNZ Label3 // JNZ will keep on jumping until the content of B register becomes null
|Memory Location||OPCODE||Operand||Label||Hex Code|<|endoftext|>
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The Australian landscape has been shaped and impacted by bushfires for tens of thousands of years, with some of the natural flora and fauna even evolving to become reliant on them. But Australia is also no stranger to the destruction and devastation they can cause.
Over the last 50 years or so, Australia’s climate has been experiencing more and more bushfire weather, and we will likely continue to see an increase in the number of ‘very high’ and ‘extreme’ fire danger rating days over the coming years.
In the past, we could only rely on ground intelligence and communication to see where a fire was. But with satellite technology, we are now able to fight fires like never before, with the potential to prevent or mitigate disasters and save lives through early bushfire detection, fire-spread modelling, thermal imaging, moisture content monitoring, and even live streaming of satellite images.
From Earth observation to inspiring action
Using satellites to monitor fires and provide fire data has been possible since 1972. That’s because in 1972, the first Earth-observing satellite ever was launched from the U.S. It was initially called the Earth Resources Technological Satellite and later renamed LANDSAT 1.
Although satellites weren’t initially launched for firefighting reasons, this became a beneficial byproduct of satellites meant for monitoring the land on Earth.
But in those early days all LANDSAT 1 could do was survey the damage that the fires had caused.
As satellites improved, so too did their capabilities and usefulness regarding fires.
In 1976, the US created the Defence Meteorological Satellite Program, which allowed us to detect fires at night; and in 1981, NASA launched the Geostationary Operational Environmental Satellite (GOES) Network, in which satellites were able to monitor active fires.
Satellites aiding Australia
Such advancements in satellite technology around the world have proven to be useful for Australia, too. During the Black Saturday bushfires in 2009, for example, satellite surveillance was used to keep track of where the fires were burning and how severely, which allowed fire authorities to fight them more effectively.
This surveillance was performed by satellites belonging to the China National Space Administration (CNSA), China’s national space agency, thanks to an agreement between the two nations that China’s satellites be used to monitor Australia when available. The high-definition imagery was sent from the satellites to experts at the University of New South Wales and then to the Country Fire Authority within 30 minutes — and the ability for quick turnarounds are imperative during a bushfire.
Australia receives further assistance from the Japanese satellite, the Himawari 8, due to its geostationary position above the Australia/Asia region. It has been in space since 2014 and provides detailed imagery of the world below.
You can see the daily mapping of all the bushfires around Australia that Himawari 8 provides here: https://sentinel.ga.gov.au/#/
In addition, NASA’s pair of MODIS (Moderate Resolution Imaging Spectroradiometer) instruments which orbits the Earth on the satellites Terra (launched in 1999) and Aqua (launched in 2002). MODIS is able to provide visual data of Australia and has been a useful aid for Australian fire prevention as well as research.
Australian scientists are starting to use NASA’s data to calculate the frequency of bushfires in Australia and are even beginning to use modelling to predict the likelihood of fires starting in any Australian location during bushfire seasons.
The potential for a worldwide response
The dangers of bushfires are experienced around the world – so in 2011, NASA’s Jet Propulsion Laboratory developed a global solution. They’ve called it FireSat which will be a network of over 200 satellites, each equipped with infrared sensors that will be able to quickly locate wildfires anywhere in the world as long as they are at least 10 metres wide.
Along with spotting them, they’ll be able to quickly contact emergency services in the relevant area. This aims to address the current issue of fires not being detected early enough and dangerously escalating.
“The system we envision will work day and night for fires anywhere in the world,” said Robert Staehle, the lead designer of FireSat at JPL. They aim to launch them this year.
Fighting fire at home – with CubeSats
While Australia has benefitted greatly from American and Asian satellites, foreign satellites may not always be available or accessible for monitoring the Australian landscape – so it’s important for Australia to develop their own satellites for fire prevention.
This led to a hot idea by three UNSW students named Siddharth Doshi, Himmat Panag and David Lam, which was unveiled at the 2016 Mission Idea Contest held in Bulgaria.
The trio proposed having a constellation of 12 CubeSats to monitor fire-prone areas of Australia. They will use thermal imaging to detect any fires in a quicker and more spatially-precise way than what weather satellites like Himawari 8 currently do.
“We came up with project after speaking to fire analysts at Queensland and ACT emergency services,” said Siddharth to UNSW Engineering. “A system which can be used to detect small fires before they spread and monitor with a quick revisit time between images. We realised that technology had advanced to the point that this was now feasible.”
In conjunction with the CubeSats, there would also be a collection of about 10 ground stations where the satellites’ images will be sent. The data would be made available to the public as well as being sent to fire agencies, who would gain important information about fires’ location and direction.
Their idea won the contest, and it was a great opportunity for the team to gain visibility and recognition for a project that could have substantial and meaningful impact if implemented.
Those who have experienced the devastation of bushfires are likely to never forget it. The Black Saturday bushfires remind us of the importance of mitigating such disasters, if and wherever possible. But perhaps some hope can be found in the knowledge that when you look up: many satellites are looking down on you, capable of aiding and perhaps, one day, effectively preventing such disasters in the future.<|endoftext|>
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What is a Nuclear Medicine VQ Scan? A ventilation–perfusion (VQ) scan is a nuclear medicine scan that uses radioactive material…Read more
Nuclear medicine is a medical speciality that involves giving a patient a small amount of radioactive medication, called a radiopharmaceutical. This makes the body slightly radioactive for a short time. A special nuclear medicine camera detects the radiation, which is emitted (released) from the body, and takes images or pictures of how the inside of the body is working. Many different organs can be imaged depending on the type of radioactive medication used. The radioactive medication is most commonly injected into the blood stream through a vein, but might be given in different ways, including:
Only a very small amount of radiopharmaceutical is given to keep the radiation dose to a minimum.
Nuclear medicine can also be used to treat some diseases or conditions. In these cases, the amount of radiopharmaceutical given is much greater, and it mostly goes to the diseased or abnormal organ. The type of radiopharmaceutical given usually emits ionising radiation that has the maximum effect on the part of the body or organ system being treated.
A nuclear medicine specialist is a doctor with specialised training in nuclear medicine. Some nuclear medicine specialists are also trained in medical specialities, such as radiology, cardiology (heart specialist), oncology (cancer specialist) or in the use of diagnostic ultrasound.
Nuclear medicine technologists are health professionals who have obtained a university degree in nuclear medicine, which among other things qualifies them to:
A radiopharmaceutical is a medication used in nuclear medicine that has a radioactive part and a pharmaceutical part.
The radioactive part is sometimes referred to as a radioactive label or a radioactive tracer. The radioactive part is an unstable element (radioisotope) that gives off energy as it decays (disintegrates or breaks down) and changes to a different element or energy state. The actual amount of the radioactive substance given for most imaging tests is usually very small; approximately millionths of a gram. The dose of ionising radiation received by a patient having a nuclear medicine test can be very low or moderate; the dose varies between different types of studies. The ionising radiation is in a similar range to that received from computed tomography (CT) imaging. The radioactive part is most commonly Technetium 99m, but other radioisotopes such as iodine 123, indium 111 and gallium 67 are also used. Fluorine 18 is a radioisotope used in positron emission tomography (PET) imaging.
The body does not feel the ionising radiation, and it does not make you ‘warmer’ or ‘glow in the dark’. The number of times the nuclear medicine camera takes images does not determine the dose of ionising radiation received during a nuclear medicine test. It is determined by the type and amount of radiopharmaceutical injected, the half-life of the radioisotope and how quickly this is eliminated from the body in urine, stools or breath. The half-life is the time taken for half of the radioactive atoms to decay or change their energy state. For most radioisotopes used in nuclear medicine, this half-life is measured in hours, so after a day or so there is very little radioactivity remaining.
The pharmaceutical part can be a few atoms or a complex molecule that helps take the radioactive part to the area of the body being studied. It is mostly the choice of the pharmaceutical part that determines where the radiopharmaceutical will go in the body and what organ system will be shown. Technetium 99m MDP is used for a nuclear bone scan, whereas technetium 99m MAG3 is used for a nuclear renal scan.
A gamma camera is a machine that is able to detect and make images from the very small amounts of ionising radiation emitted from patients having a nuclear medicine study. The gamma camera usually has a table, often narrow, on which the patient lies. The images are taken using the camera ‘head’.
A camera might have one, two or occasionally three heads, with one or more being used to obtain the images. Each camera head has a flat surface that has to be very close to the patient. The camera heads might be supported in a number of different ways using strong metal arms or a gantry. There are no unusual sensations associated with having images taken with a gamma camera and the machine makes no noise.
During a normal X-ray or CT examination, an image is formed from the ‘shadow’ created by the body as it is positioned between the X-ray machine (source of the X-ray beam) and the X-ray detector. The body stops some, but not all, of the X-rays and the patient is not made radioactive by the X-rays.
In nuclear medicine studies, the radiopharmaceutical given to the patient makes them, and the organ system or body part being studied, radioactive for a short time. This ionising radiation (usually a gamma ray) is emitted or released from the body, and can be detected and measured using a nuclear medicine gamma camera. All living things contain some radioisotopes (such as carbon 14 and potassium 40); a nuclear medicine study will make them ‘more radioactive than normal’ for a short time – hours or days.
An X-ray or CT image is formed from ionising radiation (X-rays) that passes through the body, but does not arise from the body; whereas a nuclear medicine image is formed from the ionising radiation (usually gamma rays) emitted from within the body. A gamma ray has similar properties to an X-ray, but it arises from the nucleus of an atom, whereas an X-ray arises from the electron shell of an atom.
Another way that nuclear medicine is different from X-ray and CT examinations is that an X-ray study shows what something looks like. This gives indirect information about how it is working: normally, abnormally, diseased, injured and so on. In nuclear medicine studies, the radiopharmaceutical usually only goes to the part of the body or organ system if it has some function and so shows how it is working. The images can also give information about what the body part or organ system looks like.
Nuclear medicine and X-ray tests are often complementary, providing different information that together make a diagnosis more certain.
There are minimal risks in having a nuclear medicine study. These are allergic reactions and radiation risk.
For children and adults
For pregnant women
A nuclear medicine study helps your doctor evaluate how a particular area of your body or organ system is working. It can give information about how an injury, disease or infection might be affecting your body. It can also be used to show improvement or deterioration of a known abnormality after any treatment you might have had. Nuclear medicine studies are very good at showing how an organ system is working, and often complement other investigations and imaging studies.
Page last modified on 26/7/2017.
RANZCR® is not aware that any person intends to act or rely upon the opinions, advices or information contained in this publication or of the manner in which it might be possible to do so. It issues no invitation to any person to act or rely upon such opinions, advices or information or any of them and it accepts no responsibility for any of them.
RANZCR® intends by this statement to exclude liability for any such opinions, advices or information. The content of this publication is not intended as a substitute for medical advice. It is designed to support, not replace, the relationship that exists between a patient and his/her doctor. Some of the tests and procedures included in this publication may not be available at all radiology providers.
RANZCR® recommends that any specific questions regarding any procedure be discussed with a person's family doctor or medical specialist. Whilst every effort is made to ensure the accuracy of the information contained in this publication, RANZCR®, its Board, officers and employees assume no responsibility for its content, use, or interpretation. Each person should rely on their own inquires before making decisions that touch their own interests.<|endoftext|>
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#### Explain solution RD Sharma class 12 Chapter 15 Tangents and Normals exercise Fill in the blanks question 1
Equation of normal, $y=-x$
Hint:
Use equation of normal formula,
$\left(y-y_{1}\right)=\frac{-1}{\frac{d y}{d x}}\left(x-x_{1}\right)$
Given:
Here given the curve , $y=\tan x$
To find:
We have to find the equation of normal to the curve at $\left ( 0,0 \right )$
Solution:
Here given,
$y=\tan x$
Differentiating both side with respect to $x$ , we get
\begin{aligned} &\Rightarrow \quad \frac{d y}{d x}=\sec ^{2} x \\\\ &\Rightarrow \quad\left(\frac{d y}{d x}\right)_{(0,0)}=\sec ^{2}(0)=1 \\\\ &\Rightarrow \quad\left(\frac{d y}{d x}\right)_{(0.0)}=1 \end{aligned}
Slope of normal at $\left ( 0,0 \right )=\frac{-1}{\frac{dy}{dx}}$
$=-1$
Now, equation of normal to the curve $y=\tan x$ at $\left ( 0,0 \right )$ is
$\left(y-y_{1}\right)=\frac{-1}{\frac{d y}{d x}}\left(x-x_{1}\right)$
$\Rightarrow$ $(y-0)=(-1) x$
$\Rightarrow$ $y=-x$
Hence, this is the required equation of normal.<|endoftext|>
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What is the percentage for 100 out of 90000?
Step 5: This gives us a pair of simple equations: 100 % = 90000(1). x % = 100(2). Therefore, 100 is 0.1111 % of 90000.
How do you find 10 percent of a number?
To calculate 10 percent of a number, simply divide it by 10 or move the decimal point one place to the left. For example, 10 percent of 230 is 230 divided by 10, or 23. 5 percent is one half of 10 percent. To calculate 5 percent of a number, simply divide 10 percent of the number by 2.
How do you find the percent of a whole number?
Finding the percentage For this type of problem, you can simply divide the number that you want to turn into a percentage by the whole. So, using this example, you would divide 2 by 5. This equation would give you 0.4. You would then multiply 0.4 by 100 to get 40, or 40%.
How do you calculate percentage of marks?
To find the percentage of the marks, divide the marks obtained in the examination with the maximum marks and multiply the result by 100.
How 10th marks will be calculated 2021?
As per the evaluation criteria, Class 10 students would be assessed for a total of 100 marks out of which 20 marks would be allocated to internal assessment that could be either practical or project work depending on the subject while 80 marks will be on the basis of their performance in various exams conducted by the …
How do you convert percentage to Marks?
Moreover, if you want to calculate total marks from here, then you can simply multiply your percentage divided by 100 to total marks (total of all subjects). So, here if you have total 5 subjects with 100 as total marks each, then your marks in 12th would be: (66.5/100) x 500= 332.5.
How do you find 120 of a number?
Multiply the decimal equivalent of the percentage by 100; or move the number’s decimal point over two places to the right. The result is the percentage amount. (This answers the question “120 is what percent of 500,” you learn that 120 is 24 percent of 500).
How do you calculate 130 of a number?
Therefore, 130 percent is the same as 1.3. This means that we need to multiply 1.3 by 70. This is the same as 1.3 multiplied by 10 multiplied by seven. 1.3 multiplied by 10 is equal to 13.
What is whole percent?
The percentage is written as a decimal and multiplied with the whole number to give the percentage of the whole number. Rules to find the percentage of a whole number. The percentage of a whole number is written as a product of the percentage and the whole number. For example: 60% of 98 is written as 60% × 98.
How do I calculate my final grade?
For percentages, divide the sum by the number of entries. For example, if you have percentage grades for 30 tasks, divide the sum by 30. The quotient represents your final percentage grade.
IS 60 is good in 10th class?
As long as you are getting admission into a school nearby you, this is not bad to score 60 percent in the 10th board.
Is 80 a good score?
A – is the highest grade you can receive on an assignment, and it’s between 90% and 100% B – is still a pretty good grade! This is an above-average score, between 80% and 89% D – this is still a passing grade, and it’s between 59% and 69%
Is class 10 Marksheet important?
Class 10th marks do not matter while applying for UPSC examinations. For that matter, neither 12th nor graduation marks are required for applying in UPSC exams. Anyone can apply for this examination to gain government jobs. Therefore, students do not need to worry if they get less marks in 10th or 12th.
What is 120g out of 200g expressed as a percentage?
Solution and how to convert 120 / 200 into a percentage 0.6 times 100 = 60. That’s all there is to it!
What percent is 42 out of 63?
Now we can see that our fraction is 66.666666666667/100, which means that 42/63 as a percentage is 66.6667%.
How do I work out 20% of a figure?
As finding 10% of a number means to divide by 10, it is common to think that to find 20% of a number you should divide by 20 etc. Remember, to find 10% of a number means dividing by 10 because 10 goes into 100 ten times. Therefore, to find 20% of a number, divide by 5 because 20 goes into 100 five times.
How do you find 60 percent of a number?
Example one First we check how much is one percent: we divide 900 by 100. We get 9. Then we multiply one percent by 60 (60% = 60 per hundred = 60 percent) so 9 x 60 = 540.<|endoftext|>
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Calendar is a staple of many preschool circle time routines and often justified as “math instruction” even though many of the skills targeted during calendar surpass Virginia’s standards for four-year-olds. Try the quiz below to see just how far. Hint: Research shows that temporal concepts like units of time (days, weeks) and their sequence… Read More Rethinking “Calendar Time” for Preschoolers
To design instruction that allows a diverse class of students to move toward grade level standards, Marian Small (2009) suggests two core strategies. First, use open questions. Secondly, use parallel tasks, that are designed to meet the needs of students at different developmental levels. Research Confident, engaged math students are contributors to classroom discourse because… Read More Designing Instruction That Moves Students Toward Grade Level Math Standards What Does It Look Like in the Classroom?<|endoftext|>
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# How to answer these questions ?
Oct 25, 2017
$n = 3 \text{ and } q = 12$.
#### Explanation:
The mean is the sum of the elements in the data set, divided by the size of the data set.
$\overline{x} = \frac{3 + 2 n + 1 + 4 n + 14 + 17 + 19}{6} = q$
$\Rightarrow \overline{x} = \frac{6 n + 54}{6} = q$
$\Rightarrow n + 9 = q \text{ " to" } \left(\textcolor{red}{1}\right)$
The median is the middle value of the data set, when it's arranged in ascending order. (If there is no middle value, the median is the average of the two middle values.)
rArrstackrel~x =(4n+14)/2=13
$\Rightarrow 4 n = 12 \Rightarrow n = 3$
Substituting in $\left(\textcolor{red}{1}\right)$:
$\Rightarrow q = 3 + 9 = 12$<|endoftext|>
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# Solving Simultaneous Equations with Common Sense
Simultaneous equations belong in elementary-school mathematics curricula. That’s been my mantra for many years, and I want to examine it now in the context of an interactive Web Sketchpad activity.
When I say that elementary-age students should encounter simultaneous equations, I don’t mean that they should be instructed in the standard algebraic procedure for solving pairs of equations like x + 2y = 9 and 3xy = –1. Rather, my interest lies in presenting students with puzzle-like situations in which they solve for multiple unknown values by using their common sense (You can see two interactive Web Sketchpad models of this approach here and here in my prior posts.)
Take a look at the interactive Web Sketchpad model below. It displays eight rows of shapes, each containing a different combination of circles and squares. Pick a row and drag the shapes across the vertical divider line. When you do, the sum of those circles and squares will appear in the right-hand column. The goal is to determine the numerical values of the circle and square.
When I’ve observed this activity in classrooms with third, fourth, or fifth graders, students usually begin by taking a guess based on what they learn about a single row. For example, dragging the top row of shapes, the square and circle, across the vertical divider reveals that square + circle = 9. Might the square equal 8 and the circle equal 1? Students check by dragging another row of shapes across the divider. Two squares plus a circle equals 11, but 8 + 8 + 1 does not equal 11. Trying other values for the circle and square soon reveals that square = 2 and circle = 7. The puzzle is now solved, but students are not finished: They find it fun to predict the sums of the other rows before dragging each across the vertical divider. This helps to drive home the message that every circle in every row shares the same value, as does every square—something that’s not always clear to students.
With a little guidance, students become more systematic in their approach to solving the puzzles. For example, knowing that circle + square = 9 means that there are 10 possible pairs of values for the two shapes. Students list these in a table like the one below and then check to see which pair of values satisfies the sums of the other combinations of shapes.
One aspect of this puzzle that I especially like is that students can choose how far across the vertical divider to drag each row of shapes. Below are two different placements for the first two rows of shapes.
The placement of the shapes on the right invariably encourages a student to make a key discovery: The shapes in both rows are nearly the same. Both contain a square and a circle, but the second row contains one extra square. That must mean that the square is equal to 11 – 9 = 2. Since the square equals 2, the circle must equal 7.
Using common sense, the student has just done—and explained—some important algebra! A problem like this can support a stimulating number talk (algebra talk?) that encourages many students to participate by describing their own numeric and proto-algebraic thinking.
Here are some of the interesting discussion questions that naturally arise when students work with this puzzle:
• Is it always possible to determine the values of the circle and square regardless of which two rows we pick?
• Which pairs of rows make it easy to solve for the circle and square? Which pairs of rows make it harder?
• Might there be more than one answer to a puzzle?
• Could a puzzle exist that has no answer?
Use the arrow buttons in the lower-right corner of the web sketch to navigate from page to page. The second page looks just like the first, but now, the possible values of the circle and square range from 0 to 20 rather than from 0 to 8. The third page of the sketch allows students to create problems for each other, deciding for themselves what values to assign to the circle and square (Should the circle equal 3,452? Should it equal –28? Students create far harder problems for each other than we might create for them!) The fourth page of the sketch adds a third symbol to the mix—a triangle—and now students must solve for three unknowns. The final page of the sketch allows student to create their own problems with three unknowns to share with each other.
If you have a chance to use this activity with your students, I’d love to hear what discoveries they make!
An annotated list of all our elementary-themed blog posts is here.
## One thought on “Solving Simultaneous Equations with Common Sense”
1. This is superb. Algebra is all about relationships, and to start off looking at equations in “x”, where we have to find an unknown quantity is the wrong place. Equations are usually the consequence of a search for specific cases of relationships, but the idea that “variables” are “unknowns” sticks for far too long. The language used doesn’t help either. I find the phrase “solve the inequality” quite unmathematical. We might as well say “solve the equation x+2y=4”. School math is very screwed up ! See some of my posts on this.
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Matrix Addition as the name suggests in the article, explores the addition of matrices and it is one of the fundamental operations in the field of Linear Algebra. Matrix Addition is very useful in various fields such as data analysis, computer graphics, image processing, cryptography, operations research, machine learning, artificial intelligence, etc. In this article, we will explore the concept of Matrix Addition, including its properties and solved examples as well.
## Matrix Definition
A matrix is a rectangular array or set of elements. The Matrix can be defined as an m×n element in the form of m horizontal lines (rows), and n vertical lines (columns) known as the m*n order matrix. Elements can be real, complex, or unknown numbers. An m×n matrix is given as follows:
In the above figure, a matrix of order m×n is shown where i and j represent the element’s exact position (i,j) i.e., ith row and jth column.
Matrix addition is the operation defined on the matrix to add two matrices to get a single matrix. Let’s suppose two matrices A and B, such A = [aij] and B = [bij], then their addition A + B is defined as [aij + bij], where ij represents the element in ith row and jth column.
Let’s consider the following examples for better understanding.
Example: For matrix and , calculate A + B.
Solution:
A + B =
There are various unique properties of matrix addition. We will be discussing the below-mentioned properties:
• Closure Property
• Commutative Property
• Associative Property
Let’s consider three matrices A, B, and C of the same order m×n, as to add two Matrices they need to have the same order, simply add the corresponding element of each Matrix. Let’s discuss the addition property of Matrix in detail.
### Closure Property of Matrix Addition
A matrix can be added with another matrix if and only if the order of matrices is the same. The addition will take place between the elements of the matrices. The resultant matrix will also be of the same order. That is [A]m×n + [B]m×n = [C]m×n
Example:
### Commutative Property of Matrix Addition
Commutative Property states that any two matrices of the same order can be added in any way i.e., the result of the sum of two matrices doesn’t depend on the order of the matrix in matrix addition. Suppose there are two matrices A and B of the same order m*n, then the commutative property of matrix addition states that: A + B = B + A
Example : For matrix
Thus, A + B = B + A., which demonstrates the commutative property of matrix addition.
### Associative Property of Matrix Addition
Similarly, If three matrices have the same order then their position does not matter in addition. Suppose there are three matrices A, B, and C of order m*n, then the associative property of matrix addition states that: A + (B + C) = (A + B) + C
Example: For
Therefore, (A + B) + C = A + (B + C), which demonstrates the associative property of matrix addition.
We have discussed zero Matrix that O matrix can be added to any matrix for the same result. According to the additive identity property of matrix addition, for a given matrix A of order m*n, there exists an m×n matrix O such that: A + O = A = O + A
Here, O is the m×n order zero Matrix.
Example: Let A be a 2×2 matrix, and let I be the 2×2 identity matrix. We want to show that A + O = A = O + A.
Solution:
So, if you add a matrix to a zero matrix, then you get the original Matrix.
There is a rule in Matrix that the inverse of any matrix A is –A of the same order. In simple words, for a given matrix A of order m*n, there exists a unique matrix B such that: A + B = O
Note: This matrix B is equal to –A i.e. B = -A
Therefore, A + (-A) = O
Example: Let A be a 2×2 matrix, and let -A be the additive inverse of A. We want to show that A + (-A) = O, where O is the 2×2 zero matrix.
Solution:
The additive inverse of A, denoted -A, is given by:
Now, let’s compute A + (-A).
Therefore, A + (-A) = O, which demonstrates the additive inverse property of matrix addition.
## What is Matrix Subtraction?
As we add two or more matrices in the same way we can subtract two matrices, if they are square matrices of the same order. Matrix addition is similar to matrix subtraction, we can assume that matrix subtraction is the addition of one matrix with the additive inverse of the second matrix.
If we have two matrices A and B the subtraction of A and B can be understood as, the addition of A and (-B), i.e.
A – B = A + (-B)
For further understanding study the following example,
Example: Let A and B be 2×2 matrices, where and then find A – B.
Solution:
Given,
Now, A – B = A + (-B)
Let’s compute A + (-B).
## Solved Problems on Matrix Addition
Problem 1: Perform the addition of the following matrices:
and
Solution:
To add matrices A and B, we need to add the corresponding elements of each matrix.
A + B =
Therefore, the sum of matrices A and B is
Problem 2: Given the matrices:
and
Calculate the sum of matrices X and Y.
Solution:
To add matrices X and Y, we add the corresponding elements of each matrix.
Therefore, the sum of matrices X and Y is
Problem 3: For matrix P and Q given as follows:
Compute the sum of matrices P and Q.
Solution:
P + Q =
Therefore, the sum of matrices P and Q is
Matrix addition is an operation performed on matrices, where corresponding elements of two matrices with same order are added together to form a new matrix.
### Q2: How to Add Two or More Matrices?
To add any two or more matrices of same order, we just need to add corresponding element of each matrices with all the other given matrices. For example, the element in the first row and first column of one matrix is added to the element in the first row and first column of the other matrix, and so on.
### Q3: What are the Requirements for Matrix Addition?
Only condition for addition of two matrices is that order of both matrices needs to be same i.e., if one matrix is of order m×n, then other matrix should be of the order m×n. Thus, matrices with different order can’t be added together.
### Q4: Can you Add more than Two Matrices together?
Yes, matrix addition can be performed on more than two matrices. To do this, you simply add the corresponding elements of each matrix together. The resulting sum will be the corresponding element of the new matrix.
### Q5: What are Properties of Matrix Addition?
Some properties of matrix Addition are:
• Closure Property
• Commutative Property
• Associative Property<|endoftext|>
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# Important Questions for CBSE Class 12 Maths Chapter 11 – Three Dimensional Geometry
## CBSE Class 12 Maths Chapter-11 Important Questions – Free PDF Download
Free PDF download of Important Questions for CBSE Class 12 Maths Chapter 11 – Three Dimensional Geometry prepared by expert Maths teachers from latest edition of CBSE(NCERT) books, On CoolGyan.Org to score more marks in CBSE board examination.
You can also Download Maths Revision Notes Class 12 to help you to revise complete Syllabus and score more marks in your examinations.
## 1 Mark Questions
1. Find the directions cosines of x, y and z axis.
Ans. 1,0,0, 0,1,0 0,0,1
2.Find the vector equation for the line passing through the points (-1,0,2) and (3,4,6)
Ans. Let be the p.v of the points A (-1,0,2) and B ( 3, 4 6)
3.Find the angle between the vector having direction ratios 3,4,5 and 4, -3, 5.
Ans. Let a1 = 3, b1 = 4, c1 = 5 and a2 = 4, b2 = -3, c2 = 5
4. What is the direction ratios of the line segment joining P(x1Â y1Â z1) and Q (x2Â y2Â z2)
Ans. x2 – x1, y2 – y, and z2-z1 are the direction ratio of the line segment PQ.
5. The Cartesian equation of a line is Find the vector equation for the line.
Ans. Comparing the given equation with the standard equation form
6.Show that the lines
are coplanar.
Ans. x1=-3, y1 = 1, z1 = 5
a1Â = -3, b1=1, c1= 5
x2Â = -1, y2=2, z2Â = 5
a2Â = -1, b2Â = 2, c2Â = 5
Therefore lines are coplanar.
7. If a line has the direction ratios -18, 12, -4 then what are its direction cosines
Ans. a = -18, b=12, c= -4
a2+b2+c2Â = (-18)2Â + (12)2Â + (-4)2
= 484
8. Find the angle between the pair of line given by
Ans.
9. Prove that the points A(2,1,3) B(5, 0,5)and C(-4, 3,-1) are collinear
Ans. The equations of the line AB are
If A, B, C are collinear, C lies in equation (1)
Hence A,B,C are collinear
10. Find the direction cosines of the line passing through the two points
(2,4,-5) and (1,2,3).
Ans. Let P(-2,4,-5) Q (1,2,3)
11. Find the equation of the plane with intercepts 2,3 and 4 on the x, y and z axis respectively.
Ans. Let the equation of the plane be
12.If the equations of a line AB is find the directions ratio of line parallel to AB.
Ans. the direction ratios of a line parallel to AB are 1, -2, 4
13. If the line has direction ratios 2,-1,-2 determine its direction Cosines.
Ans.Â
14. The Cartesian equation of a line is . Write its vector form
Ans.Â
15. Cartesian equation of a line AB is write the direction ratios of a line parallel to AB.
Ans. Given equation of a line can be written is
The direction ratios of a line parallel to AB are 1, -7, 2.
## 4 Mark Questions
1. Find the vector and Cartesian equation of the line through the point (5, 2,-4) and which is parallel to the vectorÂ
Ans:
Vector equation of line is
Cartesian equation is
2. Find the angle between the lines
Ans:
Let is the angle between the given lines
3. Find the shortest distance between the lines
Ans:
4. Find the direction cosines of the unit vector to the plane passing through the origin.
Ans:
Dividing equation 1 by 7
Hence direction cosines of isÂ
5. Find the angle between the two planes 3x – 6y + 2z = 7 and 2x + 2y – 2z = 5
Ans:Â Comparing the giving eq of the planes with the equations
A1Â x +B1y +C1Z + D = 0 , A2Â x + B2y + C2Â Z + D2Â = 0
A1Â = 3, B1Â = -6, C1Â = 2
A2Â = 2, B2Â = 2, C2Â = -2
6. Find the shortest between the l 1 and l2 whose vectors equations are
Ans:
7. Find the angel between lines
Ans:
The angle between them is given by
8. Show that the lines Are perpendicular to each others
Ans:
ForÂ
a1a2+b1b2+c1c2=0
L.H. S
9.Find the vector equations of the plane passing through the points R(2,5,-3), Q(-2,-3,5) and T (5,3,-3)
Ans:Let
Vector equation is
10. Find the Cartesian equation of the planeÂ
Ans:Let
Which is the required equation of plane.
11. find the distance between the lines l1Â and l2Â given by
Ans:
Hence line are parallel
12. Find the angle between lines
Ans:
13. Find the shortest distance between the lines
Ans:
14. Find the vector and Cartesian equations of the plane which passes through the point (5,2,-4) and to the line with direction ratios (2,3,-1)
Ans:
Vector equation is
Cartesian equation is
15. Find the Cartesian equation of the plane
Ans:
16. Find the distance of a point (2,5,-3) from the planeÂ
Ans:
17. Find the shortest distance
Ans:
18. Find the vector equation of a plane which is at a distance of 7 units from the origin and normal to the vectorÂ
Ans:
19. Find the Cartesian equation of planeÂ
Ans:Â
20. Find the angle between the line and the plane 10x +2y-11z=3
Ans:Â
21. Find the value of P so that the lines are at right angles.
Ans:
22. Find the shortest distance between the lines whose vector equation are
Ans:Â
23. Find x such that four points A(3,2,1) B(4,x,5)(4,2,-2) and D (6,5,-1)are coplanar.
Ans:Â The equation of plane through
A(3,2,1), C(4,2,-2) and D (6,5,-1) is
The point A,B,C,D are coplanar
24. Find the angle between the two planes 2x +y-2z=5 and 3x -6y -2z = 7using vector method.
Ans.Â
25. Find the angle b/w the line
Ans:
## 6 Marks Questions
1.Find the vector equation of the plane passing through the intersection of plane And the point (1,1,1)
Ans.
Using the relation
2. Find the coordinate where the line thorough (3,-4,-5) and ((2,-3,1) crosses the plane 2x + y + z = 7
Ans. Given points are A(3,-4,-5)
B(2,-3,1)
Direction ration of AB are 3-2, -4+3, -5-1
1,-1,-6
Eq. of line AB
are the required point
3. Find the equation of the plane through the intersection of the planes
3x – y + 2z -4 = 0 and x + y + z – 2 = 0 and the point (2,2,1)
Ans. Equation of any plane through the
intersection of given planes can be taken as
The point (2,2,1) lies in this plane
put in eq ….(i)
4. If the points (1,1p) and (-3,0,1)be equidistant from the plane , then find the value of p.
Ans.The given plane is
This plane is equidistant from the points (1,1,P) and (-3,0,1)
5. Find the equation of the plane through the line of intersection of the planes
x +y +z = 1 and 2x + 3y + 4z = 5 which is of the plane x-y + z = 0
Ans. Equations of any plane through the intersection of given planes are be written is
This plane is it right angle to the plane x-y+z
6. Find the distance of the point (-1,-5,-10) from the point of intersection of the line and the planeÂ
Ans.
Are the coordinate of the point of intersection of the given line and the planeÂ
7. Find the equation of the plane that contains the point (1,-1,2) and is to each of the plane 2x+3y-2z=5 and x+2y-3z = 8
Ans. The equation of the plane containing the given point is
A(x-1)+B(y-2)+C(Z-3)= 0….[i]
Condition of to the plane given in (i) with the plane
2x+3y-2z=5, x+2y-3z=8
2A+3B-2C=0
A+2B-3C=0
On solving
A=-5c, B=4C
5x-4y-Z=7
8. Find the vector equation of the line passing through (1,2,3) and to the planesÂ
Ans.Â
9. Find the equation of the s point where the line through the points A(3,4,1) and B(5,1,6) crosses the XY plane.
Ans. The vector equation of the line through the point A and B is
Let P be the point where the line AB crosses the XY plane. Then the position vector of the point P is the form
10. Prove that if a plane has the intercepts a,b,c is at a distance of p units from the origin then
Ans. The equation of the plane in the
intercepts from is distance of
this plane from the origin is given to be p<|endoftext|>
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This English Language quiz is called 'Verbs - Linking, Action, Transitive and Intransitive' and it has been written by teachers to help you if you are studying the subject at middle school. Playing educational quizzes is a fabulous way to learn if you are in the 6th, 7th or 8th grade - aged 11 to 14.
It costs only $12.50 per month to play this quiz and over 3,500 others that help you with your school work. You can subscribe on the page at Join Us
Learn the difference between linking, action, transitive and intransitive verbs by playing this quiz.
A linking verb connects the subject in a sentence with the predicate of the sentence.
The linking verb is always derived from the root verb “to be.” An example of a linking verb would be as follows:
The cat is Siamese.
In this sentence, “cat” is the subject and “Siamese” is the predicate. “Is” is the linking verb.
An action verb tells us what the subject is doing or what kind of movement it is performing. An example of an action verb would be the following:
She slept through the entire movie.
In this sentence “she” is the subject. Looking to find what she is doing or how she is performing, we learn that she “slept” through the entire movie. The action she took was to sleep.
A transitive verb is when an object receives an action. An example of a transitive verb is as follows:
The waves lashed against the boat.
In this sentence, the “boat” is the object and the verb is “lashed”. “Lashed is the action taking place upon the boat making “lashed” a transitive verb.
An intransitive verb is found in a sentence that does not have an object. An example of an intransitive verb is as follows:
The ball bounced.
This sentence has a subject, the ball, and a verb “bounced” but no object. Because there is no object, “bounced” in this sentence is an intransitive verb.
For each sentence below, determine if the verb is a linking verb, an action verb, a transitive verb or an intransitive verb.<|endoftext|>
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# A Guide to Drawing Spheres
When drawing a sphere turned in space, it can be difficult or tedious to accurately determine the relationships between the x, y, and z axes, and their respective ellipses. Here, I hope to show an approach that strikes a good balance between simplicity and accuracy. It is based upon three principles:
1. Each ellipse will share its minor axis with a dimensional axis (xy, or z).
2. The ellipses will intersect at angles perpendicular to one another.
3. The dimensional axes are also perpendicular to one another.
Because the intersections of the ellipses and the dimensional axes are both sets of three perpendicular lines, we can treat them as being identical.
This is combined with the observation that the minor axis of an ellipse will also be the same as a dimensional axis. With this knowledge, every line we place will allow us to deduce the other two. Don't worry about the technical details of this for now, just keep in mind that these sets of lines are related. Look for these relationships as you work through the diagram below.
To keep things from getting too complex, this method is demonstrated in an orthographic view.
This graphic requires JavaScript in order to render.
Draw a circle and its center point.
Draw a line for the y-axis through the center. It can be at any angle you like.
The x-ellipse will share it's minor axis with the y-axis, so the major axis must be drawn perpendicular to it. The major axis will touch the edges of the circle, but the minor axis can be any length you want.
Place the x-ellipse.
Note: You can now interact with the diagram.
Draw the x-axis through the center of the x-ellipse, at any angle. The rest of the sphere can now be deduced.
Draw two lines parallel to the x-axis, tangent to either side of the sphere.
Draw a line connecting where the tangent lines touch the ellipse. This is the z-axis.
This technique is based on the geometry of how a circle fits inside of a square. Two lines parallel to a center line, if drawn tangent to the edges of the circle, will touch the circle at points directly opposite one another. Connecting those two points will give you a line perpendicular to the center line.
This also works in perspective, but rather than being parallel, the tangent lines must point towards the same vanishing point as the center line.
Next are the axes for the z-ellipse. The minor axis will be identical to the x-axis, and the major axis must be perpendicular to it.
The z-ellipse will touch the edges of the circle on its major axis, and cross the points where the z-axis meets the x-ellipse. Remember, the z-axis is the line where the x and z ellipses intersect.
There is only one possible ellipse that can satisfy these constraints.*
* You may run into trouble if the sphere is at an angle where the y-ellipse is seen directly from the side. In this circumstance, the major axis of the z-ellipse will overlap the x-axis, and the two sets of points will be identical. If you need to draw a sphere at an angle like this, you can transfer lines from a side view in order to determine how wide the visible ellipses will be.
The y-axis can now be shortened to where it meets the z-ellipse. This is the line where the y and z ellipses will intersect.
For the y-ellipse, the minor axis will share the z-axis, and the major axis will be perpendicular to it.
The y-ellipse will touch the edges of the circle on its major axis. The x and y axes mark its intersections, so its border needs to cross the points where the y-axis meets the z-ellipse, and where the x-axis meets the x-ellipse.
Keep the minor axis in mind as you determine the degree at which the y-ellipse must be drawn.
Finished. Although it may seem complicated at first, you'll soon start to intuitively understand the relationships between the ellipses, dimensional axes, and intersections. When you're comfortable with this method, try it without drawing all the construction lines. You can always add them in afterwards to see how you did.<|endoftext|>
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Students (Level: K-6th grade) connect running to STEM concepts in the following ways:
1. Why does running come “naturally”? Why don’t I need to think about how to run?: Students calculate how many steps they have taken in their lifetime and muscle memory is explained.
2. How did I learn to run?: Students demonstrate and explain the process they went through as babies to learn how to run.
3. How is my body engineered to run?: Students make muscle and knee joint models.
4. How does my body have the energy to run?: Connections are made with fuel needed by machines.
5. Why do I sweat? A hands-on activity is conducted to demonstrate how sweating cools down the body.
6. How does my body work with its surroundings to move?: Demonstrations and calculations are used to explain how Newton’s 3 Laws of Motion are connected to running.
7. Why do I need running shoes?: After some discussion, students have the opportunity to design their own running shoe.<|endoftext|>
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What are Infographics?
Infographics are visual presentations of information that use the elements of design to display content. Infographics express complex messages to viewers in a way that enhances their comprehension. Images are often an extension of the content of a written article, but infographics convey a self-contained message or principle. If a road sign has too much information on it, then it is difficult to read. Infographics compress and display this information in a visually pleasing way so that drivers or viewers don’t miss the message. Infographics communicate complex data quickly and clearly, and they are considered to be effective worldwide.
How do you use Infographics in the classroom?
First, check out our 46 tools to create infographics. What you decide to do with those tools depends on if you want to make them, read them, or repackage them as other media forms. In a literature or language class for example, you might:
introduce the protagonist of a story
talk about a character’s decision in literature
highlight an important event or the climax in a story
compare a book with a movie
discuss the historical setting of a book
preteach a new subject
present a new idea or topic
Infographics can be intriguing for e-learners because they are able to combine pictures with information in a creative format using bright colors. They might be used as supplements to lesson plans or as starting points to get class discussions started.
Any discipline area can use infographics, if they have data or information to present to others.
Watch Kathy Shrock’s Presentation on Infographics as a creative assessment.
ISTE Standards Addressed:
1. Creativity and innovation
Students demonstrate creative thinking, construct knowledge, and develop innovative products and processes using technology.
a. Apply existing knowledge to generate new ideas, products, or processes
b. Create original works as a means of personal or group expression
d. Identify trends and forecast possibilities
2. Communication and collaboration
Students use digital media and environments to communicate and work collaboratively, including at a distance, to support individual learning and contribute to the learning of others.
b. Communicate information and ideas effectively to multiple audiences using a variety of media and formats
3. Research and information fluency
Students apply digital tools to gather, evaluate, and use information.
b. Locate, organize, analyze, evaluate, synthesize, and ethically use information from a variety of sources and media
d. Process data and report results
4. Critical thinking, problem solving, and decision making
Students use critical thinking skills to plan and conduct research, manage projects, solve problems, and make informed decisions using appropriate digital tools and resources.
c. Collect and analyze data to identify solutions and/or make informed decisions.
Places to Create Infographics:<|endoftext|>
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# Square root of a 2 by 2 matrix
A square root of a 2×2 matrix M is another 2 by 2 matrix R such that M = R2, where R2 stands for the matrix product of R with itself. In general there can be no, two, four or even an infinitude of square root matrices. In many cases such a matrix R can be obtained by an explicit formula.
A 2×2 matrix with two distinct nonzero eigenvalues has four square roots. A positive-definite matrix has precisely one positive-definite square root.
Square roots of a matrix of any dimension come in pairs: If R is a square root of M, then –R is also a square root of M, since (–R)(–R) = (–1)(–1)(RR) = R2 = M.
## One formula
Let[1][2]
${\displaystyle M={\begin{pmatrix}A&B\\C&D\end{pmatrix}}}$
where A, B, C, and D may be real or complex numbers. Furthermore, let τ = A + D be the trace of M, and δ = AD – BC be its determinant. Let s be such that s2 = δ, and t be such that t2 = τ + 2s. That is,
${\displaystyle s=\pm {\sqrt {\delta }},\qquad t=\pm {\sqrt {\tau +2s}}.}$
Then, if t ≠ 0, a square root of M is
${\displaystyle R={\frac {1}{t}}{\begin{pmatrix}A+s&B\\C&D+s\end{pmatrix}}={\frac {1}{t}}\left(M+sI\right).}$
Indeed, the square of R is
{\displaystyle {\begin{aligned}R^{2}&={\frac {1}{t^{2}}}{\begin{pmatrix}(A+s)^{2}+BC&(A+s)B+B(D+s)\\C(A+s)+(D+s)C&(D+s)^{2}+BC\end{pmatrix}}\\[1ex]&={\frac {1}{A+D+2s}}{\begin{pmatrix}A(A+D+2s)&(A+D+2s)B\\C(A+D+2s)&D(A+D+2s)\end{pmatrix}}=M.\end{aligned}}}
Note that R may have complex entries even if M is a real matrix; this will be the case, in particular, if the determinant δ is negative.
### Positive determinant
When a matrix can be expressed as real multiple of the exponent of a matrix, ${\textstyle r\exp(A),}$ then the square root is ${\textstyle {\sqrt {r}}\exp \left({\frac {1}{2}}A\right).}$ In this case the square root is real, and can be interpreted as the square root of a type of complex number.[3]
## Special cases of the formula
If M is an idempotent matrix, meaning that MM = M, then if it is not the identity matrix its determinant is zero, and its trace equals its rank which (excluding the zero matrix) is 1. Then the above formula has s = 0 and ${\textstyle \tau }$ = 1, giving M and –M as two square roots of M.
In general, the formula above will provide four distinct square roots R, one for each choice of signs for s and t. If the determinant δ is zero but the trace τ is nonzero, the formula will give only two distinct solutions. It also gives only two distinct solutions if δ is nonzero and τ2 = 4δ (the case of duplicate eigenvalues), in which case one of the choices for s will make the denominator t be zero.
The formula above fails completely if δ and τ are both zero; that is, if D = −A and A2 = −BC, so that both the trace and the determinant of the matrix are zero. In this case, if M is the null matrix (with A = B = C = D = 0), then the null matrix is also a square root of M, as are
${\displaystyle R={\begin{pmatrix}0&0\\c&0\end{pmatrix}}\quad {\text{and}}\quad R={\begin{pmatrix}0&b\\0&0\end{pmatrix}}}$
for any real or complex values of b and c. Otherwise M has no square root.
## Simpler formulas for special matrices
### Diagonal matrix
If M is diagonal (that is, B = C = 0), one can use the simplified formula
${\displaystyle R={\begin{pmatrix}a&0\\0&d\end{pmatrix}}}$
where a = ±√A and d = ±√D; which, for the various sign choices, gives four, two, or one distinct matrices, if none of, only one of, or both A and D are zero, respectively.
#### Identity matrix
Because it has duplicate eigenvalues, the 2×2 identity matrix ${\displaystyle \left({\begin{smallmatrix}1&0\\0&1\end{smallmatrix}}\right)}$ has infinitely many symmetric rational square roots given by
${\displaystyle {\frac {1}{t}}{\begin{pmatrix}s&r\\r&-s\end{pmatrix}},\ {\frac {1}{t}}{\begin{pmatrix}s&-r\\-r&-s\end{pmatrix}},\ {\frac {1}{t}}{\begin{pmatrix}-s&r\\r&s\end{pmatrix}},\ {\frac {1}{t}}{\begin{pmatrix}-s&-r\\-r&s\end{pmatrix}},\ {\begin{pmatrix}1&0\\0&\pm 1\end{pmatrix}},{\text{ and }}{\begin{pmatrix}-1&0\\0&\pm 1\end{pmatrix}},}$
where (r, s, t) is any Pythagorean triple—that is, any set of positive integers such that ${\textstyle r^{2}+s^{2}=t^{2}.}$[4] In addition, any non-integer, irrational, or complex values of r, s, t satisfying ${\textstyle r^{2}+s^{2}=t^{2}}$ give square root matrices. The identity matrix also has infinitely many non-symmetric square roots.
### Matrix with one off-diagonal zero
If B is zero but A and D are not both zero, one can use
${\displaystyle R={\begin{pmatrix}a&0\\{\frac {C}{a+d}}&d\end{pmatrix}}.}$
This formula will provide two solutions if A = D or A = 0 or D = 0, and four otherwise. A similar formula can be used when C is zero but A and D are not both zero.
## References
1. ^ Levinger, Bernard W.. 1980. “The Square Root of a 2 × 2 Matrix”. Mathematics Magazine 53 (4). Mathematical Association of America: 222–24. doi:10.2307/2689616.[1]
2. ^ P. C. Somayya (1997), Root of a 2x2 Matrix, The Mathematics Education, Vol.. XXXI, no. 1. Siwan, Bihar State. INDIA
3. ^ Anthony A. Harkin & Joseph B. Harkin (2004) Geometry of Generalized Complex Numbers, Mathematics Magazine 77(2):118–29
4. ^ Mitchell, Douglas W. "Using Pythagorean triples to generate square roots of I2". The Mathematical Gazette 87, November 2003, 499-500.<|endoftext|>
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# Aptitude – Problems on Logarithms
#### Aptitude – Problems on Logarithms
In this unit, You can Completely learn Aptitude – Problems on Logarithms.
#### Problems on Logarithms Important Formula:
1. Logarithm:If a is a positive real number, other than 1 and am = x, then we write:
m = logax and we say that the value of log x to the base a is m.Examples:(i). 103 1000 log10 1000 = 3.(ii). 34 = 81 log3 81 = 4.
(iii). 2-3 = 1 log2 1 = -3. 8 8
(iv). (.1)2 = .01 log(.1) .01 = 2.
2. Properties of Logarithms:1. loga (xy) = loga x + loga y
2. loga x = loga x – loga y y
3. logx x = 1
4. loga 1 = 0
5. loga (xn) = n(loga x)
6. loga x = 1 logx a
7. loga x = logb x = log x . logb a log a
3. Common Logarithms:Logarithms to the base 10 are known as common logarithms.
4. The logarithm of a number contains two parts, namely ‘characteristic’ and ‘mantissa’.Characteristic: The internal part of the logarithm of a number is called its characteristic.Case I: When the number is greater than 1.In this case, the characteristic is one less than the number of digits in the left of the decimal point in the given number.Case II: When the number is less than 1.In this case, the characteristic is one more than the number of zeros between the decimal point and the first significant digit of the number and it is negative.Instead of -1, -2 etc. we write 1 (one bar), 2 (two bar), etc.Examples:-
Number Characteristic Number Characteristic 654.24 2 0.6453 1 26.649 1 0.06134 2 8.3547 0 0.00123 3
Mantissa:
The decimal part of the logarithm of a number is known is its mantissa. For mantissa, we look through log table.
YOU
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One reason for the importance of art, claims Dewey, is that it supplies “the only media of complete and unhindered communication between man and man that can occur in a world full of gulfs and walls that limit community of experience.” Since art communicates, it requires, like language, a triadic relation of speaker (the artist), the thing said (the art product), and the hearer (the spectator). All language involves what is said and how it is said—substance and form. In art, substance is the content of the work itself; form is the organization of this content.
Each art has its own medium, fitted for a particular kind of communication. When there is a complete set of relations within a chosen medium, there is aesthetic form. Form is relation, and relations are modes of interaction: pushes, pulls, lightness, heaviness. In a successful work of art, the stresses are so adapted to one another that a unity results. The work of art satisfies many ends, none of which is laid down in advance. Artists experiment. They communicate an individual experience through materials that belong to the public world. They mean the work of art, and the work of art means whatever anyone can honestly get out of it.
Art as Experience differentiates between the art product and the work of art. The art product—the statue, the painting, the printed poem—is physical. The work of art is active and experienced. When the art product enters into experience, it takes part in a complex interaction. It is the work of art with its fixed order of elements that is perceived. However, the work of art is like an organism: It manifests movement, it has a past and present, a career, a history. Energy is organized toward some result. The spectator interacts with the work of art so that energies are given rhythmic organization, are intensified, clarified, concentrated.
The fact that art organizes energy explains its power to move and to stir, to calm and to tranquilize. Paintings that seem dead in whole or in part are those that arrest movement rather than carry it forward toward a dynamic whole. Thus aesthetic perception differs from ordinary...
(The entire section is 881 words.)
Art as Experience (1934) is John Dewey's major writing on aesthetics, originally delivered as the first William James Lecture at Harvard (1932). Dewey's aesthetics have been found useful in a number of disciplines, including new media.
Dewey had previously written articles on aesthetics in the 1880s and had further addressed the matter in Democracy and Education (1915). In his major work, Experience and Nature (1925), he laid out the beginnings of a theory of aesthetic experience, and wrote two important essays for Philosophy and Civilization (1931).
Dewey's theory, here, is an attempt to shift the understandings of what is important and characteristic about the art process from its physical manifestations in the ‘expressive object’ to the process in its entirety, a process whose fundamental element is no longer the material ‘work of art’ but rather the development of an ‘experience’. An experience is something that personally affects your life. That is why these theories are so important to our social and educational life.
Such a change in emphasis does not imply, though, that the individual art object has lost significance; far from it, its primacy is clarified: the object is recognized as the primary site for the dialectical processes of experience, as the unifying occasion for these experiences. Through the expressive object, the artist and the active observer encounter each other, their material and mental environments, and their culture at large.
The description of the actual act of experiencing is drawn heavily from the biological/psychological theories Dewey expounded in his development of functional psychology. In Dewey's article on reflex arc psychology, he writes that sensory data and worldly stimulus enter into the individual via the channels of afferent sense organs, and that the perception of these stimuli are a 'summation':
This sensory motor coordination is not a new act, supervening upon what preceded. Just as the response is necessary to constitute the stimulus, to determine it as sound and as this kind of sound…so the sound experience must persist as a value in the running, to keep it up, to control it. The motor reaction involved in the running is, once more, into, not merely to, the sound. It occurs to change the sound…The resulting quale, whatever it may be, has its meaning wholly determined by reference to the hearing of the sound. It is that experience mediated.
The biological sensory exchange between man, whom Dewey calls 'the Live Creature' in Art as Experience, and the environment, is the basis of his aesthetic theory:
...An experience is a product, one might almost say bi-product, of continuous and cumulative interaction of an organic self with the world. There is no other foundation upon which esthetic theory and criticism can build.
This is a dramatic expansion of the bounds of aesthetic philosophy, for it demonstrates the connections of art with everyday experience and in doing so reminds us of the highest responsibilities that art and society and the individual have always owed to each other:
...works of art are the most intimate and energetic means of aiding individuals to share in the arts of living. Civilization is uncivil because human beings are divided into non-communicating sects, races, nations, classes and cliques.
To emphasize what is aesthetic about an experience is not, finally, to emphasize what is apolitical or impractical or otherwise marginal about that experience; rather, it is to emphasize in what ways that experience, as aesthetic, is a 'manifestation, a record and celebration of the life of a civilization, a means for promoting its development' and, insofar as that aesthetic experience relates to the kinds of experiences had in general, it is also the 'ultimate judgment upon the quality of a civilization.'
See his Experience and Nature for an extended discussion of 'Experience' in Dewey's philosophy.
The Live Creature
John Dewey offers a new theory of art and the aesthetic experience. Dewey proposes that there is a continuity between the refined experience of works of art and everyday activities and events, and in order to understand the aesthetic one must begin with the events and scenes of daily life. This idea stands in opposition to the aesthetic theories presented by Immanuel Kant and also the proponents of German Idealism, which have historically been shown to favor certain heavily-classicized forms of art, known commonly as 'High Art' or Fine Art. Dewey argues for the validity of 'popular art' stating:
So extensive and subtly pervasive are the ideas that set art on upon a remote pedestal, that many a person would be repelled rather than pleased if told that he enjoyed his casual recreations, at least in part, because of their esthetic quality. The arts which today have most vitality for the average person are the things he does not take to be arts; for instance, the movie, jazzed music, the comic strip…
We must recover the continuity of aesthetic experience with the normal processes of living. It is the duty of the theorist to make this connection and its implications clear. If art were understood differently by the public, art would gain in public esteem and have wider appeal.
The task is to restore continuity between the refined and intensified forms of experience that are works of art and the everyday events, doings, and sufferings that are universally recognized to constitute experience.
His criticism of existing theories is that they "spiritualize" art and sever its connection with everyday experience. Glorifying art and setting it on a pedestal separates it from community life. Such theories actually do harm by preventing people from realizing the artistic value of their daily activities and the popular arts (movies, jazz, newspaper accounts of sensational exploits) that they most enjoy, and drives away the aesthetic perceptions which are a necessary ingredient of happiness.
Art has aesthetic standing only as it becomes an experience for human beings. Art intensifies the sense of immediate living, and accentuates what is valuable in enjoyment. Art begins with happy absorption in activity. Anyone who does his work with care, such as artists, scientists, mechanics, craftsmen, etc., are artistically engaged. The aesthetic experience involves the passing from disturbance to harmony and is one of man's most intense and satisfying experiences.
Art cannot be relegated to museums. There are historic reasons for the compartmentalization of art into museums and galleries. Capitalism, nationalism and imperialism have all played a major role.
The Live Creature and Ethereal Things
The title of the chapter is taken from John Keats who once wrote, in a letter to Benjamin Robert Haydon,
The Sun, the Moon, the Earth and its contents are material to form greater things, that is, ethereal things- greater things than the Creator himself has made.
In Dewey, this statement can be taken several ways: the term 'ethereal' is used in reference to the theorists of idealist aesthetics and other schools that have equated art with elements inaccessible to sense and common experience because of their perceived transcendent, spiritual qualities. This serves as a further condemnation of aesthetic theory that unjustly elevates art too far above the pragmatic, experiential roots that it is drawn from.
Another interpretation of the phrase could be that the 'earth and its contents' being, presumably, the ingredients to form 'ethereal things' further expounds the idea of Dewey's pragmatist aesthetics. In other words, the 'earth and its contents' could refer to 'human experience' being used to create art, (the 'ethereal things') which, though derived from the earth and experience, still contains a godly, creative quality not inherent in original creation.
Apart from organs inherited from animal ancestry, ideas and purpose would be without a mechanism of realization...the intervention of consciousness adds regulation, power of selection, and redisposition...its intervention leads to the idea of art as a conscious idea- the greatest intellectual achievement in the history of humanity.
Addressing the intrusion of the supernatural into art, mythology, and religious ceremony, Dewey defends the need for the esoteric in addition to pure rationalism. Furthermore, the human imagination is seen by Dewey to be a powerful synthesizing tool to express experience with the environment. Essentially, rationality alone can neither suffice to understand life completely or ensure an enriched existence.
Dewey writes that religious behaviors and rituals were
enduringly enacted, we may be sure, in spite of all practical failures, because they were immediate enhancements of the experience of living…delight in the story, in the growth and rendition of a good yarn, played its dominant part then as it does in the growth of popular mythologies today.
Art and (aesthetic) mythology, according to Dewey, is an attempt to find light in a great darkness. Art appeals directly to sense and the sensuous imagination, and many aesthetic and religious experiences occur as the result of energy and material used to expand and intensify the experience of life.
Returning to Keats, Dewey closes the chapter by making reference to another of Keat's passages,
Beauty is truth, and truth beauty—that is all ye know on Earth, and all ye need to know.
Concerning the passage, Dewey addresses the doctrine of divine revelation and the role of the imagination in experience and art.
Reasoning must fail man—this of course is the doctrine long taught by those who have held the necessity of divine revelation. Keats did not accept this supplement and substitute for reason. The insight of the imagination must suffice...ultimately there are but two philosophies. One of them accepts life and experience in all its uncertainty, mystery, doubt, and half knowledge and turns that experience upon itself to deepen and intensify its own qualities—to imagination and art. This is the philosophy of Shakespeare and Keats.
Having an Experience
John Dewey distinguishes between experience in general and "an" experience. Experience occurs continually, as we are always involved in the process of living, but it is often interrupted and inchoate, with conflict and resistance. Much of the time we are not concerned with the connection of events but instead there is a loose succession, and this is non-aesthetic. Experience, however, is not an experience.
An experience occurs when a work is finished in a satisfactory way, a problem solved, a game is played through, a conversation is rounded out, and fulfillment and consummation conclude the experience. In an experience, every successive part flows freely. An experience has a unity and episodes fuse into a unity, as in a work of art. The experience may have been something of great or just slight importance.
Such an experience has its own individualizing quality. An experience is individual and singular; each has its own beginning and end, its own plot, and its own singular quality that pervades the entire experience. The final import is intellectual, but the occurrence is emotional as well. Aesthetic experience cannot be sharply marked off from other experiences, but in an aesthetic experience, structure may be immediately felt and recognized, there is completeness and unity and necessarily emotion. Emotion is the moving and cementing force.
There is no one word to combine "artistic" and "aesthetic," unfortunately, but "artistic" refers to the production, the doing and making, and "aesthetic" to appreciating, perceiving, and enjoying. For a work to be art, it must also be aesthetic. The work of the artist is to build an experience that will be experienced aesthetically.
The Act of Expression
Artistic expression is not "spontaneous." The mere spewing forth of emotion is not artistic expression. Art requires long periods of activity and reflection, and comes only to those absorbed in observing experience. An artist's work requires reflection on past experience and a sifting of emotions and meanings from that prior experience. For an activity to be converted into an artistic expression, there must be excitement, turmoil and an urge from within to go outward. Art is expressive when there is complete absorption in the subject and a unison of present and past experience is achieved.
There are values and meanings best expressed by certain visible or audible material. Our appetites know themselves better when artistically transfigured. Artistic expression clarifies turbulent emotions. The process is essentially the same in scientists and philosophers as well as those conventionally defined as artists. Aesthetic quality will adhere to all modes of production in a well-ordered society.
The Expressive Object
The fifth chapter Dewey turns to the expressive object. He believes that the object should not be seen in isolation from the process that produced it, nor from the individuality of vision from which it came. Theories which simply focus on the expressive object dwell on how the object represents other objects and ignore the individual contribution of the artist. Conversely, theories that simply focus on the act of expressing tend to see expression merely in terms of personal discharge.
Works of art use materials that come from a public world, and they awaken new perceptions of the meanings of that world, connecting the universal and the individual organically. The work of art is representative, not in the sense of literal reproduction, which would exclude the personal, but in that it tells people about the nature of their experience.
Dewey observes that some who have denied art meaning have done so on the assumption that art does not have connection with outside content. He agrees that art has a unique quality, but argues that this is based on its concentrating meaning found in the world. For Dewey, the actual Tintern Abbey expresses itself in Wordsworth's poem about it and a city expresses itself in its celebrations. In this, he is quite different from those theorists who believe that art expresses the inner emotions of the artist. The difference between art and science is that art expresses meanings, whereas science states them. A statement gives us directions for obtaining an experience, but does not supply us with experience. That water is H
2O tells us how to obtain or test for water. If science expressed the inner nature of things it would be in competition with art, but it does not. Aesthetic art, by contrast to science, constitutes an experience.
A poem operates in the dimension of direct experience, not of description or propositional logic. The expressiveness of a painting is the painting itself. The meaning is there beyond the painter's private experience or that of the viewer. A painting by Van Gogh of a bridge is not representative of a bridge or even of Van Gogh's emotion. Rather, by means of pictorial presentation, Van Gogh presents the viewer with a new object in which emotion and external scene are fused. He selects material with a view to expression, and the picture is expressive to the degree that he succeeds.
Dewey notes that formalist art critic Roger Fry spoke of relations of lines and colors coming to be full of passionate meaning within the artist. For Fry the object as such tends to disappear in the whole of vision. Dewey agrees with the first point and with the idea that creative representation is not of natural items as they literally happen. He adds however that the painter approaches the scene with emotion-laden background experiences. The lines and colors of the painter's work crystallize into a specific harmony or rhythm which is a function also of the scene in its interaction with the beholder. This passion in developing a new form is the aesthetic emotion. The prior emotion is not forgotten but fused with the emotion belonging to the new vision.
Dewey, then, opposes the idea that the meanings of the lines and colors in a painting would completely replace other meanings attached to the scene. He also rejects the notion that the work of art only expresses something exclusive to art. The theory that subject-matter is irrelevant to art commits its advocates to seeing art as esoteric. To distinguish between aesthetic values of ordinary experience (connected with subject-matter) and aesthetic values of art, as Fry wished, is impossible. There would be nothing for the artist to be passionate about if she approached the subject matter without interests and attitudes. The artist first brings meaning and value from earlier experience to her observation giving the object its expressiveness. The result is a completely new object of a completely new experience.
For Dewey, an artwork clarifies and purifies confused meaning of prior experience. By contrast, a non-art drawing that simply suggests emotions through arrangements of lines and colors is similar to a signboard that indicates but does not contain meaning: it is only enjoyed because of what they remind us of. Also, whereas a statement or a diagram takes us to many things of the same kind, an expressive object is individualized, for example in expressing a particular depression.
Substance and Form
Consistent with his non-dualistic thinking, Dewey does not draw a sharp distinction between substance and form. He states that “there can be no distinction drawn, save in reflection, between form and substance.” For Dewey, substance is different from subject. One could say that Keats’ Ode to a Nightingale has a nightingale for a subject, but for Dewey the substance of the poem is the poem. Substance represents the culmination of the artist’s creative efforts. Form for Dewey is the quality of having form. Having form allows the substance to be evoked in such a way that “it can enter into the experiences of others and enable them to have more intense and more fully rounded out experiences of their own.” This process exemplifies Dewey’s triadic relationship between artist, art object, and creative viewer.
Natural History of Form
In this chapter, Dewey states that the “formal conditions of artistic form” are “rooted deep in the world itself.” The interaction of the living organism with its environment is the source of all forms of resistance, tension, furtherance, balance – that is, those elements essential for aesthetic experience and which, themselves, constitute form. These elements of interaction are subsumed in one broad term for Dewey, rhythm. He states: “There is rhythm in nature before poetry, painting, architecture and music exist.” These larger rhythms of nature include the cycles of day and night, the seasons, the reproduction of plants and animals, as well as the development of human craft necessary for living with these changes in nature. This gives rise to the development of the rituals for planting, harvest, and even war. These rhythms of change and repetition have seated themselves deep in human subconsciousness. Via this path from nature, we find the essential rhythms of all the arts. Dewey writes: “Underneath the rhythm of every art and of every work of art there lies, as a substratum in the depths of the subconsciousness, the basic pattern of the relations of the live creature to his environment.” The aesthetic deployment of these rhythms constitutes artistic form.
Organization of Energies
Energy pervades the work of art, and the more that energy is clarified, intensified, and concentrated, the more compelling the work of art should be. Dewey gives the example of young children intending to act a play. “They gesticulate, tumble and roll, each pretty much on his own account, with little reference to what others are doing.” This is contrasted with the “well-constructed and well-executed” play. However, it does not necessarily follow that the latter play will be better than the former. This is merely an extreme case of contrasting aesthetic values based on different organizations of energy. The organization of energy manifests itself in patterns or intervals, now more now less. This patterning is related to Dewey’s earlier ideas on rhythm. He writes that instances of energy are “piecemeal, one replacing another…And thus we are brought again to rhythm.” However, the organization of energies is not the same as rhythm. The organization of energy is important as “the common element in all the arts” for “producing a result.” Artistic skill exemplifies skillful organization of energy. An over-emphasis of a single source of energy (at the expense of others sources of energy) in a work of art shows poor organization of energy. At the end of the chapter, Dewey states that art is, in fact, “only definable as organization of energies.” The power of art to “move and stir, to calm and tranquilize” is intelligible only when “the fact of energy” is made central to an understanding of art. The qualities of order and balance in works of art follow from the selection of significant energy. Great art, therefore, finds and deploys ideal energy.
The Common Substance of the Arts
In this chapter Dewey examines several qualities that are common to all works of art. Early in the chapter, Dewey discusses the feeling of a “total seizure”, a sense of “an inclusive whole not yet articulated” that one feels immediately in the experiencing of a work of art. This sense of wholeness, of all the parts of the work coalescing, can only be intuited. Parts of the work of art may be discriminated, but their sense of coalescence is a quality of intuition. Without this “intuited enveloping quality, parts are external to one another and mechanically related.”
This sense of wholeness conveyed by the work of art distinguishes the work from the background in which it sits. Evidence of this idea of the artwork standing apart from its background is “our constant sense of things as belonging or not belonging, of relevancy, a sense which is immediate.” Yet the background represents the “unlimited envelope” of the world we live in, and the work of art, though seen as a discrete thing, is intimately connected with the larger background. We intuit this connection, and in this process there is something mystical. “An experience becomes mystical in the degree which the sense, the feeling, of the unlimited envelope becomes intense – as it may do in the experience of an art object.” Though this mystical quality may not be a common substance of all art objects, the sense of wholeness within the object and its relation to a background are.
A further common substance to all works of art is related to the idea of means and ends. In aesthetic works and aesthetic experience, means and ends coalesce. Means are ends in the aesthetic. The non-aesthetic has a clear separation of means and ends: means are merely means, mechanical steps used solely to achieve the desired end. Dewey uses the idea of “journeying” as an example. Non-aesthetic journeying is undertaken merely to arrive at the destination; any steps to shorten the trip are gladly taken. Aesthetic journeying is undertaken for “the delight of moving about and seeing what we see.” Extending non-aesthetic experience may lead to frustration and impatience, whereas drawing out aesthetic experience may increase a feeling of pleasure.
Every artwork and art discipline has a “special medium” that it exploits. In doing so, the different disciplines achieve the sense of wholeness in a given work, and the coalescing of ends and means in qualitatively different ways. “Media are different in the different arts. But possession of a medium belongs to them all. Otherwise they would not be expressive, nor without the common substance could they possess form.”
Dewey discusses another matter that is common to the substance of all works of art: space and time. Both space and time have qualities of room, extent, and position. For the concept of space, he identifies these qualities as spaciousness, spatiality, and spacing. And for the concept of time: transition, endurance, and date. Dewey devotes most of the remainder of the chapter to a discussion of these qualities in different art works and disciplines.
In the final paragraphs, Dewey summarizes the chapter. He claims that there must be common substance in the arts “because there are general conditions without which an experience is not possible.” Ultimately, then, it is the person experiencing the artwork who must distinguish and appreciate these common qualities, for “the intelligibility of a work of art depends upon the presence to the meaning that renders individuality of parts and their relationship in the whole directly present to the eye and ear trained in perception.”
The Varied Substance of the Arts
The Human Contribution
The Challenge to Philosophy
Criticism and Perception
Art and Civilization
- ^Stanford Encyclopedia of Philosophy
- ^Art as Experience p. 220
- ^Art as Experience p. 336
- ^Art as Experience p. 326
- ^Art as Experience p. 06
- ^Art as Experience p. 03
- ^Art as Experience p.20
- ^Art as Experience p. 25
- ^Art as Experience p.30
- ^Ode on a Grecian Urn
- ^Art as Experience p.34<|endoftext|>
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Child labor is a serious problem in many parts of the world, especially in developing countries. It has been linked to many nations and cultures for hundreds of years. Child labor is defined by Article 32 of the Convention on the Rights of the Child: as any economic exploitation or work that is likely to be hazardous or interferes with the child’s education, or is harmful to the child’s health or physical, mental, spiritual, moral, or social development. Labor is defined as a difficult, or fatiguing mental and/or physical work.
It wasn’t until the Industrial Revolution that it became the problem it is today. With the arrival of the factory system in the 18th century, during the 1700s, children as young as five were being used as workers in England. During this period, a law called the English Poor Act gave the government the responsibility to care for children that had no parents or whose parents were too poor to care for them. Under this law, the government would take these “pauper children” and place them in jobs where they could become apprentices and learn a trade.
The law was not usually affective because when children were handed over to the factory owners and usually became slaves. This is a violation of the “Human Rights Document: Universal Declaration of Human Rights” in article 4, which states: no one shall be held in slavery or servitude; slavery and the slave trade shall be prohibited in all their forms. Children were used to tend to machines in factories and many worked in the dark, damp coalmines, carrying coal on their backs up ladders. Many children would work 10 to 15 hour days. This is a violation of the “Human Rights Document” in article 24, which states: everyone has the right to rest and leisure, including reasonable limitation of working hours and periodic holidays with pay. They were forced to work in dangerous and unhealthy conditions, and their wages were incredibly small. There are many reasons why these children work; poverty, lack of education, lack of knowledge of one’s rights, and cultural tradition are all contributing factors. These children are often deprived and mistreated. They may get beaten or severely punished for making even the slightest mistake. This is another violation of the “Human Rights Document” in article 1, which states: all human beings are born free and equal in dignity and rights. They are endowed with reason and conscience and should act toward one another in a spirit of brotherhood. Also in article 3, which states: Everyone has the right to life, liberty, and security of a person. The U.S. Congress passed the first federal child labor law in 1916.
The International Labor organization estimates that there are 250 million children worldwide, between the ages of five and fourteen, who are now working. Africa and Asia together account for over 90 percent of total child employment. Usually there are no age requirements for work. By 1890, nearly 20 percent of U.S. children were employed full time.
In a recent story, a boy named Iqbal Masih, in Pakistan, was forced into child labor as a carpet weaver and suffered terrible abuse. At the age of four, the boy was sold as an indentured servant to a factory owner for the equivalent of sixteen dollars. Iqbal’s parents were forced to sell him in order to feed and clothe the rest of their family, a situation that is extremely common in the poor villages of India. At the factory, Iqbal would begin work around 6 a.m., working 14- hour days with one 30- minute break for lunch. The conditions in the factory were very poor with very little lighting and no fresh air. The children that worked there were not allowed to speak and were often beaten if they broke the rules or made mistakes. When Iqbal turned 10 years old, he was severely beaten by the factory owner, and decided to escape and report it to the police. When the police looked the other way, he was sent back to the factory and was chained to his loom. Some time later, Iqbal escaped and went to a meeting of the Bonded Labor Liberation Front, an organization whose goal was to free Pakistan’s bonded workers. With help from the organization, he could be set free and started to attend a school. Child labor is a violation of the “Human Rights Document” in article 26, which states: Everyone has the right to an education. Education shall be directed to the full development of the human personality and to the strengthening of respect for human rights and fundamental freedoms. It shall promote understanding, tolerance, and friendship among all nations. The ILO, is in charge of the monitoring of worker’s rights by the United Nations.
In the current expanding economy, multinational corporations take advantage of child labor to keep their prices down. A 1996 ILO study concluded that another reason for the high amount of children workers is because children are less aware of their rights, less troublesome, and more willing to take orders without complaining.
The town of Sialkot, Pakistan, is the site of some of the worse child labor practices in the world. Over 7,500 children under the age of fourteen make surgical instruments like scalpels and forceps out of metal. They are exposed to harmful metal vapor and extreme heat that could instantly burn them critically without safety precautions. This is another violation of the “Human Rights Document” in article 23, which states: everyone has the right to work, free choice of employment, to just and favorable conditions of work and to protection against unemployment. Everyone, without any discrimination, has the right to equal pay for equal work. India’s Finance Minister stated, “We have laws prohibiting child labor, but the government has found it’s not always possible to enforce them in a country as large as India.”
Major export industries which utilize child labor include hand-knotted carpets, gemstone polishing, brass and base metal articles, glass, footwear, textiles, silk, and fireworks. Other industries include, slate mining, furniture making, and food processing.
Annually there are over 200,000 injuries of children in our Nation’s workplaces and 100 deaths among our working youth. During the last 5 months of 1997, reporters from the Associated Press (AP) investigated various workplaces in 16 states and found 165 children working illegally.
According to the U.S. News & World Report in Malaysia, children have worked up to seventeen hours on plantations, exposed to insect and snake- bites. In the United Republic of Tanzania, they pick coffee, inhaling pesticides. In Portugal, children as young as twelve, are subjected to heavy labor and dangers of the construction industry. In Morocco, they receive little pay for knotting the strands of luxury carpets for export. In boot factories, children are forced to sit so close together that they poke each other with needles; many have lost an eye in this way.
In some countries, ideas about kinds of activities are based on the caste system, which categorizes people from birth into economic groups ranging from a ruling upper class to a low class almost as powerless as slaves. In Pakistan, for example, the children with the lowest castes become laborers almost as soon as they can walk.
Another recent chilling story was of a repeated abuse on a domestic worker Dhiraj K.C. When he was a very young child, he began to work for a medical company. According to CWIN, an agency caring for abused child laborers, reported that the children were physically and mentally abused over a period of five years. Dhiraj had numerous scars from being beaten with a hot iron, forced to wear chains from his neck to his feet while he worked, and chained naked outside all night in freezing weather. On one occasion, the employer used a hypodermic needle to inject an anesthetic into Dhiraj’s lip, causing numbness and preventing him from speaking. Another time, the employer pushed handfuls of raw chilies down his throat and then forced him to eat boiling hot rice. He finally escaped by crawling in chains to the streets where the police picked him up; he was then rescued by the CWIN. This was another violation of the “Human Rights Document” in article 5, which states: no one shall be subjected to torture or cruel, inhuman or degrading treatment or punishment.
Though there are more child workers in Asia than anywhere else, a higher percentage of African children participate in the work force. Asia is led by India, which has 44 million child laborers, giving it the largest child work force in the world. In Pakistan, 10 percent of all workers are between the ages of ten and fourteen years old. Nigeria has 12 million child workers. Children are sent to work to help support their families who might be in such desperate conditions that even the little salary they receive will help. This is a violation of the “Human Rights Document” in article 25, which states: everyone has the right to a standard of living adequate for the health and well-being of himself and of his family, including food, clothing, housing, and medical care and necessary social services.
A number of approaches have been suggested to fight child labor. The major attempted solutions have consisted of reducing poverty, educating children, providing support services for working children, raising public awareness, legislating and regulating child labor, and promoting elimination of abusive child labor through international measures. These approaches are, of course, not equally exclusive and are adopted in various combinations in child labor reduction strategies. Not all of these have been adopted, however, the legislation and regulation are major concerns of many governments. Other measures aimed at the direct elimination of child labor include, rescue by NGOs of children in the worst conditions and the establishment of motivational camps in which children leave work and attend informal education and recreational facilities on a residential basis for a period of time.
Dozens of International Labor Organizations conventions and other international treaties pertain to child labor and set guidelines for national laws and policies to eliminate the exploitation of children. The 1989 United Nations (CRC) is one international agreement that indicates broad measures to protect children’s rights. As the preamble to the convention points out, “children, because of their vulnerability, need special care and protection. It emphasizes the responsibility of the family for primary care and protection and also “the need for legal and other protection of the child before and after birth, the importance of respect for the cultural values of the child’s community is the vital role of international cooperation in securing children’s rights.
Several bills were introduced in the U.S. Congress during the early 1900s to regulate child labor in businesses involved in interstate commerce (selling and transporting goods across state lines) but the NCLC did not support federal legislation. In 1995, Senator Tom Harkin, of Iowa, proposed a federal law that calls for a ban on the commercial exploitation of children and prohibits the import of products made by child labor. Companies violating the prohibition against importing these products would be subject to firm penalties.
Working towards a solution, there are many problem areas that need to be addressed when it comes to child labor. One possible solution can be found in education, of both children and adults, in the countries where child labor is common. The more educated the population, the more aware they will be of what is going on around them and how they can make the necessary changes. Their needs to be some type of social awareness in order for any changes to take place. There are so many different organizations here in America that try to raise awareness about child labor. One of these organizations is called Free The Children And Child Labor Coalition.
The ILO could not put an end to all the child labor; they don’t have any legal power. The trade unions are weak and don’t have the funds to do the job. Over several years the proposed law, now known as the Child Labor Deterrence Act, has been reintroduced along with a companion bill in the House. However, no vote has been taken on the House bill and the proposal was still pending at the beginning of 1998.
Some U.S. cities are passing laws to ensure that the goods they purchase are not made in foreign or domestic sweatshops. In 1992, the organization established the International Program on the Elimination of Child Labor (IPEC), which has implemented more than 600 action programs in 27 countries. The goal of these programs is to prevent and fight child labor by helping children withdraw from work in selected villages, provide support services for the children and their families, and change community attitudes towards child labor.
Putting an end to child labor requires changes on many fronts, especially on attitudes about child labor and the world’s poor. To help bring about changes in attitudes, activists in many countries are raising awareness that child labor violates fundamental human rights.
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Directions: Divide the class into two groups. Group #1 learns the
Group #2 learns the “chuck a” part.
The following pattern is used: Group #1 – How much wood would a wood chuck chuck, if a wood
chuck would chuck wood?
Group #2 – Chucka, chucka, chucka, chucka (continuously said over and over).
Groups #1 and #2 – Both parts are said at the same time.<|endoftext|>
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Greeting fellow coder.
Thank you for checking out my blog on breaking down Hash table. I will go over what it is, how to use it, and why you need to know this data-structure.
A hash table, is a data structure that uses a hash function to efficiently map keys to values, for efficient search/retrieval, insertion, and/or removals.
Hash table is one of many data structure in computer science, for which their purpose is to essentially organize data, using a variety of management and storage format that enables us to efficiently access and modify them.
There are many other data structures like array, linked list, binary tree, etc.
For this article I will focus on Hash Table, which is widely used in many kinds of computer software, particularly for associative arrays, database indexing, caches, and sets.
Like any data structure, hash table is use to help solve data problems.
Basically how efficient in time and space can you....
- searching for an item
- insert an item
- delete an item
The way a Hash table work is using Key => value lookup
A.) You take input keys run it through a hash function where it will map those input keys into numbers which corresponds to number of indexes in an array.
Lets say I have a list of names Michael, Bob, Jack, Becky. (these are my input keys)
There are many ways you can code a hash function, but essentially the hash function should take in a input string (the names we listed) converts them into an integer, and then remaps that integer into an index in an arrays.
C.) Boom we have associative values. Where we can now search, insert, and delete our data by using the Array index.
note: The array that stores the data from the hash table will likely always be much smaller than all of the available potential hash code or key inputs.
So lets picture we ran those names listed earlier into a hash function that holds the a max index of 7.
[undefined, [Bob], undefined, undefined,[Becky], [[Michael], [Jack]], undefined,]
So you can see there is 7 index in the array and all of those names have been map to a particular index.
We can now search for a particular name, like Bob is at array Becky is at so on and so forth.
*but what about array which holds Michael and Jack.....well what a perfect segway into my-
"last but not least" note: because of a finite index, this opens the door for "collision" which is when 2 or more hash code is map in the same index.
There are different ways to resolve a collision, a very common way is by storing them in a linked list rather than just the strings. Just think of it as assigning an id to each name then storing it on a hash table.
So when looping through an index with multiple keys you are able to reference the specific name you want with their linked id.
That's about the basics of how a hash table operates. If you wish to learn more about hash tables the website below VisuAlgo does a great job in presenting hash tables and other data structure in easy to understand slides and interactive activities.
To do well in tech interview of course....
Technically yes, but also remember data structures like hash table are methods to efficiently search, insert, and delete data. And hash table is one of the more popular methods use because of how efficient they are.
In terms of Big O notation, the average time to search, insert, and delete data is O(1) which is pretty fast compare to all of the other data structure methods.
hopefully this article was helpful.
Thanks for reading me !<|endoftext|>
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The introspection illusion is a cognitive bias in which people wrongly think they have direct insight into the origins of their mental states, while treating others' introspections as unreliable. In certain situations, this illusion leads people to make confident but false explanations of their own behaviour (called "causal theories") or inaccurate predictions of their future mental states.
The illusion has been examined in psychological experiments, and suggested as a basis for biases in how people compare themselves to others. These experiments have been interpreted as suggesting that, rather than offering direct access to the processes underlying mental states, introspection is a process of construction and inference, much as people indirectly infer others' mental states from their behaviour.
When people mistake unreliable introspection for genuine self-knowledge, the result can be an illusion of superiority over other people, for example when each person thinks they are less biased and less conformist than the rest of the group. Even when experimental subjects are provided with reports of other subjects' introspections, in as detailed a form as possible, they still rate those other introspections as unreliable while treating their own as reliable. Although the hypothesis of an introspection illusion informs some psychological research, the existing evidence is arguably inadequate to decide how reliable introspection is in normal circumstances. Correction for the bias may be possible through education about the bias and its unconscious nature.
- 1 Components
- 2 Unreliability of introspection
- 3 Choice blindness
- 4 Attitude change
- 5 A priori causal theories
- 6 Explaining biases
- 7 Correcting for the bias
- 8 See also
- 9 Notes
- 10 Sources
- 11 Further reading
- 12 External links
- People give a strong weighting to introspective evidence when assessing themselves.
- They do not give such a strong weight when assessing others.
- People disregard their own behaviour when assessing themselves (but not others).
- Own introspections are more highly weighted than others. It is not just that people lack access to each other's introspections: they regard only their own as reliable.
Unreliability of introspection
A 1977 paper by psychologists Richard Nisbett and Timothy D. Wilson challenged the directness and reliability of introspection, thereby becoming one of the most cited papers in the science of consciousness. Nisbett and Wilson reported on experiments in which subjects verbally explained why they had a particular preference, or how they arrived at a particular idea. On the basis of these studies and existing attribution research, they concluded that reports on mental processes are confabulated. They wrote that subjects had, "little or no introspective access to higher order cognitive processes". They distinguished between mental contents (such as feelings) and mental processes, arguing that while introspection gives us access to contents, processes remain hidden.
Although some other experimental work followed from the Nisbett and Wilson paper, difficulties with testing the hypothesis of introspective access meant that research on the topic generally stagnated. A ten-year-anniversary review of the paper raised several objections, questioning the idea of "process" they had used and arguing that unambiguous tests of introspective access are hard to achieve.
Updating the theory in 2002, Wilson admitted that the 1977 claims had been too far-reaching. He instead relied on the theory that the adaptive unconscious does much of the moment-to-moment work of perception and behaviour. When people are asked to report on their mental processes, they cannot access this unconscious activity. However, rather than acknowledge their lack of insight, they confabulate a plausible explanation, and "seem" to be "unaware of their unawareness".
The idea that people can be mistaken about their inner functioning is one applied by eliminative materialists. These philosophers suggest that some concepts, including "belief" or "pain" will turn out to be quite different from what is commonly expected as science advances.
The faulty guesses that people make to explain their thought processes have been called "causal theories". The causal theories provided after an action will often serve only to justify the person's behaviour in order to relieve cognitive dissonance. That is, a person may not have noticed the real reasons for their behaviour, even when trying to provide explanations. The result is an explanation that mostly just makes themselves feel better. An example might be a man who discriminates against homosexuals because he is embarrassed that he himself is attracted to other men. He may not admit this to himself, instead claiming his prejudice is because he believes that homosexuality is unnatural.
A study conducted by philosopher Eric Schwitzgebel and psychologist Russell T. Hurlburt was set up to measure the extent of introspective accuracy by gathering introspective reports from a single individual who was given the pseudonym "Melanie". Melanie was given a beeper which sounded at random moments, and when it did she had to note what she was currently feeling and thinking. After analyzing the reports the authors had mixed views about the results, the correct interpretation of Melanie's claims and her introspective accuracy. Even after long discussion the two authors disagreed with each other in the closing remarks, Schwitzgebel being pessimistic and Hurlburt optimistic about the reliability of introspection.
Factors in accuracy
Nisbett and Wilson conjectured about several factors that they found to contribute to the accuracy of introspective self-reports on cognition.
- Availability: Stimuli that are highly salient (either due to recency or being very memorable) are more likely to be recalled and considered for the cause of a response.
- Plausibility: Whether a person finds a stimulus to be a sufficiently likely cause for an effect determines the influence it has on their reporting of the stimulus.
- Removal in time: The greater the distance in time since the occurrence of an event, the less available and more difficult to accurately recall it is.
- Mechanics of judgment: People do not recognize the influence that judgment factors (e.g., position effects) have on them, leading to inaccuracies in self-reporting.
- Context: Focusing on the context of an object distracts from evaluation of that object and can lead people to falsely believe that their thoughts about the object are represented by the context.
- Non-events: The absence of an occurrence is naturally less salient and available than an occurrence itself, leading nonevents to have little influence on reports.
- Nonverbal behaviour: While people receive a large amount of information about others via nonverbal cues, the verbal nature of relaying information and the difficulty of translating nonverbal behaviour into verbal form lead to its lower reporting frequency.
- Discrepancy between the magnitudes of cause and effect: Because it seems natural to assume that a certain size cause will lead to a similarly-sized effect, connections between causes and effects of different magnitudes are not often drawn.
Unawareness of error
Several hypotheses to explain people's unawareness of their inaccuracies in introspection were provided by Nisbett and Wilson:
- Confusion between content and process: People are usually unable to access the exact process by which they arrived at a conclusion, but can recall an intermediate step prior to the result. However, this step is still content in nature, not a process. The confusion of these discrete forms leads people to believe that they are able to understand their judgment processes. (Nisbett and Wilson have been criticized for failing to provide a clear definition of the differences between mental content and mental processes.)
- Knowledge of prior idiosyncratic reactions to a stimulus: An individual's belief that they react in an abnormal manner to a stimulus, which would be unpredictable from the standpoint of an outside observer, seems to support true introspective ability. However, these perceived covariations may actually be false, and truly abnormal covariations are rare.
- Differences in causal theories between subcultures: The inherent differences between discrete subcultures necessitates that they have some differing causal theories for any one stimulus. Thus, an outsider would not have the same ability to discern a true cause as would an insider, again making it seem to the introspector that they have the capacity to understand the judgment process better than can another.
- Attentional and intentional knowledge: An individual may consciously know that they were not paying attention to a certain stimulus or did not have a certain intent. Again, as insight that an outside observer does not have, this seems indicative of true introspective ability. However, the authors note that such knowledge can actually mislead the individual in the case that it is not as influential as they may think.
- Inadequate feedback: By nature, introspection is difficult to be disconfirmed in everyday life, where there are no tests of it and others tend not to question one's introspections. Moreover, when a person's causal theory of reasoning is seemingly disconfirmed, it is easy for them to produce alternative reasons for why the evidence is actually not disconfirmatory at all.
- Motivational reasons: Considering one's own ability to understand their reasoning as being equivalent to an outsider's is intimidating and a threat to the ego and sense of control. Thus, people do not like to entertain the idea, instead maintaining the belief that they can accurately introspect.
The claim that confabulation of justifications evolved to relieve cognitive dissonance is criticized by some evolutionary biologists for assuming the evolution of a mechanism for feeling dissonanced by a lack of justification. These evolutionary biologists argue that if causal theories had no higher predictive accuracy than prejudices that would have been in place even without causal theories, there would be no evolutionary selection for experiencing any form of discomfort from lack of causal theories. The claim that studies in the United States that appear to show a link between homophobia and homosexuality can be explained by an actual such link is criticized by many scholars. Since much homophobia in the United States is due to religious indoctrination and therefore unrelated to personal sexual preferences, they argue that the appearance of a link is due to volunteer-biased erotica research in which religious homophobes fear God's judgment but not being recorded as "homosexual" by Earthly psychologists while most non-homophobes are misled by false dichotomies to assume that the notion that men can be sexually fluid is somehow "homophobic" and "unethical".
Inspired by the Nisbett and Wilson paper, Petter Johansson and colleagues investigated subjects' insight into their own preferences using a new technique. Subjects saw two photographs of people and were asked which they found more attractive. They were given a closer look at their "chosen" photograph and asked to verbally explain their choice. However, in some trials, the experimenter had slipped them the other photograph rather than the one they had chosen, using sleight of hand. A majority of subjects failed to notice that the picture they were looking at did not match the one they had chosen just seconds before. Many subjects confabulated explanations of their preference. For example, a man might say "I preferred this one because I prefer blondes" when he had in fact pointed to the dark-haired woman, but had been handed a blonde. These must have been confabulated because they explain a choice that was never made. The large proportion of subjects who were taken in by the deception contrasts with the 84% who, in post-test interviews, said that hypothetically they would have detected a switch if it had been made in front of them. The researchers coined the phrase "choice blindness" for this failure to detect a mismatch.
A follow-up experiment involved shoppers in a supermarket tasting two different kinds of jam, then verbally explaining their preferred choice while taking further spoonfuls from the "chosen" pot. However, the pots were rigged so that, when explaining their choice, the subjects were tasting the jam they had actually rejected. A similar experiment was conducted with tea. Another variation involved subjects choosing between two objects displayed on PowerPoint slides, then explaining their choice when the description of what they chose had been altered.
Research by Paul Eastwick and Eli Finkel (relationship psychologist) at Northwestern University also undermined the idea that subjects have direct introspective awareness of what attracts them to other people. These researchers examined male and female subjects' reports of what they found attractive. Men typically reported that physical attractiveness was crucial while women identified earning potential as most important. These subjective reports did not predict their actual choices in a speed dating context, or their dating behaviour in a one-month follow-up.
Consistent with choice blindness, Henkel and Mather found that people are easily convinced by false reminders that they chose different options than they actually chose and that they show greater choice-supportive bias in memory for whichever option they believe they chose.
It is not clear, however, the extent to which these findings apply to real-life experience when we have more time to reflect or use actual faces (as opposed to gray-scale photos). As Prof. Kaszniak points out: "although a priori theories are an important component of people's causal explanations, they are not the sole influence, as originally hypothesized by Nisbett & Wilson. Actors also have privileged information access that includes some degree of introspective access to pertinent causal stimuli and thought processes, as well as better access (than observers) to stimulus-response covariation data about their own behaviour".[better source needed] Other criticisms point out that people who volunteer to psychology lab studies are not representative of the general population and also are behaving in ways that do not reflect how they would behave in real life. Examples include people of many different non-open political ideologies, despite their enmity to each other, having a shared belief that it is "ethical" to give an appearance of humans justifying beliefs and "unethical" to admit that humans are open-minded in the absence of threats that inhibit critical thinking, making them fake justifications.
Studies that ask participants to introspect upon their reasoning (for liking, choosing, or believing something, etc.) tend to see a subsequent decrease in correspondence between attitude and behaviour in the participants. For example, in a study by Wilson et al., participants rated their interest in puzzles that they had been given. Prior to rating, one group had been instructed to contemplate and write down their reasons for liking or disliking the puzzles, while the control group was given no such task. The amount of time participants spent playing with each puzzle was then recorded. The correlation between ratings of and time spent playing each puzzle was much smaller for the introspection group than the control group.
A subsequent study was performed to show the generalizability of these results to more "realistic" circumstances. In this study, participants were all involved in a steady romantic relationship. All were asked to rate how well-adjusted their relationship was. One group was asked to list all of the reasons behind their feelings for their partner, while the control group did not do so. Six months later, the experimenters followed up with participants to check if they were still in the same relationship. Those who had been asked to introspect showed much less attitude-behaviour consistency based upon correlations between earlier relationship ratings and whether they were still dating their partners. This shows that introspection was not predictive, but this also probably means that the introspection has changed the evolution of the relationship.
The authors theorize that these effects are due to participants changing their attitudes, when confronted with a need for justification, without changing their corresponding behaviours. The authors hypothesize that this attitude shift is the result of a combination of things: a desire to avoid feeling foolish for simply not knowing why one feels a certain way; a tendency to make justifications based upon cognitive reasons, despite the large influence of emotion; ignorance of mental biases (e.g., halo effects); and self-persuasion that the reasons one has come up with must be representative with their attitude. In effect, people attempt to supply a "good story" to explain their reasoning, which often leads to convincing themselves that they actually hold a different belief. In studies wherein participants chose an item to keep, their subsequent reports of satisfaction with the item decreased, suggesting that their attitude changes were temporary, returning to the original attitude over time.
Introspection by focusing on feelings
In contrast with introspection by focusing on reasoning, that which instructs one to focus on their feelings has actually been shown to increase attitude-behaviour correlations. This finding suggests that introspecting on one's feelings is not a maladaptive process.
The theory that there are mental processes that act as justifications do not make behaviour more adaptive is criticized by some biologists who argue that the cost in nutrients for brain function selects against any brain mechanism that does not make behaviour more adapted to the environment. They argue that the cost in essential nutrients causes even more difficulty than the cost in calories, especially in social groups of many individuals needing the same scarce nutrients, which imposes substantial difficulty on feeding the group and lowers their potential size. These biologists argue that the evolution of argumentation was driven by the effectiveness of arguments on changing risk perception attitudes and life and death decisions to a more adaptive state, as "luxury functions" that did not enhance life and death survival would lose the evolutionary "tug of war" against the selection for nutritional thrift. While there have been claims of non-adaptive brain functions being selected by sexual selection, these biologists criticize any applicability to introspection illusion's causal theories because sexually selected traits are most disabling as a fitness signal during or after puberty but human brains require the highest amount of nutrients before puberty (enhancing the nerve connections in ways that make adult brains capable of faster and more nutrient-efficient firing).
A priori causal theories
In their classic paper, Nisbett and Wilson proposed that introspective confabulations result from a priori theories, of which they put forth four possible origins:
- Explicit cultural rules (e.g., stopping at red traffic lights)
- Implicit cultural theories, with certain schemata for likely stimulus-response relationships (e.g., an athlete only endorses a brand because he is paid to do so)
- Individual observational experiences that lead one to form a theory of covariation
- Similar connotation between stimulus and response
The authors note that the use of these theories does not necessarily lead to inaccurate assumptions, but that this frequently occurs because the theories are improperly applied.
Pronin argues that over-reliance on intentions is a factor in a number of different biases. For example, by focusing on their current good intentions, people can overestimate their likelihood of behaving virtuously.
In perceptions of bias
The bias blind spot is an established phenomenon that people rate themselves as less susceptible to bias than their peer group. Emily Pronin and Matthew Kugler argue that this phenomenon is due to the introspection illusion. In their experiments, subjects had to make judgments about themselves and about other subjects. They displayed standard biases, for example rating themselves above the others on desirable qualities (demonstrating illusory superiority). The experimenters explained cognitive bias, and asked the subjects how it might have affected their judgment. The subjects rated themselves as less susceptible to bias than others in the experiment (confirming the bias blind spot). When they had to explain their judgments, they used different strategies for assessing their own and others' bias.
Pronin and Kugler's interpretation is that when people decide whether someone else is biased, they use overt behaviour. On the other hand, when assessing whether or not they themselves are biased, people look inward, searching their own thoughts and feelings for biased motives. Since biases operate unconsciously, these introspections are not informative, but people wrongly treat them as reliable indication that they themselves, unlike other people, are immune to bias.
Pronin and Kugler tried to give their subjects access to others' introspections. To do this, they made audio recordings of subjects who had been told to say whatever came into their heads as they decided whether their answer to a previous question might have been affected by bias. Although subjects persuaded themselves they were unlikely to be biased, their introspective reports did not sway the assessments of observers.
When asked what it would mean to be biased, subjects were more likely to define bias in terms of introspected thoughts and motives when it applied to themselves, but in terms of overt behaviour when it applied to other people. When subjects were explicitly told to avoid relying on introspection, their assessments of their own bias became more realistic.
Additionally, Nisbett and Wilson found that asking participants whether biases (such as the position effect in the stocking study)[clarification needed] had an effect on their decisions resulted in a negative response, in contradiction with the data.
In perceptions of conformity
Another series of studies by Pronin and colleagues examined perceptions of conformity. Subjects reported being more immune to social conformity than their peers. In effect, they saw themselves as being "alone in a crowd of sheep". The introspection illusion appeared to contribute to this effect. When deciding whether others respond to social influence, subjects mainly looked at their behaviour, for example explaining other student's political opinions in terms of following the group. When assessing their own conformity, subjects treat their own introspections as reliable. In their own minds, they found no motive to conform, and so decided that they had not been influenced.
In perceptions of control and free will
Psychologist Daniel Wegner has argued that an introspection illusion contributes to belief in paranormal phenomena such as psychokinesis. He observes that in everyday experience, intention (such as wanting to turn on a light) is followed by action (such as flicking a light switch) in a reliable way, but the processes connecting the two are not consciously accessible. Hence though subjects may feel that they directly introspect their own free will, the experience of control is actually inferred from relations between the thought and the action. This theory, called "apparent mental causation", acknowledges the influence of David Hume's view of the mind. This process for detecting when one is responsible for an action is not totally reliable, and when it goes wrong there can be an illusion of control. This could happen when an external event follows, and is congruent with, a thought in someone's mind, without an actual causal link.
As evidence, Wegner cites a series of experiments on magical thinking in which subjects were induced to think they had influenced external events. In one experiment, subjects watched a basketball player taking a series of free throws. When they were instructed to visualise him making his shots, they felt that they had contributed to his success.
If the introspection illusion contributes to the subjective feeling of free will, then it follows that people will more readily attribute free will to themselves rather than others. This prediction has been confirmed by three of Pronin and Kugler's experiments. When college students were asked about personal decisions in their own and their roommate's lives, they regarded their own choices as less predictable. Staff at a restaurant described their co-workers' lives as more determined (having fewer future possibilities) than their own lives. When weighing up the influence of different factors on behaviour, students gave desires and intentions the strongest weight for their own behaviour, but rated personality traits as most predictive of other people.
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However, criticism of Wegner's claims regarding the significance of introspection illusion for the notion of free will has been published.
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Research shows that human volunteers can estimate their response times accurately, in fact knowing their "mental processes" well, but only with substantial demands made on their attention and cognitive resources (i.e. they are distracted while estimating). Such estimation is likely more than post hoc interpretation and may incorporate privileged information. Mindfulness training can also increase introspective accuracy in some instances. Nisbett and Wilson's findings were criticized by psychologists Ericsson and Simon, among others.
Correcting for the bias
A study that investigated the effect of educating people about unconscious biases on their subsequent self-ratings of susceptibility to bias showed that those who were educated did not exhibit the bias blind spot, in contrast with the control group. This finding provides hope that being informed about unconscious biases such as the introspection illusion may help people to avoid making biased judgments, or at least make them aware that they are biased. Findings from other studies on correction of the bias yielded mixed results. In a later review of the introspection illusion, Pronin suggests that the distinction is that studies that merely provide a warning of unconscious biases will not see a correction effect, whereas those that inform about the bias and emphasize its unconscious nature do yield corrections. Thus, knowledge that bias can operate during conscious awareness seems the defining factor in leading people to correct for it.
Timothy Wilson has tried to find a way out from "introspection illusion", recounted in his book Strangers to Ourselves. He suggests that the observation of our own behaviours more than our thoughts can be one of the keys for clearer introspective knowledge.
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Some 21st century critical rationalists argue that claims of correcting for introspection illusions or other cognitive biases pose a threat of immunizing themselves to criticism by alleging that criticism of psychological theories that claim cognitive bias are "justifications" for cognitive bias, making it non-falsifiable by labelling of critics and also potentially totalitarian. These modern critical rationalists argue that defending a theory by claiming that it overcomes bias and alleging that critics are biased, can defend any pseudoscience from criticism; and that the claim that "criticism of A is a defense of B" is inherently incapable of being evidence-based, and that any actual "most humans" bias (if it existed) would be shared by most psychologists thus make psychological claims of biases a way of accusing unbiased criticism of being biased and marketing the biases as overcoming of bias.
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- Gopnik, Alison (1993). "How We Know Our Own Minds: The Illusion of First-person Knowledge of Intentionality". In Alvin I. Goldman (ed.). Readings in philosophy and cognitive science (2 ed.). MIT Press. pp. 315–346. ISBN 978-0-262-57100-5.
- Wilson, Timothy D. (2003). "Knowing When to Ask: Introspection and the Adaptive Unconscious". In Anthony Jack; Andreas Roepstorff (eds.). Trusting the subject?: the use of introspective evidence in cognitive science. Imprint Academic. pp. 131–140. ISBN 978-0-907845-56-0.
- Pronin, Emily; Gilovich, Thomas; Ross, Lee (2004). "Objectivity in the Eye of the Beholder: Divergent Perceptions of Bias in Self Versus Others". Psychological Review. 111 (3): 781–799. doi:10.1037/0033-295X.111.3.781. PMID 15250784.
- Gibbs Jr., Raymond W. (2006). "Introspection and cognitive linguistics: Should we trust our own intuitions?". Annual Review of Cognitive Linguistics. 4 (1): 135–151. doi:10.1075/arcl.4.06gib.
- Johansson, Petter; Hall, Lars; Sikström, Sverker (2008). "From change blindness to choice blindness" (PDF). Psychologia. 51 (2): 142–155. doi:10.2117/psysoc.2008.142. Archived from the original on 2016-05-18.CS1 maint: BOT: original-url status unknown (link)
- Choice Blindness Video on BBC Horizon site
- Choice Blindness Lab at Lund University
- ‘Choice blindness’ and how we fool ourselves by Ker Han, MSNBC.com, October 7, 2005
- Choice blindness: You don't know what you want (Opinion column by Lars Hall and Petter Johansson) New Scientist. April 18, 2009
- “People Always Follow the Crowd. But Not Me!”: The Introspection Illusion blog post by Dr. Giuseppe Spezzano, November 4, 2009
- Do Others Know You Better Than You Know Yourself? blog post by psychology professor Joachim Krueger, September 28, 2012<|endoftext|>
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What’s the issue?
Sweets, pumpkins…consumers are bombarded with Halloween ‘essentials’. Halloween is the UK’s 3rd biggest
The carved ‘Jack-o’-lantern’- is iconic to the Halloween celebration.
According to Hubub, 2 in 5 British households carve at least 1 pumpkin. Yet 7 out of 10 carved pumpkins aren’t eaten! 64% of carved pumpkins are ‘binned’ either as rubbish (25%) or, if available, in a local council food-waste bin (20%) or composted (19%). Only 33% cook their pumpkin!
The 15 million pumpkins that are bought and uneaten annually, could be classified as avoidable food-waste. According to WRAP food-waste includes:
- Avoidable food-waste– food edible at some point prior to it’s disposal. (e.g. uneaten pumpkins)
- Possibly avoidable food-waste -that some eat but others don’t (e.g. pumpkin skin).
- Unavoidable food-waste– which isn’t edible ‘normally.’ (e.g. pumpkin stalk)
Avoidable food-waste is influenced by individual behaviour, e.g. whether we choose to eat or bin pumpkin.
But, why should we care?
Nationally and globally there’s a paradox between food-waste and food insecurity. (Although UK government may deny this with no official figures). Food insecurity can vary in severity:
“Food insecurity exists when people don’t have physical, social and economic access to sufficient, safe and nutritious food which meets their dietary needs and food preferences for an active and healthy life”
In the UK in 2014, 8.4 million people lived in households with insufficient food, whilst there was 4.5 million tonnes of avoidable household food-waste. (This includes drink-waste, but still highlights the disparity)
We must rethink the human/food relationship, if we’re to tackle food insecurity and the scale of avoidable food-waste, to create a just foodscape. How we value food underpins this.
How does something ‘become’ and ‘unbecome’ food? When and why does food lose/gain value?
This blog uses a pumpkin to give ‘food-for-thought’ about food’s value in relation to avoidable food waste.
Why are pumpkins wasted at a household level?
Before writing this, I recalled the last time I ate pumpkin… in a restaurant years ago. Perhaps pumpkins feature reguarly in your diet? Or perhaps you’re thinking, pumpkins are food? Over half the respondents in a Consensus wide survey didn’t think pumpkin was food! Is this understandable when marketing focuses on carving?
Despite pumpkins being part of the popular cucurbitaceae family, which includes: squash, it appears we associate pumpkins with flavoured products, not the vegetable.
The pumpkin is a prime example that avoidable food-waste is about how individuals value ‘food’. A reconsideration of which is necessary to create a just system.
Individual actions influence what food is wasted. Unlike mouldy bread, where people may consider it inedible and no longer valuable (compared to ‘non-mouldy’ bread), many never associate pumpkin as food. Therefore the decomposition process doesn’t result in pumpkin unbecoming food if it’s not valued (as edible food) in the first place.
Pumpkin must become food, before people recognise they’re disposing of avoidable food-waste. How does something ‘become’ food? Culture matters. What we understand as food and how we relate to food is context and place specific, e.g. cooking practices. Middle Eastern and North African cuisine includes pumpkin. Eating, preparing and cooking pumpkin displays a culture where pumpkin is valued as food. Associations influence food preferences and values e.g. if a relative you’re fond of, uses that ingredient.
Other cultural practices hide food value. For example, social media trends photographing uneaten pumpkins at pumpkin farms- ‘the insta-pumpkin’.
Or disposal of carved pumpkins in food waste bins or compost.
These practices don’t value pumpkin as food, but as a commodity (to purchase and photograph or a compostable component of the food chain).
How can we reduce avoidable household food-waste?
So, we need to reconsider what we value as a food to establish a just food system.
It’s that simple! Pumpkin = nutritious food!
Before this blog I’d never cooked pumpkin. Now I’ve cooked: risotto, soup and tagine. Yes, preparation is time-consuming and carving pumpkins can be watery. But that doesn’t stop people eating other watery food e.g. courgettes. They should still be valued as a food.
Food safety advice concerning eating carved pumpkins is blurred, but carving a pumpkin and eating it immediately or using alternative decorations ensures edibility.
Carving exposes the interior to oxygen, resulting in decomposition. Alternative decorations allow you to utlisie and acknowledge pumpkin’s food value e.g. washi tape or edible paint. You may argue this doesn’t follow tradition. But traditionally turnips were carved instead of pumpkins- tradition evolves. If we’re to reconsider the value of food and inequality inherent in the food system, we must constantly question our relationship to food and what is valuable.
GIVE THE PUMPKIN AWAY
You don’t like pumpkin’s taste? OLIO, a food sharing app, allows you to share edible food with others in your locality, reducing avoidable food-waste and valuing the pumpkin as a food.
PUMPKIN FARM TO FORK
How does your farm visit connect to your plate? It’s the perfect opportunity to understand the food source and what’s required to grow a pumpkin. Recognsing that not eating pumpkin wastes resources (water, nutrients, time…) Harvest it, eat it – reconsider its food value.
- Although Halloween is over this year, the pumpkin season is October- December. Use this time to reconsider pumpkins as valuable food.
- Multiple factors influence food-waste and food insecurity, which simply eating pumpkins won’t resolve.
- But, I have illustrated that rethinking how and what we value in our food system is important. Recognsing the value of food, especially before it becomes avoidable food-waste, is a step to altering behaviour at individual, national and global scales.
- Just because pumpkin makes it onto a plate doesn’t mean it will be eaten, but recognsing it’s a food is a necessary shift.
- Pumpkins are just one product in our global food system. But they epitomise the scale of avoidable food-waste. We have the means to alter our behaviour and practices, by valuing and eating a nutritious meal from an otherwise wasted item.<|endoftext|>
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