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url string | text string | date timestamp[s] | meta dict |
|---|---|---|---|
https://math.stackexchange.com/questions/2834409/how-to-design-a-nim-game | # How to design a nim game?
I am required to give an example of nim game such that:
1. the initial position is an N-position,
2. there are exactly three optimal moves from the initial position,
3. every pile has at least 20 chips,
4. every pile has a different (nonempty) number of chips
How could I design such a nim?... | 2021-11-28T23:47:27 | {
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http://mathhelpforum.com/advanced-algebra/68751-special-matrix-product.html | 1. ## special matrix product
Hi, I'm not native English, what is the name the following product. Let a n-column vector and b m-row vector, than c = a × b resultes a n-by-m-matrix:
c_ij = a_i * b_j.
2. Originally Posted by Skalkaz
Hi, I'm not native English, what is the name the following product. Let a n-column vecto... | 2013-05-19T20:07:24 | {
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https://mathoverflow.net/questions/420328/can-we-use-formal-groups-to-recover-lie-theoretic-representation-theory-in-chara | # Can we use formal groups to recover Lie-theoretic representation theory in characteristic p?
In differential geometry, Lie's theorems allow us to integrate any Lie algebra representation to a Lie group representation. The algebraic version of this is more complicated (and I'm not terribly familiar with it), but over... | 2023-03-24T20:00:51 | {
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https://www.questarter.com/q/understanding-gaps-in-concept-of-radius-of-convergence-of-power-series-21_2925231.html | # Understanding Gaps in concept of Radius of Convergence of Power Series
by MathLover Last Updated September 21, 2018 12:20 PM
I had done this topic Many time Thinking it is easy But When I today done its theorem , I come across that I had certain gaps in My Knowelege about it.
$$\sum a_nz^n$$ is power series. $$1... | 2018-10-18T10:27:33 | {
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https://online.stat.psu.edu/stat200/book/export/html/65 | # 3.4 - Two Quantitative Variables
3.4 - Two Quantitative Variables
Later in the course, we will devote an entire lesson to analyzing two quantitative variables. In this lesson, you will be introduced to scatterplots, correlation, and simple linear regression. A scatterplot is a graph used to display data concerning ... | 2020-01-17T20:19:55 | {
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... |
https://quantumcomputing.stackexchange.com/questions/13164/are-all-pure-entangled-states-robust | # Are all pure entangled states `robust'?
Let $$\mathcal{H}_A \otimes \mathcal{H}_B$$ be the tensor product of two finite dimensional Hilbert spaces, let $$d = \operatorname{dim}(\mathcal{H}_A \otimes \mathcal{H}_B)$$ and let $$| \psi \rangle \in \mathcal{H}_A \otimes \mathcal{H}_B$$ be a pure entangled state.
We say... | 2020-12-01T15:48:17 | {
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https://www.bartleby.com/questions-and-answers/a-gasoline-tank-is-in-the-shape-of-a-right-circular-cylinder-lying-on-its-side-of-length-14-ft-and-r/90f03097-8d0c-4d0d-88cc-673a85605d1c | # A gasoline tank is in the shape of a right circular cylinder (lying on its side) of length 14 ft and radius 5 ft. Set up an integral that represents the volume of the gas in the tank if it is filled to a depth of 8 ft. Let the variable of integration be the vertical distance up from the center line of the tank. 5 ft ... | 2021-02-25T19:27:26 | {
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"openwebmath_score": 0.9262772798538208,
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... |
https://hkumath1111.wordpress.com/2014/10/23/lecture-17-2/ | # Linear Algebra II
## October 23, 2014
### Lecture 17
Filed under: 2014 Fall — Y.K. Lau @ 8:25 PM
We learnt how to represent a linear transformation ${T:V\rightarrow W}$ by a matrix. Remember that we need to fix an ordered basis ${B}$ for ${V}$ and an ordered basis for ${W}$ in order to represent ${T}$ by a matrix... | 2017-06-28T20:47:57 | {
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https://stacks.math.columbia.edu/tag/09JZ | ## 22.14 Projective modules over algebras
In this section we discuss projective modules over algebras analogous to Algebra, Section 10.77. This section should probably be moved somewhere else.
Let $R$ be a ring and let $A$ be an $R$-algebra, see Section 22.2 for our conventions. It is clear that $A$ is a projective r... | 2023-01-31T01:25:24 | {
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http://usecase.harmis.com.br/7lp44oa/cube-root-of-1728-by-division-method-a4f73f | ## 27 nov cube root of 1728 by division method
If a number ends in an odd number of zeros, then its square root is not a natural number. , but if we have to calculate the side of a square we need to take the square root of the area. Prime factorization method and Long Division method. Use prime factorization method to... | 2021-04-17T12:29:07 | {
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https://math.stackexchange.com/questions/2241718/which-maps-are-box-continuous | # Which Maps are Box-Continuous?
The box topology on the set $\mathbb R^\infty$ is defined to have sub-basis of sets $U_1 \times U_2 \times \ldots$ for each $U_i \subset \mathbb R$ open. Observe this is different from the product topology which also demands all but finitely many $U_i = \mathbb R$.
The box topology is... | 2020-05-31T01:13:20 | {
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https://math.stackexchange.com/questions/1922574/likelihood-ratio-test-x-has-the-density-function-gx-frac1-thetae-f | # Likelihood ratio test: $X$ has the density function $g(x)=\frac{1}{\theta}e^{-\frac{x}{\theta}};x>0,0<\theta\leq 1$. Find a test for the hypothesis'.
Likelihood ratio test: $X$ has the density function $g(x)=\frac{1}{\theta}e^{-\frac{x}{\theta}}; x>0, 0<\theta\leq 1$. Find a test for the hypothesis' $H_0(\theta=1)$ ... | 2019-10-23T03:20:29 | {
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"l... |
http://math.stackexchange.com/questions/46706/how-to-solve-this-problem-using-set-theory | How to solve this problem using set theory?
$36$ students took English and Math test. $25$ passed English, and $28$ passed Math. $20$ passed both subjects.
a. How many students failed both subject?
b. How many students passed english only?
c. How many students passed math only?
-
What does the question has to do wit... | 2013-05-20T08:51:46 | {
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"lm_q1_score": 0.9715639636617... |
http://hyperion.chemistry.uoc.gr/plfi73/39c0f9-moderate-scatter-plot | Linearly related variables Scatter plot Transform data Both variables are normally distributed Histograms of variables/ Shapiro Wilk ... 0.001) which is moderate. Find scatter plots that seem to show some correlation and lines drawn through the data. This map allows you to see the relationship that exists between the t... | 2021-06-19T06:02:39 | {
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"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.9715639636617015,
"lm_q2_score": 0.67... |
https://homework.cpm.org/category/CCI_CT/textbook/pc3/chapter/6/lesson/6.1.1/problem/6-11 | ### Home > PC3 > Chapter 6 > Lesson 6.1.1 > Problem6-11
6-11.
Given $log_{b}\left(M\right) = 2.1$, $log_{b}\left(N\right) = 0.6$ and $log_{b}\left(P\right) = −1.8$, evaluate $\log_b\left(\frac{\sqrt{NP}}{M^2}\right)$.
Rewrite the given logarithmic expression as the logarithmic terms, each with a single variable.
$\... | 2021-10-21T23:44:40 | {
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"... |
http://openstudy.com/updates/509c5adce4b0077374589894 | math456 2 years ago Can anyone help me with solving this integral?
1. math456
$\int\limits_{2}^{5} (4-2x)dx$
2. amistre64
which part is giving you night terrors?
3. math456
lol the 2nd one!
4. amistre64
what is the integration rule for x^n ?
5. math456
$\int\limits_{2}^{5} 4.dx - 2\int\limits_{2}^{5}x.dx$
6.... | 2015-10-09T05:25:46 | {
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"lm_q2_score": 0.672331692613781... |
http://matlabtricks.com/post-26/tutorial-on-2d-convolution-of-images | 07 November, 2013
# Tutorial on 2D convolution of images
• How convolution can be done in two dimensions?
• Can you show me an example and explanation of the 2D convolution?
• How can two dimensional convolution be done in MATLAB?
In a previous post the basics of convolution was already discussed with some examples.... | 2018-08-17T23:16:19 | {
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https://www.coursehero.com/file/13039/intpartsprac/ | intpartsprac - Use integration by parts to find the following integrals 1 xe dx x 2(x 1)ex dx 3(5x 9)e-3x dx 4(6x 3)e-2x dx 5 2x 1 dx ex 1 6 0 1-x dx
# intpartsprac - Use integration by parts to find the...
• Homework Help
• 1
This preview shows page 1 out of 1 page.
Use integration by parts to find the following i... | 2021-06-19T10:30:15 | {
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"lm_q1_score": 0.9715639636617014,
"lm_q2_score": 0.672331692613781... |
https://www.clutchprep.com/questions/1683/3-known-charges-and-1-unknown-create-a-given-electric-field-find-the-value-of-the-magnitude-of-the-un | # 3 known charges and 1 unknown create a given electric field. Find the value of the magnitude of the unknown charge
An unknown positive point charge is placed at x = -0.36 m, y = 0 m, a charge of -4.8 micro-coulombs is placed at x = 0 m, y = -0.23 m, a charge of +2.4 micro-coulombs is placed at x = +0.37 m, y = -0.2 ... | 2020-09-25T23:27:47 | {
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"openwebmath_score": 0.9289552569389343,
"openwebmath_perplexity": 542.879536666758,
"lm_name": "Qwen/Qwen-72B",
"lm_label":... |
http://archive.arrayfire.com/arrayfire/c/group__image__func__cpp__gaussiankernel.htm | Documentation
gaussiankernel
Creates a Gaussian kernel. More...
array gaussiankernel (int rows, int cols, double sigma_r=0, double sigma_c=0) Generate kernels. More...
## Detailed Description
Creates a Gaussian kernel.
This function creates a kernel of a specified size that contains a Gaussian distribution. This ... | 2018-12-13T20:57:43 | {
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"url": "http://archive.arrayfire.com/arrayfire/c/group__image__func__cpp__gaussiankernel.htm",
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9715639702485929,
"... |
https://math.stackexchange.com/questions/3141026/the-law-of-quadratic-reciprocity-or-statement | # The law of quadratic reciprocity 'or' statement
I have just seen written that $$(\frac{17}{101})$$ = $$(\frac{101}{17})$$. But doesn't the law of quadratic reciprocity state that $$(\frac{p}{q})$$ = $$(\frac{q}{p})$$ if $$p\equiv1 mod 4$$ OR $$q\equiv1mod4$$?
• In mathematics, "or" is almost always inclusive, so we... | 2019-08-23T04:27:13 | {
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.971563... |
https://www.physicsforums.com/threads/prime-ideal-problem.486331/ | # Prime ideal problem.
Let R be a ring with ideals I, J, and P. Prove that if P is a prime ideal and I intersect J is a subset of P, then I is a subset of P or J is a subset of P.
If i like ab in I intersect J, then ab is in P. Therefore a in P or b in P since P is prime. Neither a or b need be in I intersect J thoug... | 2021-02-27T03:42:35 | {
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"lm_q1_score": 0.9715639702485929,
"lm_q2_score": 0... |
http://mathhelpforum.com/calculus/51895-constant-circumference-tear-drop.html | # Thread: Constant circumference of tear drop
1. ## Constant circumference of tear drop
A tear drop can be represented by the parametric equations:
$x(t)=r \cos(t)$
$y(t)=r \sin(t)\sin^{n-1}(t/2)$
The arc length is:
$A(n)=\int_0^{2\pi}\sqrt{(x'(t))^2+(y'(t))^2}dt$
Find $r(n)$ such that $A(n)=K$. That is, how mus... | 2017-04-25T02:24:21 | {
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"lm_q1_score": 0.9715639702485929,
... |
https://www.nag.com/numeric/nl/nagdoc_latest/clhtml/c02/c02abc.html | # NAG CL Interfacec02abc (poly_real_fpml)
Settings help
CL Name Style:
## 1Purpose
c02abc finds all the roots of a real polynomial equation, using a fourth-order convergent modification of Laguerre's method.
## 2Specification
#include
void c02abc (const double a[], Integer n, Integer itmax, Nag_Root_Polish po... | 2021-07-31T21:32:53 | {
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"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.9715639702485929,
"lm_q2_score": 0.67... |
https://www.gradesaver.com/textbooks/math/calculus/calculus-early-transcendentals-8th-edition/appendix-c-graphs-of-second-degree-equations-c-exercises-page-a-23/30 | ## Calculus: Early Transcendentals 8th Edition
$x = \frac{1}{2}(y+3)^2-2$ This is the equation of a parabola with vertex $(-2,-3)$
$y^2-2x+6y+5 = 0$ $2x = y^2+6y+5$ $2x = y^2+6y+9-9+5$ $2x = (y+3)^2-4$ $x = \frac{1}{2}(y+3)^2-2$ This is the equation of a parabola with vertex $(-2,-3)$ | 2019-11-21T08:07:04 | {
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"openwebmath_score": 0.5868946313858032,
"openwebmath_perplexity": 59.528956040959116,
"lm_name": "Qwen/Qw... |
https://www.gradesaver.com/textbooks/science/physics/physics-10th-edition/chapter-5-dynamics-of-uniform-circular-motion-check-your-understanding-page-128/8 | ## Physics (10th Edition)
In an unbanked curve, static friction provides the centripetal force stopping the car from sliding. We have $$F_c=f_s^{max}=\mu_sF_N$$ Assume there is no vertical acceleration, so that $F_N=mg$ $$F_c=\mu_smg$$ On the other hand, $F_c$ equals $\frac{mv^2}{r}$, so $$\frac{mv^2}{r}=\mu_smg$$ $$\... | 2021-06-15T13:03:51 | {
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"url": "https://www.gradesaver.com/textbooks/science/physics/physics-10th-edition/chapter-5-dynamics-of-uniform-circular-motion-check-your-understanding-page-128/8",
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"lm_name": "Qwen/Qwen-72B",
... |
http://math.stackexchange.com/questions/358093/approximation-of-stochastic-integral | # Approximation of stochastic integral
Let $f \in C^2_C(\mathbb{R})$ and $$X_t = X_0 + \int_0^t \sigma(s) \, dB_s + \int_0^t b(s) \, ds$$ be an (one-dimensional) Itô process where $\sigma,b: [0,\infty) \times \Omega \to \mathbb{R}$ progressively measurable and pathwise bounded. Let $(\tau_n)_n$ be a common localizatio... | 2016-05-01T22:08:46 | {
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http://math.stackexchange.com/questions/375305/how-can-i-prove-det-overline-m-overline-detm | How can I prove $\det(\overline M)=\overline{\det(M)}$?
Of course $\overline M$ is the complex conjugate of an $n\times n$ matrix $M$.
Someone gave me advice to use the definition of determinant, then it means I have to use cofactor expasion here?
-
It is easier with the closed expression of $\det(A)$ as a sum over ... | 2014-12-18T00:44:51 | {
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http://math.stackexchange.com/questions/284370/on-finite-solvable-groups | # On finite solvable groups
Let $G$ be a finite group such that all subgroups of it (except $G$) are nilpotent. Then prove that $G$ is solvable.
-
This is Schmidt-Iwasawa theorem. Observe that it is enough to prove that such a group is not simple. Once you have this then you can argue by induction on the order of G. ... | 2016-07-27T13:42:14 | {
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"lm_q2_sc... |
https://stats.stackexchange.com/questions/523611/binomial-mle-based-on-2-experiments | # Binomial MLE based on 2 experiments
I need to estimate a parameter for Binomially distributed variable.
Suppose I want to estimate the probability of hitting the target. I first do 5 trials out of which I hit the target twice.
Then I try again for another 5 times and this time I hit the target only once.
Now i kn... | 2022-10-06T00:23:38 | {
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https://rigidgeometricalgebra.org/wiki/index.php?title=Bulk_and_weight | # Bulk and weight
The components of an element of a rigid geometric algebra can be divided into two groups called the bulk and the weight of the element. The bulk of an element $$\mathbf x$$ is denoted by $$\mathbf x_\unicode{x25CF}$$, and it consists of the components of $$\mathbf x$$ that do not have the projective ... | 2022-12-02T23:53:44 | {
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"url": "https://rigidgeometricalgebra.org/wiki/index.php?title=Bulk_and_weight",
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http://math.stackexchange.com/questions/226274/levys-theorem | # Levy's theorem? [duplicate]
Possible Duplicate:
how to show convergence in probability imply convergence a.s. in this case?
Good evenig! I stumbled upon this theorem:
For independent random variables $(X_n)_{n\in\mathbb{N}}$ and $S_n := \sum_{i=1}^n X_i$ the following two statements are equivalent:
1. $\exists S_... | 2016-05-31T18:15:18 | {
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http://www.math.stonybrook.edu/~tony/whatsnew/may15/sewing-machine.html | This page has been translated into Estonian
Matematika y Shveynaya mashina (this page in Russian)
.
Math and the Sewing Machine
The sewing machine is one of the marvels of 19th-century mechanical invention. (Mahatma Ghandi is said to have called it "one of the few useful things ever invented.") Unlike the typewriter... | 2018-07-17T00:22:11 | {
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"lm_q2_score... |
http://www.chegg.com/homework-help/questions-and-answers/let-x-t-continuous-time-band-limited-signal-fourier-transform-x-j-omega-let-p-t-represent--q4664682 | please solve the question
Image text transcribed for accessibility: Let x(t) be a continuous-time band-limited signal with Fourier transform X(j omega): Let p(t) represent the impulse train with period T: Now, we will sample x(t) by multiplying it with p(t) giving: Sketch Xp(j omega), the Fourier transform of Xp(t) as... | 2014-11-28T00:25:02 | {
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http://mathhelpforum.com/number-theory/133239-modulus-proof.html | 1. ## Modulus Proof
Show that if n is the sum of two squares, then it CAN"T be congruent to 3 mod 4.
Proof:
Let n = x^2 + y^2
Assume, aiming for a contradiction, that n is congruent to 3 mod 4.
So, x^2 + y^2 is congruent to 3 mod 4
This implies that 4 | x^2 + y^2 -3
I'm trying to get a contradiction, but I'm stuck ... | 2017-01-20T02:31:39 | {
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http://mathoverflow.net/questions/173588/bases-for-spaces-of-smooth-functions | # Bases for spaces of smooth functions
Let $S$ denote the space of rapidly decreasing sequences, which means sequences $a=(a_k)_{k=1}^\infty$ such that the numbers $p_d(a)=\sup\{k^d|a_k| : 1\leq k<\infty\}$ are finite for all $d\in\mathbb{N}$. We give this space the topology generated by the family of seminorms $p_d$.... | 2016-06-30T17:54:06 | {
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http://mathoverflow.net/questions/120033/why-are-the-holomorphic-line-bundle-sections-finite-dimensional?answertab=active | # Why are the holomorphic line bundle sections finite dimensional?
I'm trying to understand the Borel--Weil theorem at the moment (not the whole Bott--Borel--Weil theorem as has been asked elsewhere). However, I am having a little difficulty finding a direct proof, so I started to try and reconstruct it for myself. Th... | 2014-03-12T11:44:24 | {
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... |
https://books.compclassnotes.com/rothphys110-2e/2021/06/27/section-7-3-v2/ | # Chapter 7: Linear momentum
## 7.3 Ballistic pendulum
ballistic pendulum is a device that used to be used to determine the velocity of a bullet; it was invented in 1742 by English mathematician Benjamin Robins for this purpose. A simple version consists of a block of wood that hangs on a rod (the mass of the rod is ... | 2023-03-29T10:18:47 | {
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https://math.stackexchange.com/questions/476253/proving-inequality-forall-x-ge1 | # Proving Inequality $\forall x\ge1$
How do I prove that $\forall x\ge1$ $$\left(\frac{x+1}x\right)^x\left(\ln\left\{1+\frac1x\right\}-\frac1{x+1}\right)>0\,?$$
I have tried rearranging this many times but I always end up with a compilicated fraction. Is there a special way I can rearrange this such that it becomes s... | 2019-06-20T03:13:04 | {
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https://math.stackexchange.com/questions/642089/theorem-20-17-in-eisenbud-a-few-questions-on-the-proof | # Theorem 20.17 in Eisenbud: a few questions on the proof
Let $k$ be a field, $S=k[x_1,\dots,x_r]$ and $M$ a finitely-generated, graded $S$-module.
Definition: We say that $M$ is weakly $m$-regular if $Ext^j(M,S)_n=0$ for all $j$ and $n=-m-j-1$. We say that $M$ is $m$-regular if $Ext^j(M,S)_n=0$ for all $j$ and $n \l... | 2019-08-20T08:25:18 | {
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"lm_q1_score": 0.... |
https://mail.roltampa.org/topps-ydt/distance-between-two-lines-in-3d-calculator-3dce0f | In 3D geometry, the distance between two objects is the length of the shortest line segment connecting them; this is analogous to the two-dimensional definition. person_outlineTimurschedule 2019-06-07 06:42:44. Here's something similar to what ElpanovEvgeniy posted. The shortest distance between the lines is the distan... | 2021-04-11T18:28:12 | {
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"url": "https://mail.roltampa.org/topps-ydt/distance-between-two-lines-in-3d-calculator-3dce0f",
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"openwebmath_perplexity": 859.8520803325928,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9715639677785088,
... |
https://www.otomas.co.id/chili-oil-tevm/page.php?page=f5ddee-solving-systems-of-equations-by-substitution-worksheet | When completed, the puzzle is designed to be 4x4 square. A large pizza at Palanzio’s Pizzeria costs $6.80 plus$0.90 for each topping. And I have another equation, 5x minus 4y is equal to 25.5. Solve the system of linear equations by substitution. Systems of Equations: Substitution Solve each system by substitution. Obj... | 2021-05-06T03:05:23 | {
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"url": "https://www.otomas.co.id/chili-oil-tevm/page.php?page=f5ddee-solving-systems-of-equations-by-substitution-worksheet",
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"openwebmath_perplexity": 711.3670490672973,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_scor... |
https://www.dsemth.com/static/question-sample/exterior-angle-of-triangl | Exterior angle of triangles
Question Sample Titled 'Exterior angle of triangles'
In the figure, ${C}{F}{D}$ , ${A}{E}{B}$ , ${C}{H}{M}{B}$ , ${D}{M}{K}{A}$ and ${F}{H}{K}{E}$ are straight lines. It is given that ${C}{F}{D}$$//$${A}{E}{B}$ , $\angle{C}{D}{M}={53}^{\circ}$ , $\angle{M}{K}{E}={173}^{\circ}$ and $\angle{... | 2021-01-20T11:30:05 | {
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"url": "https://www.dsemth.com/static/question-sample/exterior-angle-of-triangl",
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"lm_q1_score": 0.9715639677785087,
"lm_q2_score": 0.... |
https://pcraster.geo.uu.nl/pcraster/4.3.2/documentation/pcraster_manual/sphinx/op_windowhighpass.html | # windowhighpass¶
windowhighpass
Increases spatial frequency within a specified square neighbourhood
Result = windowhighpass(expression, windowlength)
expression
spatial scalar
windowlength
spatial, non spatial scalar
Result
spatial scalar
## Options¶
--unittrue or --unitcell
--unittrue
windowlength is mea... | 2022-01-21T04:47:32 | {
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http://clay6.com/qa/49384/a-and-b-are-two-events-such-that-p-a-0-54-p-b-0-69-and-p-a-cap-b-0-35-find- | Browse Questions
# A and B are two events such that P(A)=0.54,P(B)=0.69 and $P(A\cap B)=0.35$.Find $P(B\cap A')$
$\begin{array}{1 1}(A)\;0.34\\(B)\;0.24\\(C)\;0.14\\(D)\;0.64\end{array}$
Can you answer this question?
Toolbox:
• $P(B \cap A')=P(B)-P(B \cap A)$
$P(B \cap A)=0.35$
$P(B)=0.69$
$P(B \cap A')=P(B)-P(B \c... | 2017-06-23T18:56:26 | {
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https://socratic.org/questions/how-do-you-use-the-squeeze-theorem-to-find-lim-tan-x-cos-sin-1-x-as-x-approaches | How do you use the Squeeze Theorem to find lim tan(x)cos(sin(1/x)) as x approaches zero?
Sep 25, 2015
We need to consider right and left limits separately.
Explanation:
For all $x \ne 0$, we have $- 1 \le \cos \left(\sin \left(\frac{1}{x}\right)\right) \le 1$
Right Limit
For $0 < x < \frac{\pi}{2}$, we have $\tan ... | 2022-11-30T21:49:43 | {
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"lm_q1_scor... |
http://lara.epfl.ch/w/sav09:chaotic_iteration_in_abstract_interpretation | • English only
# Chaotic Iteration in Abstract Interpretation: How to compute the fixpoint?
In Abstract Interpretation Recipe, note that if the set of program points is , then we are solving the system of eqautions in variables
where
The approach given in Abstract Interpretation Recipe computes in iteration values ... | 2018-08-14T19:45:59 | {
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"lm_q2_score":... |
http://mathhelpforum.com/pre-calculus/156823-solve-y-x-1-x-0-x-1-x-terms-y-print.html | # Solve y = x + 1/x with 0 \< x \< 1 for x in terms of y.
• September 20th 2010, 01:35 PM
hsidhu
Solve y = x + 1/x with 0 \< x \< 1 for x in terms of y.
I need help with this assignment, Problem 3:
Solve y = x + 1/x with 0 \< x \< 1 for x in terms of y.
Any clues as to how to do this, would be greatly appreciated :)... | 2015-07-28T14:36:22 | {
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"lm_q1_score": 0.97156396695... |
http://mathhelpforum.com/calculus/31392-nasty-derivative.html | 1. ## Nasty derivative
Once again. After missing a week of school and a test, its not fun to catch up, especially in calculus.
Heres the question.
Find the slope of the tangent to $h(x)=2x(x+1)^3(x^2+2x+1)^2$ at
$x=-2$
Explain how to find the equation of the normal at x= -2.
Ok so if anyone solves this, can they pl... | 2016-10-27T22:17:34 | {
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https://mathoverflow.net/questions/191225/can-a-positive-measure-subset-of-a-free-group-be-nowhere-dense | Can a positive measure subset of a free group be nowhere dense?
Let $F$ be a finitely generated free group and let $S \subseteq F$ be a subset for which there is some $\epsilon > 0$ such that for any epimorphism to a finite group $\phi \colon F \to G$ we have that $\frac{|\phi(S)|}{|G|} \geq \epsilon$ (that is, the cl... | 2022-01-18T02:02:21 | {
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": ... |
https://discuss.codechef.com/questions/70882/stdytab-editorial | ×
# STDYTAB - Editorial
Author: Pavel Sheftelevich
Tester: Mahbubul Hasan and Sunny Aggarwal
Editorialist: Balajiganapathi Senthilnathan
Russian Translator: Sergey Kulik
Mandarian Translator: Gedi Zheng
Easy
# PREREQUISITES:
Combinatorics, DP
# PROBLEM:
You have to fill a $N x M$ matrix with non negative numbers... | 2018-06-24T08:42:52 | {
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"lm_q1_score": 0.9715639669551474,
"lm_q2_score": 0.672331... |
https://mathoverflow.net/questions/359168/physical-measures-that-are-not-srb/359208 | # Physical measures that are not SRB
It is quite easy to construct a dynamical system which has a physical measure with a positive Lyapunov exponent and zero entropy, just a figure $$\infty$$ system. By Pesin's entropy formula such a measure can not be a Sinai-Ruelle-Bowen measure. Now my question is, if there exists ... | 2021-07-27T06:48:15 | {
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"url": "https://mathoverflow.net/questions/359168/physical-measures-that-are-not-srb/359208",
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"lm_name": "Qwen/Qwen-72B",
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... |
https://mathhelpboards.com/threads/mechanics-help.24941/ | # PhysicsMechanics help
#### cake81
##### New member
Hello! I need help with this question:
A tennis ball is thrown in the air by a man so that at the instant when the ball leaves his hand, the ball is 2m above the ground and is moving vertically upwards with speed9m/s^-1
The motion of the ball is modlledas that of a... | 2020-09-27T13:07:51 | {
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"lm_q1_score": 0.9715639661317859,
"lm_q2_score": 0.672... |
https://proofwiki.org/wiki/Sequence_of_Integers_whose_Cube_is_Palindromic | # Sequence of Palindromic Cubes
## Sequence
The sequence of positive integers whose cube is palindromic begins:
$1, 2, 7, 11, 101, 111, 1001, 2201, 10 \, 001, 10 \, 101, \ldots$
Note that $2201$ is the smallest (and only one one known) which is itself non-palindromic.
The corresponding sequence of palindromic cube... | 2019-12-16T12:26:15 | {
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"lm_q2_sc... |
http://adrianbell.me/?cat=14 | # Pumping Lemma
Way way off the beaten path here, but this is the best example of usage of the pumping lemma I've seen. Just need somewhere to put it... The below is taken from here. Theorem: Let $L$ be a regular language, and $w$ be a string. Then there exists a constant $c$ s.t. $\forall w \in L, |w| \geq c$. We can... | 2018-12-16T15:11:14 | {
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9715639661317859,
"lm_q2_score": 0.6723316860482762,
"lm_q1q2_score": 0.6... |
https://www.physicsforums.com/threads/horizontal-tangent.755977/ | # Horizontal Tangent
1. May 31, 2014
### mill
If the tangent is horizontal, it is where the tangent is zero. In single var. calc. that would be at max. or min. for example. I am confused about what horizontal tangent refers to when I am given a parametric equation.
E.g. At what value of t does x=t^2 -t and y=t^2 +t... | 2017-08-18T08:28:08 | {
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https://etonstem.com/problem-of-the-week-answers | No 34:
Discussion: For those of you that don’t know, $\log_b a$ represents the quantity $x$, where $b^x = a$ for any $a,b$ where $b > 0$. ‘log’ is an abbreviation of ‘logarithm’. So unless you have some experience working with logarithms, it might be useful to convert the end-statement out of logarithm-world and into ... | 2021-04-11T13:35:01 | {
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"... |
http://math.stackexchange.com/questions/114419/calculating-the-standard-error-of-a-maximum-likelihood-estimator | Calculating the standard error of a maximum likelihood estimator
Suppose that $X$ is a discrete random variable with
• $P(X= 0) = 2θ/3$
• $P(X=1) = 1θ/3$
• $P(X=2) = 2(1-θ)/3$
• $P(X=3) = (1-θ)/3$
where $0\le θ\le 1$ is a parameter. The following $n=10$ independent observations were taken from such a distribution: $... | 2015-10-06T18:40:47 | {
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"lm... |
https://math.stackexchange.com/questions/1779143/integrate-sin2nx-csc2xdx | # Integrate $\sin^2(nx)\csc^2(x)dx$
I need help to integrate $$\int{\sin^2(nx)\csc^2(x)dx}$$ Integral of each part is easy $$\int{\sin^2(nx)}dx=\frac{x}{2}+\frac{\sin(2nx)}{4n}+C$$ $$\int{\csc^2(x)}dx=-\cot(x)+C$$ I then tried to use the integral by parts but failed to make it work. Also tried Walfram calculator but i... | 2019-09-17T23:13:29 | {
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"lm_q2_s... |
http://physics.stackexchange.com/questions/20768/how-to-find-maximum-velocity | # How to find maximum velocity
I stack a question about projectile question.
The question was
A projectile is being launched from ground level with no air resistance. You want to avoid having it enter a temperature inversion layer in the atmosphere a height $h$ above the ground (a) what us the maximum launch speed y... | 2014-07-30T19:42:14 | {
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"... |
https://www.physicsforums.com/threads/deriving-the-constant-e-using-a-sequence-limit.578707/ | # Deriving the constant e using a sequence limit
1. Feb 17, 2012
### Fibo's Rabbit
1. The problem statement, all variables and given/known data
Why does lim( (1+(1/n))^n ) = e?
2. Relevant equations
If a_n convergent to a, and b_n converges to b, then (a_n * b_n) converges to (a * b)
3. The attempt at a solution
... | 2019-02-17T12:04:22 | {
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"lm_q1_score": 0.97156396... |
http://math.stackexchange.com/questions/169578/mathcalk-mathcalh-is-separable | # $\mathcal{K}(\mathcal{H})$ is separable?
I am reading Arveson's Notes On Extensions of $C^*$-algebras, in proving the Corollary to Thm2, he seems to assume that $\mathcal{K}(\mathcal{H})$, the space of compact operators on a separable Hilbert space, is separable as a topological space, i.e., it contains a countable ... | 2016-05-24T23:38:44 | {
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"lm... |
https://practice.geeksforgeeks.org/problems/sum-of-fifth-powers-of-the-first-n-natural-numbers3415/1 | Sum of fifth powers of the first n natural numbers
Basic Accuracy: 23.08% Submissions: 26 Points: 1
Given a number N.Find the sum of fifth powers of natural numbers till N i.e. 15+25+35+..+N5.
Example 1:
Input:
N=2
Output:
33
Explanation:
The sum is calculated as 15+25=1+32=33.
Example 2:
Input:
N=3
Output:
276
Ex... | 2020-09-28T12:05:07 | {
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https://www.muchlearning.org/?page=62&ccourseid=1437§ionid=2703 | # Step By Step Calculus » 4.4 - Equalities and Inequalities
Synopsis
Given two functions f(x)f(x) and g(x)g(x), we are interested in finding the exact solution set for an equation of the form f(x)=g(x)f(x)=g(x) and for inequalities of the form f(x)<g(x), f(x)\le g(x), f(x)>g(x), f(x)\ge g(x)f(x)<g(x), f(x)\le g(x), f(... | 2019-03-22T02:46:57 | {
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"lm_q2_score": ... |
https://plainmath.net/3846/solution-second-homogeneous-linear-differential-equation-suppose-general | Let y_1 and y_2 be solution of a second order homogeneous linear differential equation y''+p(x)y'+q(x)=0, in R. Suppose that y_1(x)+y_2(x)=e^{-x}, W[y_1(x),y_2(x)]=e^x, where W[y_1,y_2] is the Wroian of y_1 and y_2. Find p(x), q(x) and the general form of y_1 and y_2.
Second order linear equations
Let $$y_1$$ and $$y_... | 2021-07-23T15:47:50 | {
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https://mathemerize.com/d-and-e-are-points-on-the-sides-ca-and-cb-respectively-of-a-triangle-abc-right-angled-at-c-prove-that-ae2-bc2-ab2-de2/ | # D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that $${AE}^2$$ + $${BC}^2$$ = $${AB}^2$$ + $${DE}^2$$.
## Solution :
From triangle ACE,
$${AE}^2$$ = $${EC}^2$$ + $${AC}^2$$ ……….(1) (By Pythagoras Theorem)
From triangle DCB,
$${BD}^2$$ = $${BC}^2$$... | 2022-08-17T23:08:03 | {
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https://tutorial.math.lamar.edu/ProblemsNS/CalcIII/DIPolarCoords.aspx | Paul's Online Notes
Home / Calculus III / Multiple Integrals / Double Integrals in Polar Coordinates
Show Mobile Notice Show All Notes Hide All Notes
Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is... | 2020-05-27T01:01:47 | {
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"lm_q2_score": 0.65... |
https://www.analyzemath.com/expfunction/Euler-constant-e.html | # Euler Constant e
## Euler Constant e
In compounding of interest it was shown that if, for example, an amount of money P (principal) is invested at an annual percentage rate r, the total amount of money A after t years is given by
$A = P(1 + r)^t$
It was also shown that if the interest is compounded n times during e... | 2021-09-22T23:43:47 | {
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https://astarmathsandphysics.com/university-maths-notes/matrices-and-linear-algebra/4498-atomic-triangular-matrices.html?tmpl=component&print=1&page= | ## Atomic Triangular Matrices
If the entries on the diagonal of an upper (or lower) triangular matrix are all 1, and all other entries are zero except for a single row or column above (or below) the main diagonal the matrix is said to be atomic upper (or lower) triangular.
Example: The matrix
$\left| \begin{array}{ccc... | 2017-10-22T04:50:46 | {
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https://www.jinhang.work/tech/solving-odes/ | # Solving Ordinary Differential Equations
Summation of solutions to ODEs.
An ordinary differential equation (ODE) is an equation that contains one or several derivatives of an unknown function.
ADVANCED ENGINEERING MATHEMATICS - ERWIN KREYSZIG
• The ORDER of an ODE is defined as the degree of the highest derivative... | 2021-06-23T00:05:23 | {
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"lm_q1... |
http://people.revoledu.com/kardi/tutorial/LinearAlgebra/ElementaryRowOperation.html | <Next | Previous | Index>
In linear algebra, there are 3 elementary row operations. The same operations can also be used for column (simply by changing the word “row” into “column”). The elementary row operations can be applied to a rectangular matrix size m by n.
1. Interchanging two rows of the matrix. Notation mea... | 2016-09-30T10:10:26 | {
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http://everything.explained.today/Function_composition/ | Function composition explained
In mathematics, function composition is an operation that takes two functions and and produces a function such that . In this operation, the function is applied to the result of applying the function to . That is, the functions and are composed to yield a function that maps in to in .
I... | 2020-02-28T20:28:11 | {
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"lm_q2_score": 0.65841750726... |
http://www.all-science-fair-projects.com/science_fair_projects_encyclopedia/Product_(category_theory) | # All Science Fair Projects
## Science Fair Project Encyclopedia for Schools!
Search Browse Forum Coach Links Editor Help Tell-a-Friend Encyclopedia Dictionary
# Science Fair Project Encyclopedia
For information on any area of science that interests you,
enter a keyword (eg. scientific met... | 2013-05-21T20:52:09 | {
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"url": "http://www.all-science-fair-projects.com/science_fair_projects_encyclopedia/Product_(category_theory)",
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https://www.parabola.unsw.edu.au/2000-2009/volume-45-2009/issue-3/article/solutions-problems-1301-1310 | # Solutions to Problems 1301 - 1310
Q1301 (Suggested by J. Guest, Victoria)
Solve the quartic $$(x+1)(x+5)(x-3)(x-7) = -135$$
ANS: (suggested by David Shaw, Geelong, Victoria)
Rearrange the equation as $$(x^2-2x-3)(x^2-2x-35) = -135$$ By setting $z=x^2-2x$, the above equation becomes $$z^2-38z+240=0$$
which has sol... | 2021-09-22T05:51:21 | {
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https://stupefied-davinci-2941e0.netlify.app/pythagorean-theorem-formula-for-b.html | # Pythagorean Theorem Formula For B
### A 2 + b 2 = c 2 the figure above helps us to see why the formula works.
Pythagorean theorem formula for b. The formula of pythagorean theorem. The pythagorean theorem states that if a triangle has one right angle, then the square of the longest side, called the hypotenuse, is e... | 2022-05-24T14:45:31 | {
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"lm_q1_score": 0.9920620070720564,
"lm... |
http://www.mathemafrica.org/?p=11407 | So, we can do basic algebra with complex numbers, take powers of them, and apply trig and exponential functions to them. There isn’t much left that we might want to do, but taking powers of them is very important and also pretty easy. Let’s say we wanted to calculate the solution to the equation:
$z^2=-1$
Well, we kn... | 2021-04-12T07:16:09 | {
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"lm_q1_score": 0.9920620070720565,
"lm_q2_score": 0.6584175072643413,
"lm_q1q2_... |
https://too-meta.neocities.org/anki/analysis/1567563680476/front/ | Let $$(a_n)_{n=m}^{\infty}$$ be a sequence of reals, and let $$L \ne L'$$ be two distinct real numbers. Then $$(a_n)_{n=m}^{\infty}$$ cannot converge to [...].
If $$L \ne L'$$, then there exists a positive real $$d = dist(L, L') = | L - L'|$$. As $$(a_n)_{n=m}^{\infty}$$ converges to $$L$$, we can choose a real $$0 < \... | 2023-02-07T02:37:08 | {
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9920620066026709,
"lm_q2_score": 0.658... |
https://mathematicalapologist.com/2020/12/28/computing-derivatives-part-2-explaining-calculus-8/ | # Computing Derivatives: Part 2 (Explaining Calculus #8)
Most recently in the series on calculus, we did some overview on some “precalculus” topics that we’d need for later calculus discussions. Having now done this, we move on to several examples of more ‘complicated’ rules that derivatives follow. We will then inves... | 2022-05-19T15:44:00 | {
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http://discrete.openmathbooks.org/dmoi3/sec_intro-functions.html | ## Section0.4Functions
A function is a rule that assigns each input exactly one output. We call the output the image of the input. The set of all inputs for a function is called the domain. The set of all allowable outputs is called the codomain. We would write $f:X \to Y$ to describe a function with name $f\text{,}$ ... | 2021-06-19T15:19:33 | {
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9920620062506319,
"lm_q2_score": 0... |
http://mathonline.wikidot.com/topological-quotients-in-euclidean-space | Topological Quotients in Euclidean Space
# Topological Quotients in Euclidean Space
Recall from the Topological Quotients page that if $(X, \tau)$ is a topological space and $\sim$ is an equivalence relation on $X$ where for all $x \in X$, $[x] = \{ y \in X : x \sim y \}$ denotes the equivalence class of $x$ with res... | 2020-03-30T07:51:07 | {
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"openwebmath_score": 0.995699942111969,
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"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9920620061332854,
"lm_q2_score": 0.... |
http://lousodrome.net/blog/light/tag/ray/ | # Intersection of a ray and a cone
Some time ago I needed to solve analytically the intersection of a ray and a cone. I was surprised to see that there are not that many resources available; there are some, but not nearly as many as on the intersection of a ray and a sphere for example. Add to it that they all use the... | 2019-12-09T07:46:07 | {
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"lm_q1_score": 0.9920620054292071,
"lm_q2_score": 0.6584175072643415,
"lm_q... |
https://en.wikipedia.org/wiki/Laguerre_polynomials | Laguerre polynomials
In mathematics, the Laguerre polynomials, named after Edmond Laguerre (1834 - 1886), are solutions of Laguerre's equation:
$xy'' + (1 - x)y' + ny = 0$
which is a second-order linear differential equation. This equation has nonsingular solutions only if n is a non-negative integer.
More generall... | 2015-08-03T07:38:23 | {
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"url": "https://en.wikipedia.org/wiki/Laguerre_polynomials",
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"lm_q2_score": 0.6584175072643415,... |
http://www.statemaster.com/encyclopedia/Twin-prime-conjecture | FACTOID # 3: South Carolina has the highest rate of violent crimes and aggravated assaults per capita among US states.
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Encyclopedia > Twin prime conjecture
The twin pri... | 2020-01-22T21:05:53 | {
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"lm_q2_score": 0.65841... |
https://byjus.com/jee/cartesian-product-in-set-relations-functions/ | # Cartesian Product in Set Relations Functions
The well-defined objects’ collection is termed as a set. A set with finite elements is a finite set whereas with infinite elements is an infinite set. A Set can be represented in a roster and set builder form. The collection of ordered pairs, which consists of one object ... | 2020-10-31T12:22:23 | {
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"lm_q1_score": 0.9920620047251288,
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https://db0nus869y26v.cloudfront.net/en/Domain_of_a_function | A function f from X to Y. The set of points in the red oval X is the domain of f.
Graph of the real-valued square root function, f(x) = x, whose domain consists of all nonnegative real numbers
In mathematics, the domain of a function is the set of inputs accepted by the function. It is sometimes denoted by ${\displays... | 2022-05-21T03:22:56 | {
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http://mathhelpforum.com/calculus/74127-improper-integral-log-floor-ceil-function.html | # Math Help - Improper integral with log, floor and ceil function
1. ## Improper integral with log, floor and ceil function
Compute for all integer $\alpha>1$ the value of $\int_{0}^{\infty }{\left\lfloor \log _{\alpha }\left\lfloor \frac{\left\lceil x \right\rceil }{x} \right\rfloor \right\rfloor \,dx}.$
2. very ha... | 2015-07-04T17:27:40 | {
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https://bookdown.org/manuele_leonelli/SimBook/poisson-process.html | ## 7.1 Poisson Process
Consider random events such as the arrival of customer at a shop, the arrival of emails to a mail server or the arrival of calls to a call-center. These events can be described by a counting function $$N(t)$$ defined for all $$t\geq 0$$. This counting function represents the number of events tha... | 2021-09-24T22:26:25 | {
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"lm_q1_score": 0.9920620042557432,
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https://www.jobilize.com/course/section/multiplying-matrices-in-general-by-openstax?qcr=www.quizover.com | # 0.1 Matrix concepts -- multiplying matrices
Page 1 / 1
This module covers multiplication of matrices.
## Multiplying a row matrix by a column matrix
A “row matrix” means a matrix with only one row. A “column matrix” means a matrix with only one column. When a row matrix has the same number of elements as a column... | 2020-11-29T15:59:32 | {
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http://techiemathteacher.com/2015/05/08/mtap-reviewer-for-grade-9-solution-series31-35/ | # MTAP Reviewer for Grade 9 Solution Series(31-35)
Here is the part 7 of the solution series in 2015 MTAP(MMC) reviewer for grade 9 elimination level. Other solutions can be found in this website as well as the PDF copy of all the problems.
Problem 31:
An equilateral triangle and a square have the same perimeter. Wh... | 2020-05-25T23:11:52 | {
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https://en.wikipedia.org/wiki/De_Morgan's_laws | # De Morgan's laws
De Morgan's laws represented with Venn diagrams
In propositional logic and boolean algebra, De Morgan's laws[1][2][3] are a pair of transformation rules that are both valid rules of inference. They are named after Augustus De Morgan, a 19th-century British mathematician. The rules allow the express... | 2017-01-19T23:53:24 | {
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"lm... |
http://zbmath.org/?q=an:1187.46067 | # zbMATH — the first resource for mathematics
##### Examples
Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "strai... | 2014-03-07T11:02:18 | {
"domain": "zbmath.org",
"url": "http://zbmath.org/?q=an:1187.46067",
"openwebmath_score": 0.8127076625823975,
"openwebmath_perplexity": 8335.488882921882,
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9920620066026709,
"lm_q2_score": 0.658417500561683,
"lm_q1q2_score": 0... |
https://crazyproject.wordpress.com/2011/12/12/compute-the-jordan-canonical-form-of-a-given-matrix-over-a-finite-field/ | ## Compute the Jordan canonical form of a given matrix over a finite field
Let $p$ be a prime. Compute the Jordan canonical form over the finite field $\mathbb{F}_p$ of the $n \times n$ matrix whose every entry is 1. ($n \geq 2$.)
Let $A = [1]$. Now the computation in this previous exercise holds over $\mathbb{F}_p$ ... | 2016-10-21T23:39:24 | {
"domain": "wordpress.com",
"url": "https://crazyproject.wordpress.com/2011/12/12/compute-the-jordan-canonical-form-of-a-given-matrix-over-a-finite-field/",
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"openwebmath_perplexity": 63.41969457700239,
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"lm_label": "1. YES\n2. YES",
"lm_... |
https://math.libretexts.org/Bookshelves/Algebra/Book%3A_Beginning_Algebra_(Redden)/09%3A_Solving_Quadratic_Equations_and_Graphing_Parabolas/9.01%3A_Extracting_Square_Roots |
# 9.1: Extracting Square Roots
Skills to Develop
• Solve quadratic equations by extracting square roots.
## Extracting Square Roots
Recall that a quadratic equation is in standard form if it is equal to 0:
$a x^{2}+b x+c=0$
where ab, and c are real numbers and $$a\neq 0$$. A solution to such an equation is call... | 2020-01-18T06:11:03 | {
"domain": "libretexts.org",
"url": "https://math.libretexts.org/Bookshelves/Algebra/Book%3A_Beginning_Algebra_(Redden)/09%3A_Solving_Quadratic_Equations_and_Graphing_Parabolas/9.01%3A_Extracting_Square_Roots",
"openwebmath_score": 0.9984081387519836,
"openwebmath_perplexity": 638.821500438081,
"lm_name": "Q... |
https://core.ac.uk/display/334940028 | ## Random points are optimal for the approximation of Sobolev functions
### Abstract
We show that independent and uniformly distributed sampling points are as good as optimal sampling points for the approximation of functions from the Sobolev space $W_p^s(\Omega)$ on bounded convex domains $\Omega\subset \mathbb{R}^d... | 2021-01-18T04:52:01 | {
"domain": "ac.uk",
"url": "https://core.ac.uk/display/334940028",
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9920620051945144,
"lm_q2_score": 0.658417500561683,
"lm_q1q2_score": 0.65... |
http://michaelsyao.com/calculus/trig-function-derivatives/ | # Derivatives of Trigonometric Functions
## Proofs
Recall the definition of the derivative that we introduced in our lesson on Introduction to Derivatives:
$\frac{df}{dx}=\lim_{h\rightarrow0}\frac{f(x+h)-f(x)}{h}$
Consider the case where $f(x)=\sin x$. Plugging this into the definition of the derivative above, we f... | 2021-03-06T01:33:08 | {
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"url": "http://michaelsyao.com/calculus/trig-function-derivatives/",
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https://artofproblemsolving.com/wiki/index.php/1998_CEMC_Gauss_(Grade_7)_Problems/Problem_15 | # 1998 CEMC Gauss (Grade 7) Problems/Problem 15
## Problem
The diagram shows a magic square in which the sums of the numbers in any row, column or diagonal are equal. What is the value of n?
[A 3x3 magic square grid is shown. 8 is in the 1st row 1st column. 9 is in the 2nd row 1st column. 4 is in the 2nd row 3rd col... | 2022-01-26T17:06:20 | {
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"url": "https://artofproblemsolving.com/wiki/index.php/1998_CEMC_Gauss_(Grade_7)_Problems/Problem_15",
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https://icsecbsemath.com/2016/07/30/class-8-chapter-22-linear-equations-exercise-22b/ | Question 1: $\displaystyle 17$ less than four times a number is $\displaystyle 11$ . Find the number.
$\displaystyle \text{Let the number } = x$
$\displaystyle \Rightarrow 4x-17 = 11$
$\displaystyle \Rightarrow x = \frac{28}{4} = 7$
$\displaystyle \\$
Question 2: If $\displaystyle 10$ be added to four times a cert... | 2022-01-25T01:10:56 | {
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"lm_q1_score": 0.9920620047251287,... |
https://significantstatistics.com/index.php/Lecture_4._E)_Uniform | # Uniform Distribution on $\left[a,b\right]$
A r.v. $X$ follows a uniform distribution $U\left(a,b\right)$ if $X$ is continuous with pdf
$f_{X}\left(X\right)=\begin{cases} \frac{1}{b-a}, & x\in\left[a,b\right]\\ 0, & otherwise \end{cases}$
Under the Uniform distribution, all values in $\left[a,b\right]$ are “equally... | 2020-10-22T15:46:33 | {
"domain": "significantstatistics.com",
"url": "https://significantstatistics.com/index.php/Lecture_4._E)_Uniform",
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"lm_q1_score": 0.9920620047251288,
"lm_q2_... |
https://math.wikia.org/wiki/Group | 1,183 Pages
A group is a set paired with an operation on the set. As such, a group can be conceptualized as an ordered pair , where is a set, and is an operation.
A set and operation is a group if and only if it satisfies the following properties:
1. Identity elementThere exists an , called an identity element, such... | 2020-12-05T06:01:23 | {
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"url": "https://math.wikia.org/wiki/Group",
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"lm_q1_score": 0.9920620044904359,
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"lm_q1q2_score":... |
https://www.princeton.edu/~achaney/tmve/wiki100k/docs/Bolzano%E2%80%93Weierstrass_theorem.html | # Bolzano–Weierstrass theorem
related topics {math, number, function} {rate, high, increase} {mi², represent, 1st}
In real analysis, the Bolzano–Weierstrass theorem is a fundamental result about convergence in a finite-dimensional Euclidean space Rn. The theorem states that each bounded sequence in Rn has a converge... | 2017-11-23T08:05:31 | {
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.99206200425... |
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