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url string | text string | date timestamp[s] | meta dict |
|---|---|---|---|
https://www.astroml.org/astroML-notebooks/chapter9/astroml_chapter9_Classification.html | # Classification¶
In density estimation we estimate joint probability distributions from multivariate data sets to identify the inherent clustering. This is essentially unsupervised classification
If we have labels for some of these data points (e.g., an object is tall, short, red, or blue) we can develop a relations... | 2021-09-26T04:27:58 | {
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"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.971563966131785... |
http://math.stackexchange.com/questions/246272/finding-fourier-coefficients-of-an-orthonormal-sequence | # Finding Fourier coefficients of an orthonormal sequence
I am trying to find the Fourier coefficients of f with respect to the sequence $$\lbrace \phi_k \rbrace_{k=1}^\infty = \lbrace \frac{1}{\sqrt{2 \pi}}, \frac{\cos(x)}{\sqrt{\pi}}, \frac{\sin(x)}{\sqrt{\pi}},..., \frac{\cos(kx)}{\sqrt{\pi}}, \frac{\sin(kx)}{\sqrt... | 2016-02-09T08:14:06 | {
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0... |
https://www.homeworklib.com/qaa/875334/how-do-you-simplify-frac-3x-2-y-3-9x-4-y-5 | Question
# How do you simplify \frac { 3x ^ { - 2} y ^ { 3} } { 9x ^ { 4} y ^ { 5} }?
How do you simplify \frac { 3x ^ { - 2} y ^ { 3} } { 9x ^ { 4} y ^ { 5} }?
Answer 1
See a solution process below:
#### Explanation:
First, rewrite this expression as:
$\frac{3}{9} \left({x}^{-} \frac{2}{x} ^ 4\right) \left({y}^... | 2022-05-23T21:05:39 | {
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"... |
https://math.stackexchange.com/questions/1169005/how-to-integrate-int-0-infty-frace-t-frac1t-sqrt-t-dt | # How to integrate $\int_0^{\infty}\frac{e^{-(t+\frac1t)}}{\sqrt t} dt$?
This is a problem given in my homework . I have to find the integral$$\int \limits_{0}^{\infty} \frac{e^{-(t+\frac{1}{t})}}{\sqrt t}dt$$
I am trying to use integral representation of the gamma function but I was not able to get it in the region ... | 2020-04-08T10:10:51 | {
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"lm_name": "Qwen/Qwen-72B",
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"lm_q1_score": ... |
https://www.baotgm.net/forum/qz2rgw.php?1d5445=continuous-random-variable-graph | # continuous random variable graph
Example 2: A person’s rounded weight (to the nearest pound) (discrete). This follows a Bernoulli distribution with only 2 possible outcomes and a single coin flip at a time.
The quantity $$f\left( x \right)\,dx$$ is called probability differential. Let’s generate data with numpy to ... | 2021-06-23T06:51:21 | {
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"url": "https://www.baotgm.net/forum/qz2rgw.php?1d5445=continuous-random-variable-graph",
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"openwebmath_perplexity": 472.2685057075407,
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9715639661317859,
"lm_q2_sc... |
http://math.stackexchange.com/questions/286100/absolute-function-continuous-implies-function-piecewise-continuous | # Absolute function continuous implies function piecewise continuous?
I have a simple true/false question that I am not sure on how to prove it.
If $|f(x)|$ is continuous in $]a,b[$ then $f(x)$ is piecewise continuous in $]a,b[$
Anyone that can point me in the right direction or give a counterexample, even though I ... | 2014-08-21T18:43:49 | {
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"lm_label": "1. YES\n2. YES",
"lm_... |
https://mathoverflow.net/questions/92456/if-any-perfect-set-is-uncountable-in-a-metric-space-which-is-not-complete/92465 | # If any perfect set is uncountable in a metric space which is not complete?
We know that every ferfect set $E$ in a complete metric space $X$ is uncountable. My question is if there exists a metric space which is not complete, but every ferfect set in it is uncountable. The ferfect set here means a closed set which h... | 2020-08-12T10:26:53 | {
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"url": "https://mathoverflow.net/questions/92456/if-any-perfect-set-is-uncountable-in-a-metric-space-which-is-not-complete/92465",
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"openwebmath_perplexity": 247.83842536049866,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
... |
http://math.stackexchange.com/questions/280785/fractal-structure-of-the-sum-of-squares-function | # fractal structure of the sum of squares function
The sum of squares function came up at a job interview, corrected for signs and symmetry.
$d_2(n)=\#\{(x,y): x^2 + y^2 = n\}$
However, want $(x,y)\sim (\pm x, \pm y) \sim (y,x)$. The first 20 numbers are:
1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0
... | 2015-01-29T12:30:31 | {
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.97156396... |
https://mathhelpboards.com/threads/problem-of-the-week-209-may-31-2016.18735/ | # Problem of the Week #209 - May 31, 2016
Status
Not open for further replies.
#### Euge
##### MHB Global Moderator
Staff member
Here is this week's POTW:
-----
Define the logarithm of an $n\times n$ matrix $A$ by the power series
$$\sum_{k = 1}^\infty \frac{(-1)^{k-1}(A - I)^k}{k}$$
which converges for $\|A - I\... | 2020-07-08T06:51:09 | {
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http://mathdl.maa.org/mathDL/23/?pa=content&sa=viewDocument&nodeId=3321&pf=1 | Thinking Outside the Box -- or Maybe Just About the Box
Abstract
We present a fresh look at an age-old calculus problem, the box problem. The box problem is traditionally used as one of the typical exemplars for the study of optimization. However, this paper illustrates that another box problem, tied much closer to r... | 2013-05-18T19:22:51 | {
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"lm_q1_score": 0.9715639636617014,
"lm_q2_score": 0... |
https://www.shaalaa.com/question-bank-solutions/using-differentials-find-approximate-value-following-up-3-places-decimal-2657-1-3-approximations_12727 | Share
# Using Differentials, Find the Approximate Value of the Following up to 3 Places of Decimal (26.57)^(1/3) - CBSE (Commerce) Class 12 - Mathematics
#### Question
Using differentials, find the approximate value of the following up to 3 places of decimal
(26.57)^(1/3)
#### Solution
(26.57)^(1/3)
Is there an ... | 2019-12-13T14:08:05 | {
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https://socratic.org/questions/what-is-the-speed-of-an-object-that-travels-from-9-4-6-to-7-1-2-over-3-s | # What is the speed of an object that travels from ( -9,4,-6) to ( 7,1,-2 ) over 3 s?
Mar 11, 2018
Well it is not said that by which path the object reached its end point from initial point of journey.
Distance is the direct path length which we need to know for calculating speed.
Let's consider that here the obj... | 2020-07-07T05:34:01 | {
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"url": "https://socratic.org/questions/what-is-the-speed-of-an-object-that-travels-from-9-4-6-to-7-1-2-over-3-s",
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"lm_q1_score": 0.971... |
https://cs.stackexchange.com/questions/7029/inapproximability-result-implies-apx-hardness | # Inapproximability result implies apx-hardness?
If an optimization problem is known to be inapproximable up to some precision, does this automatically imply that the problem is apx-hard?
If P$=$NP then there is a polytime algorithm for any NP optimization problem, and so every problem is APX-hard. So from now on, su... | 2021-04-15T08:04:04 | {
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"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.971563970248... |
http://mathoverflow.net/questions/15415/infinitely-many-prime-numbers-of-the-form-n2k1/15418 | # Infinitely many prime numbers of the form $n^{2^k}+1$?
I am not a specialist of number theory, so please excuse my ignorance: is the following question still an open problem? Let $k \in \mathbb{N}^*$, are there infinitely many prime numbers of the form $n^{2^k}+1$?
-
What's known about the problem if both n and k a... | 2016-05-02T20:04:30 | {
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"lm_name": "Qwen/Qwen-72B",
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"lm_q1_score": 0.97156... |
https://math.stackexchange.com/questions/1343266/binary-quadratic-optimization-problem | I am trying to solve the following binary quadratic program.
$$\min_{\Delta} \Delta^T H \Delta + c^T\Delta \\ \text{Such that:} ~~~\Delta\in \{0,1\}^n ~~\text{and}~~ \sum_{i=1}^n \Delta_i \leq \Gamma$$
where $H$ is not a positive semidefinite matrix (and hence the minimization problem is not convex) and $\Gamma$ is a... | 2019-07-20T15:34:52 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/1343266/binary-quadratic-optimization-problem",
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"openwebmath_perplexity": 132.63891623084695,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.97156397024859... |
https://www.gradesaver.com/textbooks/math/algebra/elementary-and-intermediate-algebra-concepts-and-applications-6th-edition/chapter-9-inequalities-and-problem-solving-9-2-intersections-unions-and-compound-inequalities-9-2-exercise-set-page-590/53 | Chapter 9 - Inequalities and Problem Solving - 9.2 Intersections, Unions, and Compound Inequalities - 9.2 Exercise Set - Page 590: 53
$$(4,8]$$
Work Step by Step
To graph a one-variable inequality, first use the rules of inequalities to solve the inequality. (Recall, when multiplying or dividing by a negative number... | 2020-03-31T21:59:10 | {
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"openwebmath_score": 0.7601... |
https://quant.stackexchange.com/questions/45551/one-period-binomial-option-valuation-model | # One Period Binomial Option Valuation Model [closed]
My question here is how is the probability of an up move calculated by $$(1+Rf-D)\over(U-D)$$ derived where Rf is the risk free rate, D is the down move factor and U represents the up move factor.
Kindly help me understand the derivation and where this formula com... | 2019-08-24T11:43:27 | {
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"url": "https://quant.stackexchange.com/questions/45551/one-period-binomial-option-valuation-model",
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"openwebmath_perplexity": 961.0639798647614,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.9715639... |
https://plainmath.net/38163/from-0-2-sin-x-2-dx-using-trapezoidal-rule-with-n-equal-4-as-well | # From 0-2 \sin(x^{2}) dx using trapezoidal rule with n=4 as well
From 0-2 $$\displaystyle{\sin{{\left({x}^{{{2}}}\right)}}}{\left.{d}{x}\right.}$$ using trapezoidal rule with n=4 as well as midpoint rule with n=4
• Questions are typically answered in as fast as 30 minutes
### Solve your problem for the price of one... | 2022-01-26T11:51:41 | {
"domain": "plainmath.net",
"url": "https://plainmath.net/38163/from-0-2-sin-x-2-dx-using-trapezoidal-rule-with-n-equal-4-as-well",
"openwebmath_score": 0.822970449924469,
"openwebmath_perplexity": 1817.710419753763,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9715639694252... |
https://onlinecourses.science.psu.edu/stat501/node/293 | Lesson 6: MLR Model Evaluation
Printer-friendly version
Introduction
For the simple linear regression model, there is only one slope parameter about which one can perform hypothesis tests. For the multiple linear regression model, there are three different hypothesis tests for slopes that one could conduct. They are... | 2018-01-20T19:13:47 | {
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"lm_q1_score": 0.9715639694252316,
"lm_q2_score": 0.6723317057447908... |
https://socratic.org/questions/how-do-you-simplify-sqrt80-sqrt5-1 | # How do you simplify sqrt80 / sqrt5?
Jun 8, 2016
$\sqrt{16} = 4$
#### Explanation:
Neither 80 nor 5 are square numbers. There are two options:
First method: When we are dividing with square roots, we can combine the two roots into one and then simplify.
$\frac{\sqrt{80}}{\sqrt{5}} = \sqrt{\frac{80}{5}}$
$\sqrt{\... | 2019-11-15T17:25:17 | {
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"url": "https://socratic.org/questions/how-do-you-simplify-sqrt80-sqrt5-1",
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"openwebmath_perplexity": 1678.724981143367,
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9715639694252316,
"lm_q2_score": 0.6723... |
http://mathhelpforum.com/differential-equations/155315-understanding-notation-1st-order-linear-differentiation-equation.html | # Math Help - Understanding notation in a 1st order linear differentiation equation
1. ## Understanding notation in a 1st order linear differentiation equation
Hi all,
I'm having difficulty understanding conventions for DE, and I suppose calculus in general. I have not had calculus in several years, so I'm trying to... | 2014-11-22T18:16:16 | {
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"url": "http://mathhelpforum.com/differential-equations/155315-understanding-notation-1st-order-linear-differentiation-equation.html",
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"openwebmath_perplexity": 701.0532553578254,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YE... |
http://bgmrodotec.com.br/service-blueprint-hwqjvj/eigenvalue-hat-matrix-544f51 | k D E γ 3 ( ) Then. {\displaystyle {\begin{bmatrix}0&0&0&1\end{bmatrix}}^{\textsf {T}}} I Each eigenvalue appears V Furthermore, an eigenvalue's geometric multiplicity cannot exceed its algebraic multiplicity. {\displaystyle d\leq n} Now we need to find the basic eigenvectors for each $$\lambda$$. . [18], The first num... | 2021-11-28T18:49:04 | {
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"openwebmath_perplexity": 670.8908166394581,
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9715639694252315,
"lm_q2_score":... |
https://commalg.subwiki.org/wiki/Euclideanness_is_localization-closed | # Euclideanness is localization-closed
This article gives the statement, and possibly proof, of a commutative unital ring property (i.e., Euclidean ring) satisfying a commutative unital ring metaproperty (i.e., localization-closed property of commutative unital rings)
View all commutative unital ring metaproperty sati... | 2022-01-24T13:18:18 | {
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9715639694252316,
"lm_q2_score": 0.67... |
https://www.coursehero.com/file/ppeo3lc/For-a-CT-ramp-signal-is-designated-by-rt-and-mathematically-defined-as-t-t-t-t/ | For a CT ramp signal is designated by rt and mathematically defined as t t t t
# For a ct ramp signal is designated by rt and
• 253
This preview shows page 124 - 137 out of 253 pages.
For a C.T. ramp signal is designated by r(t) and mathematically defined as 0 0 0 ) ( t t t t r Graphical representation We can also ... | 2020-08-04T12:15:56 | {
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"openwebmath_perplexity": 1099.5550101191993,
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"lm_label": "1. YES\n2. YES\n\n",... |
http://farmaciacoverciano.it/elliptic-paraboloid-general-equation.html | # Elliptic Paraboloid General Equation
While analysing several examples of the use of the hyperbolic paraboloid surface in architecture, the paper proposes three modes of symbolic use of the surface: operative, demonstrative and figurative. How does one derive the equations for hyperboloids, cone, ellipsoids (really, ... | 2020-05-26T10:12:39 | {
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http://mathhelpforum.com/business-math/180186-now-value-summation-problem.html | # Math Help - Now-value? Summation problem.
1. ## Now-value? Summation problem.
This is the problem from the book:
A winner in a lottery can receive 50.000kr(swedish currency) every month for 25 years. The winner wants to know what the prise money is worth today.
a) What monthly interest rate is equivalent of a yea... | 2014-03-12T10:37:39 | {
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"lm... |
https://mathhelpboards.com/threads/partial-differential-equations-problem-finding-the-general-solution.25111/ | # Partial differential equations problem - finding the general solution
#### Another
##### Member
$$\displaystyle 4\frac{\partial u}{\partial t}+\frac{\partial u}{\partial x} = 3u$$ , $$\displaystyle u(x,0)=4e^{-x}-e^{-5x}$$
let $$\displaystyle U =X(x)T(t)$$
so
$$\displaystyle 4X\frac{\partial T}{\partial t}+T\fra... | 2021-06-14T11:18:51 | {
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http://bmccompany.com.ua/princess-bride-nkghuhb/symbolab-turning-point-486de0 | # symbolab turning point
A Turning Point is an x-value where a local maximum or local minimum happens: How many turning points does a polynomial have? The Degree of a Polynomial with one variable is the largest exponent of that variable. Free Parabola Foci (Focus Points) calculator - Calculate parabola focus points gi... | 2021-04-17T03:21:00 | {
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"lm_q1_score": 0.9715639686018702,
"lm_q2_scor... |
http://math.stackexchange.com/questions/264082/find-minimum-of-a-function-with-abs-and-squares-analytically?answertab=oldest | # find minimum of a function with abs and squares analytically
maybe someone here can help me. I want to find the analytical minimum '$x_\mathrm{opt} = \arg\min f(x)$' of the following function: $$f(x) = \alpha |c + x| + \beta x^2$$ where $x$ is a real number ($x$ is_element_of $\mathbb{R}$), $c$ is a real constant ($... | 2015-12-01T04:18:45 | {
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"openwebmath_perplexity": 389.1511708180629,
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"lm_label": "1. YES\n2. YE... |
http://math.stackexchange.com/questions/87752/checking-for-meeting-clashes | # Checking for Meeting Clashes
I've been sent here from StackOverflow with my mathematical / algorithm question.
I am currently working with an organisation developing a web system, one area attempting to resolve in-house training clashes.
An example (as best as I can describe is):
What the company is attempting to... | 2016-02-14T04:51:54 | {
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https://www.physicsforums.com/threads/simple-tension-problem.327606/ | # Simple Tension problem
1. Jul 28, 2009
### PhysicsMark
1. The problem statement, all variables and given/known data
A 125 lb weight is suspended from the ceiling by means of two perpendicular flexible cables. Find the tension (in pounds) in each cable. There is a picture attached. I'm new at posting so I'll try m... | 2017-11-19T01:49:55 | {
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http://www.epsilon-delta.org/2012/03/extraneous-solutions-of-log-equations.html | ## Tuesday, March 27, 2012
### Extraneous Solutions of Log Equations--A Graphical Representation
Last semester when I taught log equations, a curious student asked, "Why is it that we sometimes get extraneous solutions?" A fantastic question that, at the time, I answered horribly. I gave some mumbo-jumbo explanatio... | 2015-09-05T01:05:54 | {
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https://www.qalaxia.com/questions/The-sum-of-two-odd-numbers-is-60-how-do | Vivekanand Vellanki
1
Let x and y be the two numbers (ignoring the fact that x and y are odd for now).
We know that x+y=60. We want to maximize the value of xy.
xy\ =\ x\left(60\ -x\right)\ =\ 60x\ -\ x^2.
If you take a function and differentiate the function, the differential will be 0 at two places - the maxima a... | 2020-08-06T00:27:44 | {
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"lm_q2_score"... |
https://jharkhandboardsolution.com/jac-class-9-maths-solutions-chapter-10-ex-10-6/ | JAC Class 9 Maths Solutions Chapter 10 Circles Ex 10.6
Jharkhand Board JAC Class 9 Maths Solutions Chapter 10 Circles Ex 10.6 Textbook Exercise Questions and Answers.
JAC Board Class 9th Maths Solutions Chapter 10 Circles Ex 10.6
Page-186
Question 1.
Prove that the line of centres of two intersecting circles subten... | 2022-12-04T06:02:50 | {
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http://math.stackexchange.com/questions/72195/correlation-function | # Correlation Function
1. Let $X, Y$ be random variables. If $\rho(X,Y) = a$ (Correlation), where $a \in (0,1)$, what can be said about the relationship between $X$ and $Y$? Is it true that $Y = bX + c + Z$, where $Z$ is a random variable? If it is true then how is $|Z|$ related to the correlation a?
-
With no indepe... | 2016-02-14T00:36:37 | {
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"lm_q1_score": 0.9715639686018701,
"lm_q2_score": ... |
https://physics.stackexchange.com/questions/211082/conditions-on-expressing-magnetic-field-in-terms-of-curl-of-current-density | # Conditions on expressing magnetic field in terms of curl of current density
Given a current density distribution $\mathbf J(\mathbf x)$ inside a closed bounded region $\Omega$, the magnetic field at any point $\mathbf y$ outside of $\Omega$ can be expressed as \begin{aligned}\mathbf B(\mathbf y)&=\frac{\mu_0}{4\pi}\... | 2021-01-26T11:38:24 | {
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"openwebmath_perplexity": 406.47348608821943,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2.... |
http://mathhelpforum.com/trigonometry/2679-need-help-2-word-problems.html | Math Help - Need Help With 2 Word Problems
1. Need Help With 2 Word Problems and Checking 2 Problems
The biggest bridge in the world is the bridge over the Royal Gorge of the Arkansas River in Colorado. Sightings to the same point at water level directly under the bridge are taken from each side of the 880-foot long ... | 2014-10-01T22:58:33 | {
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"url": "http://mathhelpforum.com/trigonometry/2679-need-help-2-word-problems.html",
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"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9715639686018701,
"lm_q2_s... |
https://mathoverflow.net/questions/288000/an-extremal-problem-related-either-to-an-uncertainty-principle-on-the-circle-or | # An extremal problem related either to an uncertainty principle on the circle, or else to the prime number theorem
Consider for $X = 1,2, \ldots$ the set $\mathcal{S}_X$ of trigonometric polynomials $f(t) := \sum_{|k| \leq X} c_k e^{2\pi i kt}$ on the circle $\mathbb{T} := \mathbb{R}/\mathbb{Z}$ of degree $\leq X$ (F... | 2020-01-19T05:52:54 | {
"domain": "mathoverflow.net",
"url": "https://mathoverflow.net/questions/288000/an-extremal-problem-related-either-to-an-uncertainty-principle-on-the-circle-or",
"openwebmath_score": 0.9333779811859131,
"openwebmath_perplexity": 107.71181217817382,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",... |
http://www.highschooltestprep.com/sat/math/practice-test-2b/ | # Practice Test 2B
## Quiz #105
Congratulations - you have completed Quiz #105.
You scored %%SCORE%% out of %%TOTAL%%.
Your performance has been rated as %%RATING%%
Question 1
The circumference of a right circular cylinder is half its height. The radius of the cylinder is x. What is the volume of the cylinder in ... | 2018-02-25T00:04:41 | {
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"lm_q1_score": 0.9715639677785087,
"lm_q2_score": 0.... |
https://robotics.stackexchange.com/questions/20333/finding-quaternion-q-where-y-q-x-q-inv | # Problem
Quaternions $$X$$, $$Y$$, which represents 3-dimensional points are given. Quaternion $$q$$ is what is to be solved.
I want to know unknown rotation between $$X$$ and $$Y$$. In other words, I want to find $$q$$ in the following equation.
$$Y = q * X * \overline{q}$$
$$\overline{q}$$ means conjugate quater... | 2021-09-27T16:24:24 | {
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"lm_q1_score": 0.971563967778... |
https://math.stackexchange.com/questions/2572531/calculate-limit-lim-x-to0-frac-log1-fracx43-sin6x-without | # Calculate limit: $\lim_{x\to0} \frac{\log(1+\frac{x^4}{3})}{\sin^6(x)}$ without de l'Hôpital rule
I want to calculate the limit:
$$\lim_{x\to0} \frac{\log(1+\frac{x^4}{3})}{\sin^6(x)}$$
Obviously the Indeterminate Form is $\frac{0}{0}$.
I've tried to calculate it writing:
$$\sin^6(x)$$
as
$$\sin^2(x) \cdot \si... | 2022-01-26T06:19:02 | {
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"url": "https://math.stackexchange.com/questions/2572531/calculate-limit-lim-x-to0-frac-log1-fracx43-sin6x-without",
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"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score... |
http://mathhelpforum.com/advanced-statistics/5766-joint-probability-density.html | 1. ## Joint probability density
If the joint probability density of X and Y is given by
f(x,y)=2 for x>0, y>0, x+y<1
and zero elsewhere
find P(X>2Y)
When I draw a picture with that restriction above( y<(1/2)x and y<1-x )
I get 1/3, but I want to solve this one by using double integral
2. Originally Posted by Judi
... | 2017-06-23T09:29:03 | {
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"lm_q1_score": 0.9715639677785088... |
https://www.lil-help.com/questions/234420/math-533-week-6-course-project-part-b-salescall-inc | MATH 533 Week 6 Course Project Part B (SALESCALL Inc.)
# MATH 533 Week 6 Course Project Part B (SALESCALL Inc.)
G
0 points
## MATH 533 Week 6 Course Project Part B - Hypothesis Testing and Confidence Intervals
a. The average (mean) sales per week exceeds 41.5 per salesperson. b. The true population proportion of sa... | 2019-10-19T02:58:27 | {
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"openwebmath_perplexity": 2304.196031605438,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.9715639677... |
https://intuitivetutorial.com/2020/12/29/intuition-behind-orthogonality/ | # What does it mean to say orthogonal?
In this article, let us explore what is meant by the concept of orthogonality.
Orthogonal or orthogonality is often introduced from a mathematical perspective. In general, most resources explains it in terms of linear algebra and vectors.
One such example is when we learn about... | 2023-03-30T23:40:35 | {
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"lm_... |
https://math.stackexchange.com/questions/3688928/how-to-prove-that-a-holomorphic-function-on-an-open-simply-connected-space-has-a | # How to prove that a holomorphic function on an open simply connected space has a primitive?
I want to prove:
Let $$\Omega$$ be an open simply connected subspace of $$\mathbb C$$. Let $$f:\Omega\to\mathbb C$$ be holomorphic. Then $$f$$ has a primitive (antiderivative) on $$\Omega$$.
I don't want to use Cauchy's int... | 2021-04-23T09:16:52 | {
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"openwebmath_perplexity": 124.22474671036694,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\... |
https://www.physicsforums.com/threads/revs-per-min-from-metres-per-second.123028/ | # Revs per min from metres per second
1. Jun 6, 2006
### Taryn
okay so here is the problem and here is wat I did!
I am just tryin to study up for exams now... and this is one of the problems!
A sample of blood is placed in a centrifuge of radius 17.5 cm. The mass of a red corpuscle is 3.00×10-16 kg, and the magnitu... | 2018-01-21T21:16:43 | {
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"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.9715639677785087... |
https://homework.cpm.org/category/CCI_CT/textbook/calc/chapter/3/lesson/3.1.1/problem/3-13 | ### Home > CALC > Chapter 3 > Lesson 3.1.1 > Problem3-13
3-13.
1. Is the function graphed below continuous at the following values of x? If not, explain which conditions of continuity fail. Homework Help ✎
x = −4, −2, 0, and 2
Now use the three conditions to test if the function is continuous at x = −2, x = 0 and x ... | 2020-01-24T21:18:34 | {
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... |
https://aas.sh/blog/laplaces-rule-of-succession/ | # Laplace's rule of succession
## A post on one of my favourite mathematical theorems.
I find myself talking to many people about this bit of maths simply because I've actually been able to apply it in my life and work. Hopefully in this post I can explain how!
Ashley Smith
# The sunrise problem
## A scientific cer... | 2022-12-08T01:47:12 | {
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"url": "https://aas.sh/blog/laplaces-rule-of-succession/",
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"lm_q1q2_... |
http://math.stackexchange.com/questions/246908/proving-that-idempotence-follows-from-other-lattice-axioms/246914 | # Proving that idempotence follows from other lattice axioms
I am supposed to prove that $x\wedge x = x$ and $x\vee x = x$ follow from the other lattice axioms (associativity, commutativity and absorption).
So far I have $$x = x\vee(x\wedge x) = x\vee(x\wedge(x\wedge(x\vee x))) = x\vee ((x\wedge x)\wedge(x\vee x))$$
... | 2016-02-10T18:36:48 | {
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"openwebmath_perplexity": 206.27311002568445,
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"lm_label": "1. YES\n2. YES",
"lm_q... |
https://economics.stackexchange.com/questions/11722/finding-an-exchange-rate-and-competitive-equilibrium-given-an-initial-allocation | # Finding an exchange rate and competitive equilibrium given an initial allocation and utility function [closed]
I am attempting to solve the following question.
"Smith and Jones are stranded on a desert island. Each has in his possession some slices of ham (H) and cheese (C).
Smith is a choosy eater and will eat ha... | 2020-06-07T03:46:25 | {
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"url": "https://economics.stackexchange.com/questions/11722/finding-an-exchange-rate-and-competitive-equilibrium-given-an-initial-allocation",
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"openwebmath_perplexity": 438.3608051097795,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YE... |
https://collegephysicsanswers.com/openstax-solutions/what-speed-would-200-times-10-textrm-kg-airplane-have-fly-have-momentum-160 | Question
(a) At what speed would a $2.00 \times 10^ \textrm{ kg}$ airplane have to fly to have a momentum of $1.60 \times 10^9 \textrm{ kg m/s}$ (the same as the ship’s momentum in the problem above)? (b) What is the plane’s momentum when it is taking off at a speed of $60.0 \textrm{ m/s}$? (c) If the ship is an aircra... | 2019-02-17T02:11:43 | {
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"openwebmath_score": 0.8425610065460205,
"openwebmath_perplexity": 453.2177483613582,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1... |
https://csdms.colorado.edu/wiki/Model_help:AgDegBW | # Model help:AgDegBW
## AgDegBW
It is the Calculator for aggradation and degradation of a river reach using a backwater formulation. This program computes 1D bed variation in rivers due to differential sediment transport. The sediment is assumed to be uniform with size D. All sediment transport is assumed to occur in... | 2022-10-02T21:41:13 | {
"domain": "colorado.edu",
"url": "https://csdms.colorado.edu/wiki/Model_help:AgDegBW",
"openwebmath_score": 0.49387770891189575,
"openwebmath_perplexity": 4323.563092485786,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9715639669551472,
"lm_q2_score": 0.6723317057447908,
... |
https://answerbun.com/mathematics/if-fabfafb-then-fagdeta/ | # If $f(AB)=f(A)f(B)$ then $f(A)=g(det(A))$
Mathematics Asked on January 1, 2022
Let $$mathbb{K}$$ a field, $$f: M_n(mathbb{K}) to mathbb{K}$$ non constant sucht that: $$f(AB)=f(A)f(B)$$.
Prove that there exist an endomorphism $$g$$ on the monoid $$(mathbb{K}, cdot)$$ such that $$f(A)=g(mathrm{det}(A))$$ for all $$A... | 2023-02-03T07:33:48 | {
"domain": "answerbun.com",
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"openwebmath_perplexity": 567.5729635171849,
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9715639669551474,
"lm_q2_score": 0.67233170574... |
https://dsp.stackexchange.com/questions/70794/dft-of-pure-sinusoidal-wave?noredirect=1 | DFT of pure sinusoidal wave
I'm writing a program in which you can synthesize waves by adding to a sound's Fourier transform, and then inverse the transform to get the modified sound. In order to do this, I need to know what to add to the DFT to synthesize a pure wave. I've tried to learn about Fourier synthesis from ... | 2021-05-07T22:24:23 | {
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"url": "https://dsp.stackexchange.com/questions/70794/dft-of-pure-sinusoidal-wave?noredirect=1",
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"openwebmath_perplexity": 267.08420323177927,
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.97156396613178... |
https://www.physicsforums.com/threads/mathematical-notation.82722/ | # Mathematical notation
1. Jul 20, 2005
### Yegor
T is an index set. And for each $$t \in T$$ $$A_t$$ is a set
$$\bigcup_{t \in T} A_t = \{x : \exists t \in T with x \in A_t \}$$
What means this $$\bigcup$$ symbol and entire expression?
And question on index set: is it used just for orderring any other set?
2. Jul ... | 2017-04-27T17:09:03 | {
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"lm_q1_score": 0.9715639661317859,
"lm_q2_sco... |
https://math.stackexchange.com/questions/3221744/family-of-linear-functionals-on-separable-banach-space-coinciding-with-norm-when | # Family of linear functionals on separable Banach space coinciding with norm when evaluated in one element
let $$B$$ be a real, separable and infinite-dimensional Banach space and let $$x_1$$, $$x_2$$, $$x_3$$, $$\dots$$ be a dense subset of $$B$$. In the proof of Lemma 2.1 on p. 2 in this article, the author takes b... | 2019-06-25T05:47:04 | {
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"openwebmath_perplexity": 174.31141999681114,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\... |
http://f7maps.com/oh-happy-adtb/g6v1thr.php?page=poincar%C3%A9-disk-model-bdd8e4 | u {\displaystyle \operatorname {arctanh} } with hyperbolic metric. ( 1 = Even the famous Poincar´e disk existed before him. 1 Opening the Geogebra Geometry in Windows 10 and crashing A "Custom Layer" option Poincar¶e Models of Hyperbolic Geometry 9.1 The Poincar¶e Upper Half Plane Model The next model of the hyperbolic... | 2021-05-15T15:20:22 | {
"domain": "f7maps.com",
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"openwebmath_score": 0.8203872442245483,
"openwebmath_perplexity": 848.4637129548809,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9715639653084245,
"lm_q2_s... |
https://math.stackexchange.com/questions/714294/the-number-of-numbers-not-divisible-by-2-3-5-7-or-11-between-multiples-of-2 | # The number of numbers not divisible by $2,3,5,7$ or $11$ between multiples of $2310$
Looking at partitions of the natural number line of the form $P=[a,b)$, I noted that
• if $a$ and $b$ are multiples of $6$, there exist at least $2$ numbers in the partition which are not divisible by $2$ or $3$
• if $a$ and $b$ ar... | 2020-07-13T21:42:58 | {
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"openwebmath_perplexity": 205.61620115861592,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YE... |
http://crypto.stackexchange.com/questions/11807/secure-function-evaluation?answertab=votes | # Secure function evaluation
Consider 3 parties, Alice, Bob and Charlie. Suppose each party has a bit as input, i.e. Alice, Bob and Charlie hold $a, b, c \in \{0, 1\}$ respectively. Show how construct a scheme with which they can compute the function $f (a, b, c) = a \oplus b \oplus c$ such that the following are sati... | 2015-07-06T23:35:23 | {
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"openwebmath_perplexity": 1081.248142399177,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.9715639... |
http://www.ni.com/documentation/en/labview/1.0/m-ref/polyvalmx/ | # polyvalmx
Version:
Evaluates a polynomial at a matrix value you specify.
## Syntax
c = polyvalmx(a, b)
Legacy name: polyvalm
## a
Coefficients in descending order of power of the polynomial you want to evaluate. a is a vector.
## b
Value at which you want to evaluate a. b is a square matrix.
## c
Evaluated ... | 2018-08-16T14:10:03 | {
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"openwebmath_perplexity": 3451.0438437929256,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.9715639653084245,
"lm_q2_score": 0.6723317... |
http://mathhelpforum.com/calculus/53259-sequences.html | # Math Help - Sequences
1. ## Sequences
Give an example of two divergent sequences X and Y such that:
A.) their sum X + Y converges
B.) their product XY converges
Note: X and Y do not need to be the same for A.) and B.)
2. Originally Posted by jkru
A.) their sum X + Y converges
$x_n = (-1)^n$ and $y_n = (-1)^{n+1}... | 2014-11-28T18:21:05 | {
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"lm_q2_score": 0.672331... |
http://math.stackexchange.com/questions/44518/differential-inequality | # Differential inequality
1. I start with simple differential inequality: find $u\in C^1[0,1]$ such that $u(0) = 0$ and $$u'(t)\leq -u(t)$$ for all $t\in [0,1]$. Using Gronwall's lemma one can see that $u\leq 0$. On the other hand it seems to be the only solution, since this inequality keep $u$ non-decreasing for $u<0... | 2015-12-02T02:09:27 | {
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9715639653084244,
"lm_q2_scor... |
http://codeforces.com/problemset/problem/1088/A | Rating changes for last rounds are temporarily rolled back. They will be returned soon. ×
A. Ehab and another construction problem
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output
Given an integer $x$, find 2 integers $a$ and $b$ such that:
• $1 \le a,b \le... | 2022-05-20T19:41:04 | {
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"... |
https://socratic.org/questions/how-do-you-test-the-alternating-series-sigma-1-n-2-n-2-1-2-n-3-5-from-n-is-0-oo-#492061 | # How do you test the alternating series Sigma (-1)^n(2^(n-2)+1)/(2^(n+3)+5) from n is [0,oo) for convergence?
Oct 19, 2017
Note that:
${a}_{n} = \frac{{2}^{n - 2} + 1}{{2}^{n + 3} + 5}$
${a}_{n} = \frac{{2}^{n} \cdot {2}^{-} 2 + 1}{{2}^{n} \cdot {2}^{3} + 5}$
${a}_{n} = \frac{{2}^{n} \left(\frac{1}{4} + {2}^{-} n... | 2022-01-25T17:37:13 | {
"domain": "socratic.org",
"url": "https://socratic.org/questions/how-do-you-test-the-alternating-series-sigma-1-n-2-n-2-1-2-n-3-5-from-n-is-0-oo-#492061",
"openwebmath_score": 0.8727567791938782,
"openwebmath_perplexity": 7493.016298284694,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q... |
https://socratic.org/questions/how-do-you-find-the-lcd-between-20c-12c-2 | # How do you find the LCD between 20c, 12c^2?
Jul 6, 2016
LCD is $60 {c}^{2}$
#### Explanation:
The LCD must be divisible by both $20 c \mathmr{and} 12 {c}^{2}$
One way to find the LCD (especially of only 2 numbers) is to consider the multiples of the larger of the two (20). Look for the first of the multiples whi... | 2021-12-06T23:41:49 | {
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"url": "https://socratic.org/questions/how-do-you-find-the-lcd-between-20c-12c-2",
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"openwebmath_perplexity": 380.7971478484487,
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.971563964485063,
"lm_q2_score": ... |
http://math.stackexchange.com/questions/103766/is-there-a-generic-function-to-find-the-area-of-any-shape | # Is there a generic function to find the area of any shape?
Given the coordinates of all points making up a two-dimensional shape and the order in which they are connected, is there any generic formula that will give the area of that shape?
EDIT: The list of points would be a list of all of the vertices.
-
There ar... | 2013-05-19T23:48:20 | {
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"openwebmath_perplexity": 255.9841027446505,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score":... |
https://www.gradesaver.com/textbooks/math/trigonometry/CLONE-68cac39a-c5ec-4c26-8565-a44738e90952/appendix-d-graphing-techniques-exercises-page-449/61 | ## Trigonometry (11th Edition) Clone
For $f(x) = -\sqrt{x}$ when $x = 9, y = -3;$ $x = 4, y = -2;$ $x = 1, y = -1;$ $x = 0, y = 0$ As seen, $f(x) = -\sqrt{x}$ is the reflection across the $x$-axis of $f(x) = \sqrt{x}$. Domain = $[0, \infty)$ Range = $(-\infty, 0]$ | 2022-07-03T17:44:49 | {
"domain": "gradesaver.com",
"url": "https://www.gradesaver.com/textbooks/math/trigonometry/CLONE-68cac39a-c5ec-4c26-8565-a44738e90952/appendix-d-graphing-techniques-exercises-page-449/61",
"openwebmath_score": 0.9144225120544434,
"openwebmath_perplexity": 616.1214262394897,
"lm_name": "Qwen/Qwen-72B",
"lm... |
https://www.meritnation.com/cbse-class-8/math/rs-aggarwal-2017/quadrilaterals/textbook-solutions/10_1_3134_5670_185_53121 | Rs Aggarwal 2017 Solutions for Class 8 Math Chapter 15 Quadrilaterals are provided here with simple step-by-step explanations. These solutions for Quadrilaterals are extremely popular among Class 8 students for Math Quadrilaterals Solutions come handy for quickly completing your homework and preparing for exams. All qu... | 2019-07-24T03:38:39 | {
"domain": "meritnation.com",
"url": "https://www.meritnation.com/cbse-class-8/math/rs-aggarwal-2017/quadrilaterals/textbook-solutions/10_1_3134_5670_185_53121",
"openwebmath_score": 0.40633925795555115,
"openwebmath_perplexity": 1214.7982942646163,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",... |
https://mod.readthedocs.io/en/latest/ | # mod – modular arithmetic in Python¶
## Description¶
Modular arithmetic is arithmetic for integers, where numbers wrap around when reaching a given value called modulus. For example 6 ≡ 1 (mod 5). Modular arithmetic has several practical applications including: music, banking, book publishing, cryptography… and of c... | 2023-03-28T15:37:50 | {
"domain": "readthedocs.io",
"url": "https://mod.readthedocs.io/en/latest/",
"openwebmath_score": 0.5715584754943848,
"openwebmath_perplexity": 4828.33777138485,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.971563964485063,
"lm_q2_score": 0.6723317057447908,
"lm_q1q2_sco... |
https://harangdev.github.io/applied-data-science-with-python/applied-social-network-analysis-in-python/3/ | # Influence Measures and Network Centrality
Categories:
Updated:
## Network Centrality
Centrality measures identify the most important nodes in a network.
Examples in real world
• Influential nodes in a social network.
• Nodes that disseminate information to many nodes or prevent epidemics.
• Hubs in a transporta... | 2020-07-10T13:36:30 | {
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"url": "https://harangdev.github.io/applied-data-science-with-python/applied-social-network-analysis-in-python/3/",
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"openwebmath_perplexity": 5326.6710403842235,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.971... |
https://www.elitedigitalstudy.com/10152/find-the-values-of-k-for-each-of-the-quadratic-equations-so-that-they-have-two-equal-roots-kx-x-2-6-0 | Find the values of k for each of the quadratic equations, so that they have two equal roots.kx (x – 2) + 6 = 0
Asked by Abhisek | 1 year ago | 195
##### Solution :-
kx(x – 2) + 6 = 0
or kx2 – 2kx + 6 = 0
Comparing the given equation with ax2 + bx + c = 0, we get
a = k, b = – 2k and c = 6
We know, Discriminant =... | 2022-12-02T23:50:14 | {
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"openwebmath_score": 0.832870364189148,
"openwebmath_perplexity": 711.494851250044,
"lm_name": "Qwen/Qwen-72B",
"lm_lab... |
https://socratic.org/questions/how-do-you-factor-6x-3-6x-2-x-1 | # How do you factor 6x^3-6x^2-x+1?
Mar 23, 2018
$6 {x}^{3} - 6 {x}^{2} - x + 1$
$= x \left(6 {x}^{2} - 6 x - 1 + 1\right)$
$= x \left(6 {x}^{2} - 6 x\right)$
$= 6 x \left({x}^{2} - x\right)$
Mar 23, 2018
$6 {x}^{3} - 6 {x}^{2} - x + 1 = \left(6 {x}^{2} - 1\right) \left(x - 1\right)$
$\textcolor{w h i t e}{6 {x}^{3... | 2020-09-19T06:15:05 | {
"domain": "socratic.org",
"url": "https://socratic.org/questions/how-do-you-factor-6x-3-6x-2-x-1",
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"openwebmath_perplexity": 4351.4445682781425,
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.971563964485063,
"lm_q2_score": 0.6723317... |
https://math.stackexchange.com/questions/1656499/convexe-functions-geometric-interpretation | # Convexe functions , geometric interpretation !!
let $\Omega$ be an open subset of $\mathbb{R}^n$ and $f$ a smooth convexe function $f:\Omega\rightarrow \mathbb{R}$, and let $x_0\in\Omega$ we have always this inequality :
$$\forall x\in\Omega\space :f(x)\geq f(x_0)+<\nabla f , x-x_0>$$
i want to know what is the ge... | 2021-09-26T13:11:51 | {
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"url": "https://math.stackexchange.com/questions/1656499/convexe-functions-geometric-interpretation",
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"openwebmath_perplexity": 118.41264612856216,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.971563964... |
https://search.r-project.org/CRAN/refmans/cmna/html/pwiselinterp.html | pwiselinterp {cmna} R Documentation
Piecewise linear interpolation
Description
Finds a piecewise linear function that interpolates the data points
Usage
pwiselinterp(x, y)
Arguments
x a vector of x values y a vector of y values
Details
pwiselinterp finds a piecewise linear function that interpolates the data... | 2022-05-28T00:50:28 | {
"domain": "r-project.org",
"url": "https://search.r-project.org/CRAN/refmans/cmna/html/pwiselinterp.html",
"openwebmath_score": 0.4147190451622009,
"openwebmath_perplexity": 4609.688140994825,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.971563964485063,
"lm_q2_score"... |
http://mathoverflow.net/questions/23960/how-big-can-the-hausdorff-dimension-of-a-function-graph-get/23972 | # How big can the Hausdorff dimension of a function graph get?
This question is inspired by How kinky can a Jordan curve get?
What is the least upper bound for the Hausdorff dimension of the graph of a real-valued, continuous function on an interval? Is the least upper bound attained by some function?
It may be note... | 2016-06-01T05:34:43 | {
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"openwebmath_perplexity": 815.3235518597054,
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"lm_label": "1. YES\n2. YES",
"lm_q1_score":... |
https://brilliant.org/discussions/thread/how-can-i-use-this/ | ×
# How can I use this?
Is there a way I could use the derivative of a polynomial $$f(x)$$, i.e, finding the slope of $$f(x)$$ at a given or any $$x$$ to solve polynomial problems, like the problems that show up in math olympiads and tests?
Thank you!
Note by Shashank Rammoorthy
2 years ago
Sort by:
Yes of course... | 2017-10-17T22:05:43 | {
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"lm_q1_score": 0.9715639636617015,
"lm_q2_score": 0.6723... |
http://mathhelpforum.com/calculus/134727-difficult-integral.html | 1. ## Difficult integral!?!
I have no idea where to go on this one:
using substitution t = sinx evaluate the following integral within the limits pi/2 to pi/6:
4cosx /(3 + (cosx)^2 dx
i thought about using t^2 = s(inx)^2 but get in a right mess!
Can you help?
Thanks D
2. Originally Posted by dojo
I have no idea ... | 2016-09-30T18:06:42 | {
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"lm_q1_score": 0.9715639636617015,
"lm_q2_score... |
https://pysit.readthedocs.io/en/latest/exercises/part_1.html | # Part 1: The Foward Problem¶
In this exercise, you will implement a solver for the 1D scalar acoustic wave equation with absorbing boundary conditions,
$\begin{split}(\frac{1}{c(x)^2}\partial_{tt}-\partial_{xx})u(x,t) & = f(x,t), \\ (\frac{1}{c(0)}\partial_t-\partial_x)u(0,t) & = 0, \\ (\frac{1}{c(1)}\partial_t+\par... | 2021-06-20T18:22:51 | {
"domain": "readthedocs.io",
"url": "https://pysit.readthedocs.io/en/latest/exercises/part_1.html",
"openwebmath_score": 0.6819044947624207,
"openwebmath_perplexity": 1106.8096359100118,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9715639636617014,
"lm_q2_score": 0.672331... |
https://math.stackexchange.com/questions/2280208/direct-product-of-projective-modules | # Direct product of projective modules
For any nonempty family like $\{ {M_\alpha}\}_{\alpha \in I}$ of $R$-modules we know that if $\prod_{\alpha \in I} M_\alpha$ is a projective $R$-module,then for all $\alpha \in I$, $\{ {M_\alpha}\}_{\alpha \in I}$ is projective too. Is the converse true? If not give me a counter-... | 2019-10-21T22:23:03 | {
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"url": "https://math.stackexchange.com/questions/2280208/direct-product-of-projective-modules",
"openwebmath_score": 0.8151372671127319,
"openwebmath_perplexity": 392.550745259559,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9715639636617014,... |
http://clay6.com/qa/70486/which-of-the-following-2-statements-is-true- | # Which of the following 2 statements is true ? $\text{Statement 1 : All squares are rectangles.}$ $\text{Statement 2 : All rectangles are squares.}$
$(A) \; Statements \;1\;and\;2 \\(B)\;None\;of\;these \\(C)\; Only\;statement\;2 \\(D)\;Only\;statement\; 1$ | 2020-06-01T08:22:59 | {
"domain": "clay6.com",
"url": "http://clay6.com/qa/70486/which-of-the-following-2-statements-is-true-",
"openwebmath_score": 0.3355986177921295,
"openwebmath_perplexity": 282.799087926155,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9715639620149783,
"lm_q2_score": 0.672... |
https://rootsoftheequation.wordpress.com/2015/07/ | ## Trying to find math inside everything else
### Fighting for the Center
At the Math Games morning session at Twitter Math Camp 15, we’ve been created curricular games that hit on some topics that there aren’t really good games for. I came up with the idea for this one, and worked on refining it with the help of Pau... | 2017-10-17T17:02:03 | {
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"url": "https://rootsoftheequation.wordpress.com/2015/07/",
"openwebmath_score": 0.3285069465637207,
"openwebmath_perplexity": 500.9869787830328,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.971563970248593,
"lm_q2_score": 0.6723316991792861,
... |
https://daaronr.github.io/micro-giving-pub/consumers-dmd.html | # 4 Consumer preferences, constraints and choice, demand functions
## 4.1 Consumer preferences, indifference curves/sets (0.5 weeks)
We will cover most of O-R chapter 4, but we will skip section 4.6 (differentiability)
### 4.1.1 “Bundles of goods” (O-R 4.1)
Let’s consider two goods only, for now.
In O-R notation:
... | 2022-06-27T19:58:19 | {
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"url": "https://daaronr.github.io/micro-giving-pub/consumers-dmd.html",
"openwebmath_score": 0.838452935218811,
"openwebmath_perplexity": 2378.9852756645423,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9715639702485929,
"lm_q2_score": 0.67233169917... |
https://math.stackexchange.com/questions/2429835/injective-mathcalo-x-module-is-flasque | Injective $\mathcal{O}_X$ module is flasque
This is a lemma from Hartshorne.
Let $(X,\mathcal{O}_X)$ be a ringed space. Then any injective $\mathcal{O}_X$ module is flasque.
I am trying to prove this. Let $V\subseteq U$ be open subsets of $X$, we need to prove that the restriction map $\mathcal{F}(U)\rightarrow \mat... | 2019-07-21T18:10:37 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/2429835/injective-mathcalo-x-module-is-flasque",
"openwebmath_score": 0.9682597517967224,
"openwebmath_perplexity": 145.95100707141853,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9715639702485... |
https://cs.stackexchange.com/questions/111620/dubins-tsp-crossing-trajectory-theorem | # Dubins TSP crossing trajectory theorem
In the Dubins TSP (DTSP for short), one needs to visit a set of given points in the plane, and return to the starting point, minimizing the distance of such a trajectory. The difference with the Euclidean TSP (ETSP for short) however is that the visiting entity is curvature con... | 2019-11-15T23:32:34 | {
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"url": "https://cs.stackexchange.com/questions/111620/dubins-tsp-crossing-trajectory-theorem",
"openwebmath_score": 0.7415285706520081,
"openwebmath_perplexity": 1080.7983741417434,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9715639702485929... |
https://blackandbrowncreations.shop/en/mathematical-induction-steps-example.html | # Mathematical induction steps example
Induction Examples Question 4. Consider the sequence of real numbers de ned by the relations x1 = 1 and xn+1 = p 1+2xn for n 1: Use the Principle of Mathematical Induction to show that xn < 4 for all n 1. Solution. For any n 1, let Pn be the statement that xn < 4. Base Case. The ... | 2022-11-27T01:20:05 | {
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"openwebmath_perplexity": 490.8550506331018,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.97156397024... |
https://open.kattis.com/problems/target | Kattis
# Target Practice
In target practice you sometimes shoot at cardboard figures. In this problem a target is described by a simple polygon which is the outline of the target. For each target you will find out where a number of shots fired at the target struck. Some may have hit the target and some may have misse... | 2020-07-10T09:15:16 | {
"domain": "kattis.com",
"url": "https://open.kattis.com/problems/target",
"openwebmath_score": 0.54581218957901,
"openwebmath_perplexity": 432.21598178095337,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9715639702485929,
"lm_q2_score": 0.672331699179286,
"lm_q1q2_score... |
https://proofwiki.org/wiki/Definition:Eigenvalue | # Definition:Eigenvalue
## General Definition
Let $H$ be a Hilbert space over $\Bbb F \in \set {\R, \C}$.
Let $A \in \map B H$ be a bounded linear operator.
A scalar $\alpha \in \Bbb F$ is said to be an eigenvalue of $A$ if and only if:
$\map \ker {A - \alpha I} \ne \paren {\mathbf 0_H}$
That is, if and only if t... | 2020-05-26T03:11:56 | {
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"url": "https://proofwiki.org/wiki/Definition:Eigenvalue",
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9715639702485928,
"lm_q2_score": 0.672331699179286,
"... |
https://math.stackexchange.com/questions/913934/process-to-show-that-sqrt-2-sqrt3-3-is-irrational?noredirect=1 | # Process to show that $\sqrt 2+\sqrt[3] 3$ is irrational
How can I prove that the sum $\sqrt 2+\sqrt[3] 3$ is an irrational number ??
• Welcome to MSE! When you post a question, please try to supply some context and indicate your own thoughts on a solution. See here for further guidelines. – vociferous_rutabaga Aug ... | 2020-12-02T03:22:09 | {
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"openwebmath_perplexity": 271.01344102182685,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_... |
https://www.physicsforums.com/threads/centroid-problem.647502/ | # Centroid problem
1. Oct 27, 2012
### 3soteric
1. The problem statement, all variables and given/known data
Find the centroid of the region in the first quadrant of the xy-plane bounded by the graphs of the equations:
x=0, x=1, y=x-x^2, and y^2=2x
2. Relevant equations
xbar: integral of x dA/ integral of dA
ybar:... | 2017-08-23T12:00:05 | {
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"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.9715639702485929,
"lm_q2_score": ... |
http://mathhelpforum.com/calculus/141274-limsup-calculation.html | # Math Help - limsup calculation
1. ## limsup calculation
How do I solve the following limit?
2. Originally Posted by GIPC
How do I solve the following limit?
The $\frac{n}{3} - \big{[}{\frac{n}{3}}\big{]}$ part only takes three values. $0$, $\frac{1}{3}$ and $\frac{2}{3}$. If you want to prove this set n to be equa... | 2014-12-26T03:18:45 | {
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"lm_q1_score": 0.9715639702485929,
"lm_q2_score... |
https://forum.math.toronto.edu/index.php?PHPSESSID=jh17fgq9gjjla8v71ncb3c64p4&topic=2418.0;prev_next=next | Author Topic: Quiz 2- Lec 5101-A (Read 617 times)
Pengyun Li
• Full Member
• Posts: 20
• Karma: 14
Quiz 2- Lec 5101-A
« on: October 01, 2020, 07:08:28 PM »
$\textbf{Question}$: Find the limit of each function at the given point, or explain why it does not exist: $f(z) = (z-2)log|z-2|$ at $z_0 = 2$.
$\textbf{Answer}... | 2022-05-26T05:50:13 | {
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"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.971... |
https://math.stackexchange.com/questions/2258326/m-is-a-square-martix-and-%CF%86-v-to-v-then-why-mt-m-%CF%86-m | # M is a square martix, and $φ^*$ : $V^* \to V^*$, then why $M^T=M_{φ^*_M}$? [duplicate]
Let M be a matrix, transpose $M^T$ is the matrix who's i,j component is the j,i component of M.
And let $\phi\in Hom(V,V)$, we define $\phi^*: V^* \to V^*$ by $\phi^*(f)(v)=f(\phi(v))$ where $V^*$ is the dual space of $V$.
$M_{φ... | 2019-10-21T07:37:00 | {
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"url": "https://math.stackexchange.com/questions/2258326/m-is-a-square-martix-and-%CF%86-v-to-v-then-why-mt-m-%CF%86-m",
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"openwebmath_perplexity": 460.13228426739926,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_... |
https://www.physicsforums.com/threads/fibonacci-sequence.252654/ | # Fibonacci sequence
1. Aug 30, 2008
### Euler_Euclid
if $$a_1, a_2, a_3 .............$$ belong to the fibonacci sequence, prove that
$$a_1a_2 + a_2a_3 + ............ + a_{2n-1}a_{2n} = (a_{2n})^2$$
2. Aug 30, 2008
### uart
If you are familiar with mathematical induction then that's the way to go with this one. ... | 2016-12-04T00:10:59 | {
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"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.9715639694252316,
"lm_q2_score":... |
http://math.stackexchange.com/questions/191306/sum-of-angles-in-mathbbrn?answertab=votes | # Sum of angles in $\mathbb{R}^n$
Given three vectors $v_1,v_2$ and $v_3$ in $\mathbb{R}^n$ with the standard scalar product the follwing is true $$\angle(v_1,v_2)+\angle(v_2,v_3)\geq \angle(v_1,v_3).$$
It tried to substitute $\angle(v_1,v_2) = cos^{-1}\frac{v_1 \cdot v_2}{\Vert v_1 \Vert \Vert v_2 \Vert}$ but I coul... | 2015-08-30T03:56:06 | {
"domain": "stackexchange.com",
"url": "http://math.stackexchange.com/questions/191306/sum-of-angles-in-mathbbrn?answertab=votes",
"openwebmath_score": 0.8958613872528076,
"openwebmath_perplexity": 724.1872229548151,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9715639694252... |
https://math.stackexchange.com/questions/1048831/calculate-winning-outcomes-of-plurality-voting | # Calculate winning outcomes of plurality voting
My problem is similar to this one, but different in some significant ways.
As in the above question, I have voting with $n$ voters and $m$ candidates. However, I care about which voter voted for which candidate. As such, there are a total of $m^n$ possible configuratio... | 2019-04-24T06:38:37 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/1048831/calculate-winning-outcomes-of-plurality-voting",
"openwebmath_score": 0.19224394857883453,
"openwebmath_perplexity": 515.5242815871771,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.97156... |
https://homework.cpm.org/category/CCI_CT/textbook/int3/chapter/7/lesson/7.2.5/problem/7-115 | ### Home > INT3 > Chapter 7 > Lesson 7.2.5 > Problem7-115
7-115.
Consider the graph at right.
1. Is the graph a function? Explain.
What causes a graph to be a function or not a function?
Look up 'function' in the glossary if you aren't sure.
2. Sketch the inverse of this graph. Is the inverse a function? Justify y... | 2020-07-04T05:43:33 | {
"domain": "cpm.org",
"url": "https://homework.cpm.org/category/CCI_CT/textbook/int3/chapter/7/lesson/7.2.5/problem/7-115",
"openwebmath_score": 0.5196684002876282,
"openwebmath_perplexity": 1695.4476645290474,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9715639694252315,
... |
https://www.ianhaberman.org/2019/05/10/setting-the-curve/ | # Setting The Curve
I teach economics.
Sometimes, at the end of the semester, the distribution of grades does not properly capture the class outcomes observed by the instructor. This happens for a variety of reasons. A common question asked by colleagues is “What should I do to correct this?”
In the long run, a cour... | 2019-08-17T21:19:18 | {
"domain": "ianhaberman.org",
"url": "https://www.ianhaberman.org/2019/05/10/setting-the-curve/",
"openwebmath_score": 0.5399166941642761,
"openwebmath_perplexity": 466.70662355792524,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9715639694252315,
"lm_q2_score": 0.67233169... |
https://proofwiki.org/wiki/Definition:Integrable_Function/Lebesgue | # Definition:Integrable Function/Lebesgue
## Definition
Let $\lambda^n$ be a Lebesgue measure on $\R^n$ for some $n > 0$.
Let $f: \R^n \to \overline \R$ be an extended real-valued function.
Then $f$ is said to be Lebesgue integrable if and only if it is $\lambda^n$-integrable.
Similarly, for all real numbers $p \g... | 2021-04-12T04:34:58 | {
"domain": "proofwiki.org",
"url": "https://proofwiki.org/wiki/Definition:Integrable_Function/Lebesgue",
"openwebmath_score": 0.9597986340522766,
"openwebmath_perplexity": 269.9405172918306,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.9715639694252315,
"lm_q2_score": ... |
https://math.stackexchange.com/questions/753130/is-there-a-simple-and-fast-way-of-computing-the-residue-at-an-essential-singular | # Is there a simple and fast way of computing the residue at an essential singularity?
Is there a simple and fast way of computing the residue at an essential singularity ?
I mean if we have a pole of order $n$ at $c$ we can use the formula :
$$\mathrm{Res}(f,c) = \frac{1}{(n-1)!} \lim_{z \to c} \frac{d^{n-1}}{dz^{n... | 2021-09-17T01:41:42 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/753130/is-there-a-simple-and-fast-way-of-computing-the-residue-at-an-essential-singular",
"openwebmath_score": 0.9593754410743713,
"openwebmath_perplexity": 157.18969803624788,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n... |
https://math.stackexchange.com/questions/3138148/cubic-runout-spline-cubic-spline | # Cubic runout spline (cubic spline)
I was studying cubic spline interpolation and then I stumbled upon "Cubic runout spline". The idea behind it is that you set the boundary conditions for second derivatives to be:
$$f_1''(x_0) = 2f_1''(x_1) - f_2''(x_2)$$
$$f_n''(x_n) = 2f_n''(x_{n-1}) - f_{n-1}''(x_{n-2})$$
As a... | 2019-05-23T09:49:28 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/3138148/cubic-runout-spline-cubic-spline",
"openwebmath_score": 0.8481559753417969,
"openwebmath_perplexity": 315.4800575979509,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9715639694252315,
... |
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