Search is not available for this dataset
url string | text string | date timestamp[s] | meta dict |
|---|---|---|---|
https://netposition-international.com/50jfrs/1e0451-diagonal-matrix-and-scalar-matrix | Write a Program in Java to input a 2-D square matrix and check whether it is a Scalar Matrix or not. If you supply the argument that represents the order of the diagonal matrix, then it must be a real and scalar integer value. Program to print a matrix in Diagonal Pattern. scalar matrix synonyms, scalar matrix pronunci... | 2021-05-08T12:33:54 | {
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"openwebmath_score": 0.7704491019248962,
"openwebmath_perplexity": 769.1851159820291,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes\n\n",
"lm_q1_score": 0.... |
http://math.stackexchange.com/questions/32095/how-can-i-can-solve-integrals-of-rational-functions-of-polynomials-in-x | # How can I can solve integrals of rational functions of polynomials in $x$?
I would like to know a way to solve integrals such as this one: $$\int \frac{x}{3x - 4}dx$$
Also, I assume similar integrals where x is squared are solved in a similar manner. (If the answer is yes then don't also show me how to solve this s... | 2014-03-10T08:17:20 | {
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"url": "http://math.stackexchange.com/questions/32095/how-can-i-can-solve-integrals-of-rational-functions-of-polynomials-in-x",
"openwebmath_score": 0.99144446849823,
"openwebmath_perplexity": 327.8362674036093,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm... |
http://gnpaperjenq.blinkingti.me/writing-piecewise-functions.html | # Writing piecewise functions
Steps to writing piecewise functions to find the equation of the line 1 find two points on the line 2 find slope 3 use point and slope in point slope form and. This is the vid to find the piecewise defined equation from a graph first i find the equations of the pieces then i find the piec... | 2018-06-25T15:38:53 | {
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"url": "http://gnpaperjenq.blinkingti.me/writing-piecewise-functions.html",
"openwebmath_score": 0.35177916288375854,
"openwebmath_perplexity": 1138.781222556325,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.9777138118632621,
"lm_q2_score": 0.91... |
https://math.stackexchange.com/questions/3144423/side-length-of-the-smallest-square-that-can-be-dissected-into-n-squares-with-i | # Side length of the smallest square that can be dissected into $n$ squares with integer sides
Let $$s_n$$ be the shortest possible side length of a square constructed from exactly $$n$$ squares of positive integer side lengths. If no such square exists, let $$s_n = 0$$.
The first few values are as follows:
n | s(n... | 2019-05-22T09:01:42 | {
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"url": "https://math.stackexchange.com/questions/3144423/side-length-of-the-smallest-square-that-can-be-dissected-into-n-squares-with-i",
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"openwebmath_perplexity": 155.73528915402062,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2.... |
http://yf-sensei.com/sd2n0z/e3b785-diagonal-matrix-and-scalar-matrix | What are synonyms for scalar matrix? This behavior occurs even if … Is it true that the only matrix that is similar to a scalar matrix is itself Hot Network Questions Was the title "Prince of Wales" originally claimed for the English crown prince via a trick? Powers of diagonal matrices are found simply by raising each... | 2021-12-08T10:07:12 | {
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"url": "http://yf-sensei.com/sd2n0z/e3b785-diagonal-matrix-and-scalar-matrix",
"openwebmath_score": 0.715437114238739,
"openwebmath_perplexity": 769.3692635243086,
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"lm_label": "1. Yes\n2. Yes\n\n",
"lm_q1_score": 0.9702399060540359,
"lm_q2_score":... |
https://math.stackexchange.com/questions/2869817/evaluate-int-0-frac-pi2-frac-sin-x-cos-x-sin4x-cos4xdx/2870118 | # Evaluate $\int_0^{\frac{\pi}{2}}\frac{\sin x\cos x}{\sin^4x+\cos^4x}dx$
Evaluate $$\int_0^{\frac{\pi}{2}}\frac{\sin(x)\cos(x)}{\sin^4(x)+\cos^4(x)}dx$$
I used the substitution $\sin x =t$, then I got the integral as $$\int_0^1 \frac{t}{2t^4-2t^2+1}dt$$
• You see how the equation looks very ugly right now? The answ... | 2019-05-25T23:14:51 | {
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"url": "https://math.stackexchange.com/questions/2869817/evaluate-int-0-frac-pi2-frac-sin-x-cos-x-sin4x-cos4xdx/2870118",
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"openwebmath_perplexity": 4408.834301154089,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_... |
https://mymathforum.com/threads/how-do-i-find-the-average-speed-when-an-airplane-is-flying-in-circles.347485/ | # How do I find the average speed when an airplane is flying in circles?
#### Chemist116
The problem is as follows:
At an air exhibition a biplane is flying in circles as shown in the figure from below. It is known that type of motion of this airplane is a rotation with constant angular acceleration. The radius of t... | 2019-12-05T19:55:32 | {
"domain": "mymathforum.com",
"url": "https://mymathforum.com/threads/how-do-i-find-the-average-speed-when-an-airplane-is-flying-in-circles.347485/",
"openwebmath_score": 0.8539042472839355,
"openwebmath_perplexity": 300.23666741283523,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES\n\n",
"lm_q1... |
https://or.stackexchange.com/questions/6078/modelling-precedence-relations/6079#6079 | # Modelling precedence relations
I have two tasks $$i$$ and $$k$$ with durations $$d_i$$ and $$d_k$$, where $$d_i$$ and $$d_k$$ are nonnegative variables.
I would like to model that $$i$$ may precede $$k$$ or $$k$$ may precede $$i$$ and that they may not overlap.
So, with $$t_i$$ and $$t_k$$ denoting the start times... | 2021-09-24T09:08:49 | {
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"url": "https://or.stackexchange.com/questions/6078/modelling-precedence-relations/6079#6079",
"openwebmath_score": 0.9552558660507202,
"openwebmath_perplexity": 696.3225962960692,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.9773707999669... |
https://math.stackexchange.com/questions/3193300/given-constraints-in-how-many-ways-can-actors-be-chosen-for-roles | # Given constraints, in how many ways can actors be chosen for roles?
Given $$13$$ actors and $$6$$ unique roles, in how many ways can the actors be assigned a role if a certain actor (Alan) will not join if another actor (Betty) joins?
My method was to compute total unrestricted number of ways less the number of way... | 2019-05-23T10:50:38 | {
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"url": "https://math.stackexchange.com/questions/3193300/given-constraints-in-how-many-ways-can-actors-be-chosen-for-roles",
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"openwebmath_perplexity": 178.6729837181932,
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"lm_label": "1. YES\n2. YES",
"lm_... |
https://math.stackexchange.com/questions/2863427/factorising-complex-numbers | # Factorising complex numbers
4 years ago, when I learned about factorising and complex numbers, me and my friend worked on factorising complex numbers.
For example, $4+2i= 3-(-1)+2i = 3-i^2+2i = -(i^2-2i-3) = -(i-3)(i+1)$
The goal was to represent $a+bi$ with product of same form. where $a$ and $b$ are integer.
An... | 2020-10-23T21:41:59 | {
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"url": "https://math.stackexchange.com/questions/2863427/factorising-complex-numbers",
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"openwebmath_perplexity": 392.94744343388356,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.983847165177859,
"lm_... |
https://stats.stackexchange.com/questions/377143/how-is-sample-mean-divided-by-sample-std-distributed-for-normal-distributions | # How is sample mean divided by sample STD distributed for normal distributions?
Let's assume that we sample N times from a normal distribution with known mean and variance. With a generated sample we calculate sample mean and sample standard deviation. Then we divide sample mean by sample standard deviation (STD) to ... | 2021-09-18T04:06:28 | {
"domain": "stackexchange.com",
"url": "https://stats.stackexchange.com/questions/377143/how-is-sample-mean-divided-by-sample-std-distributed-for-normal-distributions",
"openwebmath_score": 0.9622633457183838,
"openwebmath_perplexity": 1957.3370992438336,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2.... |
https://www.physicsforums.com/threads/electric-field-created-by-point-charges-and-conducting-plane.909946/ | # I Electric field created by point charges and conducting plane
Tags:
1. Apr 2, 2017
### KV71
I came upon this:
http://physics.stackexchange.com/qu...change-if-we-place-a-metal-plat/323006#323006
question on Physics Stackexchange which I found very interesting.
The configuration is basically two positive point ch... | 2018-01-21T18:58:17 | {
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"url": "https://www.physicsforums.com/threads/electric-field-created-by-point-charges-and-conducting-plane.909946/",
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"openwebmath_perplexity": 484.3853374788014,
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"lm_label": "1. Yes\n2. Yes",
"lm_q1_score... |
https://math.stackexchange.com/questions/3172005/find-all-triplets-a-b-c-less-than-or-equal-to-50-such-that-a-b-c-be-div | # Find all triplets $(a,b,c)$ less than or equal to 50 such that $a + b +c$ be divisible by $a$ and $b$ and $c$.
Find all triplets $$(a,b,c)$$ less than or equal to 50 such that $$a + b +c$$ be divisible by $$a$$ and $$b$$ and $$c$$.(i.e $$a|a+b+c~~,~~b|a+b+c~~,~~c|a+b+c$$) for example $$(10,20,30)$$ is a good triplet... | 2019-05-23T21:13:24 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/3172005/find-all-triplets-a-b-c-less-than-or-equal-to-50-such-that-a-b-c-be-div",
"openwebmath_score": 0.5972553491592407,
"openwebmath_perplexity": 210.0160019481613,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
... |
https://math.stackexchange.com/questions/1020066/puzzle-of-gold-coins-in-the-bag/1020151 | Puzzle of gold coins in the bag
At the end of Probability class, our professor gave us the following puzzle:
There are 100 bags each with 100 coins, but only one of these bags has gold coins in it. The gold coin has weight of 1.01 grams and the other coins has weight of 1 gram. We are given a digital scale, but we ca... | 2019-10-23T23:26:28 | {
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"url": "https://math.stackexchange.com/questions/1020066/puzzle-of-gold-coins-in-the-bag/1020151",
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"openwebmath_perplexity": 425.22829000385326,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.982287700259... |
http://mathhelpforum.com/algebra/134779-compounding-interest-problem-help.html | # Math Help - Compounding interest problem help
1. ## Compounding interest problem help
Hello everyone, I am working on a math project relating to logarithms, exponential growth and decay, and I have the following problem to work on:
8. The final amount for $5000 invested for 25 years at 10% annual interest compound... | 2014-12-18T20:41:05 | {
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"url": "http://mathhelpforum.com/algebra/134779-compounding-interest-problem-help.html",
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"openwebmath_perplexity": 1187.416238672969,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9893474872757474,
"lm... |
https://math.stackexchange.com/questions/1596629/alternate-solution-to-circular-permutation-problem-with-restrictions | # Alternate solution to circular permutation problem with restrictions
Ten chairs are evenly spaced around a round table and numbered clockwise from $1$ through $10$. Five married couples are to sit in the chairs with men and women alternating, and no one is to sit either next to or across from his/her spouse. How man... | 2019-07-22T20:12:49 | {
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"url": "https://math.stackexchange.com/questions/1596629/alternate-solution-to-circular-permutation-problem-with-restrictions",
"openwebmath_score": 0.7147206664085388,
"openwebmath_perplexity": 244.52457619018728,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
... |
https://mathematica.stackexchange.com/questions/157983/solving-the-heat-equation-on-the-semi-infinite-rod | # Solving the heat equation on the semi-infinite rod
Cross posted in scicomp.SE.
I want to test the solution which is given below is right by Mathematica.
Please look the post in mathstackexhange
or
Question: Solve the following heat equation on the semi-infinite rod
$\qquad u_t=ku_{xx}$
where $x,t>0$ and
$\qqu... | 2021-10-27T22:42:05 | {
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"url": "https://mathematica.stackexchange.com/questions/157983/solving-the-heat-equation-on-the-semi-infinite-rod",
"openwebmath_score": 0.5426247119903564,
"openwebmath_perplexity": 2063.240177378497,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score"... |
https://math.stackexchange.com/questions/2556569/find-the-sum-of-the-series-of-frac11-cdot-3-frac13-cdot-5-frac15 | # Find the sum of the series of $\frac{1}{1\cdot 3}+\frac{1}{3\cdot 5}+\frac{1}{5\cdot 7}+\frac{1}{7\cdot 9}+…$
Find the sum of the series $$\frac1{1\cdot3}+\frac1{3\cdot5}+\frac1{5\cdot7}+\frac1{7\cdot9}+\frac1{9\cdot11}+\cdots$$ My attempt solution: $$\frac13\cdot\left(1+\frac15\right)+\frac17\cdot\left(\frac15+\fra... | 2019-11-17T14:43:36 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/2556569/find-the-sum-of-the-series-of-frac11-cdot-3-frac13-cdot-5-frac15",
"openwebmath_score": 0.9605997204780579,
"openwebmath_perplexity": 445.5246107828509,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q... |
http://mathhelpboards.com/members/albert/?s=9278ceb6188b675b9c2ddddfeb0e6f5e | Tab Content
• Today, 21:33
The region $R$ is a rectangle having the vertices: (0,1),\,(1,1),\,(1,-1),\,(0,-1) One way we can compute the volume is: ...
4 replies | 47 view(s)
• Today, 19:41
MarkFL replied to a thread logs in Pre-Algebra and Algebra
Okay, we are given: \ln\left(x-\frac{1}{x}-3\right)=2 Converting from l... | 2017-08-24T02:50:30 | {
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"lm_q1_score": 1,
"lm_q2_score": 0.894... |
https://math.stackexchange.com/questions/180150/alternating-sum-of-squares-of-binomial-coefficients | # Alternating sum of squares of binomial coefficients
I know that the sum of squares of binomial coefficients is just $${2n}\choose{n}$$ but what is the closed expression for the sum $${n\choose 0}^2 - {n\choose 1}^2 + {n\choose 2}^2 + \cdots + (-1)^n {n\choose n}^2$$?
• Can you do it with generating functions? – Nik... | 2020-04-08T22:47:15 | {
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"openwebmath_perplexity": 183.23535947541004,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9... |
https://qa.engineer.kmitl.ac.th/ngttmi/linear-equation-graph-problems-18ff3a | # linear equation graph problems
Matrix Calculator. Graphing linear equations using method 1. Type a math problem. Graphing linear relationships word problems Get 3 of 4 questions to level up! You can enter linear equations, quadratic equations, cubic equations, trigonometric functions, etc. $\begin{cases}5x +2y =1 \\... | 2021-05-07T00:22:16 | {
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"url": "https://qa.engineer.kmitl.ac.th/ngttmi/linear-equation-graph-problems-18ff3a",
"openwebmath_score": 0.3519676923751831,
"openwebmath_perplexity": 661.8729807266412,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.9817357195106375,
"lm_q2_score": 0.... |
https://casmusings.wordpress.com/2015/07/27/infinite-ways-to-an-infinite-geometric-sum/ | # Infinite Ways to an Infinite Geometric Sum
One of my students, K, and I were reviewing Taylor Series last Friday when she asked for a reminder why an infinite geometric series summed to $\displaystyle \frac{g}{1-r}$ for first term g and common ratio r when $\left| r \right| < 1$. I was glad she was dissatisfied wit... | 2020-05-29T08:12:07 | {
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"openwebmath_perplexity": 1014.8520394689638,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9932024699586652,... |
https://math.stackexchange.com/questions/2965262/if-x-n-is-a-sequence-s-t-x-2k-rightarrow-x-and-x-2k-1-rightarrow | # If $\{x_n\}$ is a sequence s.t. $x_{2k} \rightarrow x$ and $x_{2k-1} \rightarrow x$, then $x_k \rightarrow x$
If $$\{x_n\}$$ is a sequence s.t. $$x_{2k} \rightarrow x$$ and $$x_{2k-1} \rightarrow x$$, then $$x_k \rightarrow x$$
Just looking for feedback on my proof attemtpt
Proof Attempt
given that the odd and ev... | 2019-11-20T19:36:07 | {
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"openwebmath_perplexity": 166.29054256668454,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_... |
http://mathhelpforum.com/algebra/281823-area-square-circle-2.html | # Thread: Area of Square in Circle
1. ## Re: Area of Square in Circle
Originally Posted by harpazo
Improve our bounds???
Yes, at the moment we have:
$\displaystyle 2<\pi<4$
Surely, we can narrow the gap...
2. ## Re: Area of Square in Circle
Originally Posted by MarkFL
Yes, at the moment we have:
$\displaystyle 2... | 2019-02-23T00:33:36 | {
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"lm_q1_score": 0.9884918499186287,
"lm_q2_scor... |
https://math.stackexchange.com/questions/2971315/how-do-i-combine-standard-deviations-of-two-groups | # How do I combine standard deviations of two groups?
I have 2 groups of people. I'm working with the data about their age. I know the means, the standard deviations and the number of people. I don't know the data of each person in the groups.
Group 1 :
Mean = 35 years old; SD = 14; n = 137 people
Group 2 :
Mean =... | 2019-07-21T13:20:42 | {
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.97... |
http://math.stackexchange.com/questions/174055/finding-the-divisors-of-a-number | # Finding the divisors of a number
My text says that $p^3q^6$ has 28 divisors. Could anyone please explain to me how they got 28 here ? Edit: $p$ and $q$ are distinct prime numbers Sorry for the late addition..
-
So far there are three answers and only one up-vote: mine. – Michael Hardy Jul 23 '12 at 3:04
@Michael -... | 2015-02-01T12:36:29 | {
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http://mathhelpforum.com/algebra/136207-simple-proof.html | 1. ## A simple proof?
Prove that:
2 + 4 + 6 + 8 ... + 2(n-1) = n * (n-1)
When n > 0
Getting the n-1 part is easy (the left side of the equation has to have n-1 terms, so the result would be something multiplied by that). I don't know how to get the n, though...
2. Use induction to prove. Show the formula holds for t... | 2016-10-28T03:35:26 | {
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"lm_q2_score": 0.9086178... |
https://math.stackexchange.com/questions/1239106/proving-6n-1-is-always-divisible-by-5-by-induction | # Proving $6^n - 1$ is always divisible by $5$ by induction
I'm trying to prove the following, but can't seem to understand it. Can somebody help?
Prove $6^n - 1$ is always divisible by $5$ for $n \geq 1$.
What I've done:
Base Case: $n = 1$: $6^1 - 1 = 5$, which is divisible by $5$ so TRUE.
Assume true for $n = k$... | 2020-02-29T14:24:32 | {
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http://nl.mathworks.com/help/matlab/ref/istril.html?s_tid=gn_loc_drop&requestedDomain=nl.mathworks.com&nocookie=true | # Documentation
### This is machine translation
Translated by
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# istril
Determine if matrix is lower triangular
## Description
example
tf = istril(A) returns logical 1 (true) if A is a lower triangular matrix; ot... | 2016-09-26T08:47:57 | {
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"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1... |
https://fr.mathworks.com/help/symbolic/piecewise.html | # piecewise
Conditionally defined expression or function
## Description
example
pw = piecewise(cond1,val1,cond2,val2,...) returns the piecewise expression or function pw whose value is val1 when condition cond1 is true, is val2 when cond2 is true, and so on. If no condition is true, the value of pw is NaN.
example... | 2021-07-27T23:47:18 | {
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9825575167960731,
"lm_q2_score": 0.909907006648818... |
https://math.stackexchange.com/questions/4510187/how-to-create-a-function-f-such-that-fx-y-is-high-when-either-x-or-y-i | # How to create a function $f$ such that $f(x,y)$ is high when either $x$ or $y$ is?
There are two variables, let's say $$x$$ and $$y$$.
I want to come up with a function $$f:[0,5]\times[0,5]\longrightarrow[0,5]$$ that respects the following rules:
1. If $$x$$ is high (close to the maximum value of 5) and $$y$$ is l... | 2022-10-07T12:44:11 | {
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"url": "https://math.stackexchange.com/questions/4510187/how-to-create-a-function-f-such-that-fx-y-is-high-when-either-x-or-y-i",
"openwebmath_score": 0.8572801947593689,
"openwebmath_perplexity": 197.11111795120058,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
... |
https://math.stackexchange.com/questions/2318951/card-draw-probability | Card Draw Probability
This is a homework question. Not something to hand in, but rather a recommended practice question.
A Card Game
Three students are playing a card game. They decide to choose the first person to play by each selecting a card from the 52-card deck and looking for the highest card in value and suit. ... | 2019-06-24T22:14:10 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/2318951/card-draw-probability",
"openwebmath_score": 0.5665358304977417,
"openwebmath_perplexity": 123.03654134228368,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9867771778588349,
"lm_q2_sco... |
https://math.stackexchange.com/questions/3180877/determinant-of-antidiagonally-constructed-matrix | # Determinant of antidiagonally constructed matrix
Let $$A_n$$ be a matrix, odd dimension $$n \times n$$, constructed from the sequence of natural numbers in such a way that we begin the sequence from the upper left corner and next numbers are inserted into the matrix along antidiagonal direction, starting from the to... | 2022-08-10T20:37:55 | {
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"url": "https://math.stackexchange.com/questions/3180877/determinant-of-antidiagonally-constructed-matrix",
"openwebmath_score": 0.8820245265960693,
"openwebmath_perplexity": 218.9267928013688,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9942... |
https://math.stackexchange.com/questions/2962351/surjective-and-injective-function | # Surjective and Injective function
Let $$N=\{1,2,3...\}$$ be the set of natural numbers and $$F:N \times N \rightarrow N$$ be such that $$f(m,n)=(2m-1)*2^n.$$
(A)F is Injective.
(B)F is Surjective.
(C)F is Bijective.
(D)None of the above.
I can see that F can never be surjective because 1 does not have a pre-ima... | 2019-04-21T22:50:42 | {
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"url": "https://math.stackexchange.com/questions/2962351/surjective-and-injective-function",
"openwebmath_score": 0.8663015961647034,
"openwebmath_perplexity": 133.04482498097448,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9896718473283829,
... |
http://mathhelpforum.com/differential-equations/72467-differential-equation.html | # Math Help - differential equation
1. ## differential equation
If we assume that a person's weight depends on the energy consumed minus energy ued, one model is that weight changes in proportion to the difference, so:
dw/dt = k(C - 38.5w) where w(0) = w subscript 0
where w(t) kg is the weight at t days, C is the d... | 2015-04-19T03:17:54 | {
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"url": "http://mathhelpforum.com/differential-equations/72467-differential-equation.html",
"openwebmath_score": 0.4771636426448822,
"openwebmath_perplexity": 1191.1487717225007,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9770226247376173,
... |
https://math.stackexchange.com/questions/1128323/are-emptyset-and-x-closed-open-or-clopen/1128325 | # Are $\emptyset$ and $X$ closed, open or clopen?
It is indeed a very basic question but I am confused:
(1) In an 2013 MSE posting under general topology here, I was told that $\emptyset$ is an open set and therefore I assume $X$ must be open too.
(2) But in Wikipedia page on clopen set here, it says "In any topolog... | 2019-10-17T12:56:35 | {
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"url": "https://math.stackexchange.com/questions/1128323/are-emptyset-and-x-closed-open-or-clopen/1128325",
"openwebmath_score": 0.8672575354576111,
"openwebmath_perplexity": 370.25085908048993,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.986... |
https://math.stackexchange.com/questions/3350525/inclusion-exclusion-principle-problem | # Inclusion–exclusion principle problem
172 business executives were surveyed to determine if they regularly read Fortune, Time, or Money magazines. 80 read Fortune, 70 read Time, 47 read Money, 47 read exactly two of the three magazines, 26 read Fortune and Time, 28 read Time and Money, and 7 read all three magazines... | 2021-03-05T20:15:52 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/3350525/inclusion-exclusion-principle-problem",
"openwebmath_score": 0.9997199177742004,
"openwebmath_perplexity": 2157.5431643183756,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.98951090966802... |
http://mathhelpforum.com/number-theory/145830-divisibility.html | # Math Help - Divisibility
1. ## Divisibility
Hi all.
I'm trying to figure out the following problem:
Find the number of positive integers not exceeding 1000 that are divisible by 3 but not by 4.
Help will be appreciated. Looking for a simple/elementary proof.
Thanks.
2. Originally Posted by pollardrho06
Hi all.... | 2014-08-27T17:10:14 | {
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"url": "http://mathhelpforum.com/number-theory/145830-divisibility.html",
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"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.9893474897884493,
"lm_q2_score":... |
https://math.stackexchange.com/questions/1887453/solving-the-differential-equation-y-y-tanx-cotx | # Solving the Differential equation $y' = y \tan(x) + \cot(x)$
I am asked to solve the following differential equation:
$$y' = y \tan(x) + \cot(x)$$
What I have so far is
\begin{align*} y' - (\tan x) y &= \cot(x)\\ \\ I &= e^{\int - \tan(x) dx} = \cos(x)\\ \\ \cos(x) \left( y' - y \tan(x) \right) &= \cos(x) \cot(x)... | 2019-10-15T16:12:53 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/1887453/solving-the-differential-equation-y-y-tanx-cotx",
"openwebmath_score": 1.0000100135803223,
"openwebmath_perplexity": 2702.3522997144087,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9848... |
https://math.stackexchange.com/questions/2724960/probability-of-getting-full-house-in-poker?noredirect=1 | # Probability of getting full house in poker
I have this problem which I have solved, but using two different methods. I am quite new to combinatorics and want to know how to intuitively understand the difference between the following two methods.
The problem consist of calculating the probability of getting a full h... | 2019-11-14T16:07:01 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/2724960/probability-of-getting-full-house-in-poker?noredirect=1",
"openwebmath_score": 0.8362991213798523,
"openwebmath_perplexity": 147.78411420095142,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score"... |
https://mathhelpboards.com/threads/find-the-image-f-n-n-r-f-x-m-2-2n.7102/ | # Find the image: F: N * N -> R , F(x) = m^2 + 2n
#### KOO
##### New member
F:N*N -> R, F(x) = m^2 + 2n
I think the answer is N. Am I right?
#### Chris L T521
##### Well-known member
Staff member
I think the answer is N. Am I right?
Based on your title, we have that $F:\mathbb{N}\times\mathbb{N}\rightarrow \mathbb... | 2021-09-18T11:33:55 | {
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"url": "https://mathhelpboards.com/threads/find-the-image-f-n-n-r-f-x-m-2-2n.7102/",
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"openwebmath_perplexity": 214.78032173086706,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9875683469514965,
"lm_q... |
https://math.stackexchange.com/questions/2816513/same-integration-with-2-different-answers | # Same integration with 2 different answers?
$$\int x(x^2+2)^4\,dx$$
When we do this integration with u substitution we get $$\frac{(x^2+2)^5}{10}$$ as $u=x^2+2$
$du=2x\,dx$ $$\therefore \int (u+2)^4\,du = \frac{(x^2+2)^5}{10} + C$$
Although when we expand the fraction and then integrate the answer we get is differ... | 2019-10-16T04:43:18 | {
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"url": "https://math.stackexchange.com/questions/2816513/same-integration-with-2-different-answers",
"openwebmath_score": 0.8379353284835815,
"openwebmath_perplexity": 630.6923798847439,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.98457544791... |
https://gmatclub.com/forum/a-train-travels-from-city-a-to-city-b-the-average-speed-of-the-train-188007.html | GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 20 Aug 2018, 23:02
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customize... | 2018-08-21T06:02:38 | {
"domain": "gmatclub.com",
"url": "https://gmatclub.com/forum/a-train-travels-from-city-a-to-city-b-the-average-speed-of-the-train-188007.html",
"openwebmath_score": 0.4615800380706787,
"openwebmath_perplexity": 3476.47835810479,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes\n",
"lm_q1_score": ... |
https://gmatclub.com/forum/if-22-n-is-a-divisor-of-97-98-what-is-the-maximum-possible-228660.html | GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video
It is currently 30 Mar 2020, 07:52
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Pr... | 2020-03-30T15:52:04 | {
"domain": "gmatclub.com",
"url": "https://gmatclub.com/forum/if-22-n-is-a-divisor-of-97-98-what-is-the-maximum-possible-228660.html",
"openwebmath_score": 0.7583616375923157,
"openwebmath_perplexity": 2428.018596790443,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 1,
"lm_q2... |
https://www.physicsforums.com/threads/general-formula-for-this.104303/ | # General formula for this
1. Dec 16, 2005
### twoflower
Hi all,
there is general formula for findind out, "Which highest power of x is divisible n! with?" Eg. Which highest power of 5 is divisable 50! with?
But I forgot it and can't find it now...will somebody help me please?
Thank you.
2. Dec 16, 2005
### AKG... | 2017-10-23T15:01:00 | {
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"openwebmath_perplexity": 621.9016523268043,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.983085085246543,
"lm_q2_score... |
http://math.stackexchange.com/questions/281604/probability-of-an-event-after-time-has-passed/281639 | # Probability of an event after time has passed
A friend of mine posed this problem and we have had a disagreement on the answer.
The problem:
• There is a 90% chance that some event will happen in the next year.
• There is a 95% chance that the event will happen eventually.
• What is the probability that it happens... | 2015-05-24T19:43:38 | {
"domain": "stackexchange.com",
"url": "http://math.stackexchange.com/questions/281604/probability-of-an-event-after-time-has-passed/281639",
"openwebmath_score": 0.8925812840461731,
"openwebmath_perplexity": 259.3947522597049,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.98... |
https://plainmath.net/algebra-ii/78503-changing-base-of-a-logarithm-by-taking-a | crossoverman9b
2022-06-20
Changing base of a logarithm by taking a square root from base?
From my homework I found
${\mathrm{log}}_{9}x={\mathrm{log}}_{3}\sqrt{x}$
and besides that an explanation that to this was done by taking a square root of the base. I fail to grasp this completely. Should I need to turn ${\mathr... | 2023-03-28T01:56:08 | {
"domain": "plainmath.net",
"url": "https://plainmath.net/algebra-ii/78503-changing-base-of-a-logarithm-by-taking-a",
"openwebmath_score": 0.7619131207466125,
"openwebmath_perplexity": 220.66687792279453,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.9873750492324249,
"lm_q... |
https://math.stackexchange.com/questions/2801467/probability-a-person-chosen-at-random-owns-an-automobile-or-a-house-but-not-bot/2801568 | # Probability a person chosen at random owns an automobile or a house, but not both
A marketing survey indicates that $60\%$ of the population owns an automobile, $30\%$ owns a house, and $20\%$ owns both an automobile and a house. Calculate the probability that a person chosen at random owns an automobile or a house,... | 2019-12-11T06:21:41 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/2801467/probability-a-person-chosen-at-random-owns-an-automobile-or-a-house-but-not-bot/2801568",
"openwebmath_score": 0.7960233092308044,
"openwebmath_perplexity": 174.42810023617778,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "... |
https://madhavamathcompetition.com/category/nature-of-mathematics/page/2/ | Miscellaneous questions: Part I: tutorial practice for preRMO and RMO
Problem 1:
The sixty four squares of a chess board are filled with positive integers one on each in such a way that each integer is the average of the of the integers on the neighbouring squares. (Two squares are neighbours if they share a common e... | 2019-12-12T16:42:32 | {
"domain": "madhavamathcompetition.com",
"url": "https://madhavamathcompetition.com/category/nature-of-mathematics/page/2/",
"openwebmath_score": 0.8531870245933533,
"openwebmath_perplexity": 396.8077610602914,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9869795098861572,
... |
https://orlandodockbuilder.com/doooz/3cd652-how-to-prove-a-parallelogram-is-congruent | Rhianna has learned the SSS and SAS congruence tests for triangles and she wonders if these tests might work for parallelograms. Diagonals of a Parallelogram Bisect Each Other. A tip from Math Bits says, if we can show that one set of opposite sides are both parallel and congruent, which in turn indicates that the poly... | 2021-07-29T22:34:14 | {
"domain": "orlandodockbuilder.com",
"url": "https://orlandodockbuilder.com/doooz/3cd652-how-to-prove-a-parallelogram-is-congruent",
"openwebmath_score": 0.5363954305648804,
"openwebmath_perplexity": 312.61253183447855,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes\n\n",
"lm_q1_score": 0.973240... |
https://mathematica.stackexchange.com/questions/204856/what-is-the-distribution-of-a-random-variable-with-pdf-proportional-to-the-produ/204908#204908 | # What is the distribution of a random variable with pdf proportional to the product of two normal pdf's
I'm working my way through a nice e-book on Kalman filters, translating to Mathematica as I go and I've hit an interesting problem. In this section: https://nbviewer.jupyter.org/github/rlabbe/Kalman-and-Bayesian-Fi... | 2021-09-27T03:56:59 | {
"domain": "stackexchange.com",
"url": "https://mathematica.stackexchange.com/questions/204856/what-is-the-distribution-of-a-random-variable-with-pdf-proportional-to-the-produ/204908#204908",
"openwebmath_score": 0.45847487449645996,
"openwebmath_perplexity": 4126.749046662051,
"lm_name": "Qwen/Qwen-72B",
... |
https://math.stackexchange.com/questions/75589/open-maps-which-are-not-continuous | # Open maps which are not continuous
What is an example of an open map $(0,1) \to \mathbb{R}$ which is not continuous? Is it even possible for one to exist? What about in higher dimensions? The simplest example I've been able to think of is the map $e^{1/z}$ from $\mathbb{C}$ to $\mathbb{C}$ (filled in to be $0$ at $0... | 2019-06-25T01:28:59 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/75589/open-maps-which-are-not-continuous",
"openwebmath_score": 0.9547765851020813,
"openwebmath_perplexity": 138.39477152368693,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9838471613889295,
... |
https://share.cocalc.com/share/b67337a608fb9911d3a0a3330eaadd1ab39e446b/week%205/assignment/FindRoots.ipynb?viewer=share | CoCalc Public Filesweek 5 / assignment / FindRoots.ipynb
Authors: Boyuan Qi, Rajvir Sidhu
Views : 31
Compute Environment: Ubuntu 20.04 (Default)
# Assignment 2: Polynomial Root Finding
## Markdown
Give the address (url) for a website that has documentation for markdown, including tables (i.e. a webpage, not a pdf or... | 2020-12-02T10:27:30 | {
"domain": "cocalc.com",
"url": "https://share.cocalc.com/share/b67337a608fb9911d3a0a3330eaadd1ab39e446b/week%205/assignment/FindRoots.ipynb?viewer=share",
"openwebmath_score": 0.4697786271572113,
"openwebmath_perplexity": 4157.842828911409,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q... |
https://math.stackexchange.com/questions/1253762/evaluate-the-indefinite-integral-int-frac1x2-sin-left-frac6x-right | # Evaluate the indefinite integral $\int \frac{1}{x^2} \sin\left(\frac{6}{x}\right) \cos\left(\frac{6}{x}\right) \, dx$
Evaluate the indefinite integral:
$$\int \frac{1}{x^2} \sin\left(\frac{6}{x}\right) \cos\left(\frac{6}{x}\right) \, dx$$
(using substitution)
The answer is: $$\frac {1}{24} \cos\left(\frac{12}{x}\... | 2022-01-18T09:10:17 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/1253762/evaluate-the-indefinite-integral-int-frac1x2-sin-left-frac6x-right",
"openwebmath_score": 0.8925501108169556,
"openwebmath_perplexity": 949.4613467960729,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm... |
https://web2.0calc.com/questions/if-there-were-3-skiers-on-plane-of-17-and-4-people-on-the-plane-died-of-a-crash-what-is-the-chance-that-all-3-skiers-survive | +0
# If there were 3 skiers on plane of 17 and 4 people on the plane died of a crash, what is the chance that all 3 skiers survive?
0
529
21
If there were 3 skiers on plane of 17 and 4 people on the plane died of a crash, what is the chance that all 3 skiers survive?
Guest May 21, 2014
#16
+889
+8
There are just ... | 2018-07-17T11:42:47 | {
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"openwebmath_score": 0.8248334527015686,
"openwebmath_perplexity": 4435.613179197472,
"lm_name": "Qwen/Qwen-72B",
"... |
https://www.physicsforums.com/threads/asymptotes-as-the-lines-y-x-an-y-x.141132/ | # Asymptotes as the lines y=x an y=-x
Hi there.
I'm a maths teacher and today was having a discussion with my Head of Department about asymptotes (as you do!)
She was me if I could think on an equation of a graph(s) which has an asymptotes at the line y=x and another at y=-x.
Thinking about it, neither of us could ... | 2020-12-01T12:28:29 | {
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https://gmatclub.com/forum/there-are-1600-jelly-beans-divided-between-two-jars-x-and-y-if-the-192785.html | GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 23 Mar 2019, 22:08
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"domain": "gmatclub.com",
"url": "https://gmatclub.com/forum/there-are-1600-jelly-beans-divided-between-two-jars-x-and-y-if-the-192785.html",
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"lm_q1_score": 0.9... |
http://math.stackexchange.com/questions/465454/how-to-show-this-obvious-and-basic-property-of-abelian-groups | # How to show this obvious and basic property of abelian groups?
I have a question that is probably very silly, but let's go. Let $(G,+)$ be an abelian group. In that case we know that $+$ is associative and commutative. This leads us to the following: if $\{a_i \in G : i \in I_n\}$ with $I_n = \{i \in \mathbb{N} : 1 ... | 2015-05-30T17:26:52 | {
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"lm_label": "1. YES\n2. YES",
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https://math.stackexchange.com/questions/2786600/invert-the-softmax-function | # Invert the softmax function
Is it possible to revert the softmax function in order to obtain the original values $$x_i$$?
$$S_i=\frac{e^{x_i}}{\sum e^{x_i}}$$
In case of 3 input variables this problem boils down to finding $$a$$, $$b$$, $$c$$ given $$x$$, $$y$$ and $$z$$:
$$\begin{cases} \frac{a}{a+b+c} &= x \\ \... | 2021-03-09T05:15:00 | {
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https://math.stackexchange.com/questions/2775869/examples-of-entire-functions-with-none-one-and-infinite-zeros/2775872 | # Examples of entire functions with none, one and infinite zeros.
I know that an entire function is one which can be differentiated on the entire complex plane, and I believe that a zero of an entire function is the z where f(z)=0.
I was tring to think of example of the following
An entire function with no zero's: I... | 2019-08-18T21:49:45 | {
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https://math.stackexchange.com/questions/3722672/does-the-alternating-composition-of-sines-and-cosines-converge-to-a-constant | # Does the alternating composition of sines and cosines converge to a constant?
Let $$f(x) = \cos(\sin(x))$$ and let $$c(f, n)(x)$$ denote the function $$\underbrace{f\circ f\circ...\circ f}_{n \text{ times}}$$. For example, $$c(f, 1)(x) = f(x)$$, $$c(f, 2)(x) = f(f(x))$$ and so on.
My question is: does $$c(f, n)(x)$... | 2022-01-25T22:29:50 | {
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https://mathhelpboards.com/threads/converting-a-repeating-decimal-to-ratio-of-integers.5632/ | Converting a repeating decimal to ratio of integers
paulmdrdo
Active member
0.17777777777 convert into a ratio.
M R
Active member
Re: converting a repeating decimal to ratio of integers
Hi,
This is $$0.1 + 0.077777=\frac{1}{10}+\frac{7}{100}+\frac{7}{1000}+...$$ where you have a GP to sum.
Or $$\text{Let } x=0.07... | 2021-01-16T05:10:24 | {
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https://math.stackexchange.com/questions/3315160/epsilon-n-proof-of-sqrt4n2n-2n-rightarrow-frac14 | # $\epsilon - N$ proof of $\sqrt{4n^2+n} - 2n \rightarrow \frac{1}{4}$
I have the following proof for $$\lim_{n\rightarrow\infty} \sqrt{4n^2+n} - 2n = \frac{1}{4}$$ and was wondering if it was correct. Note that $$\sqrt{4n^2+n} - 2n = \frac{n}{\sqrt{4n^2+n} + 2n}$$. $$\left|\frac{n}{\sqrt{4n^2+n} + 2n} - \frac{1}{4}\r... | 2022-08-19T23:37:40 | {
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"lm_q1_score": 0.9905... |
http://www.framtidsgalan.se/faithless-new-dab/058cca-scalene-obtuse-triangle | # scalene obtuse triangle
In an equiangular triangle, all the angles are equal—each one measures 60 degrees. Hypotenuse. This is one of the three types of triangles, based on sides.. We are going to discuss here its definition, formulas for perimeter and area and its properties. Step 2: Let x be one of the two equal a... | 2023-03-27T14:50:35 | {
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"openwebmath_perplexity": 816.1558441323414,
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"lm_label": "1. Yes\n2. Yes\n\n",
"lm_q1_score": 0.9817357184418847,
"l... |
https://thompsoncontractfurnishings.ca/femme-fatale-vzyibej/binomial-coefficient-c-e0c584 | = { 2 The formula does exhibit a symmetry that is less evident from the multiplicative formula (though it is from the definitions). The symbol H . ) If n is large and k is linear in n, various precise asymptotic estimates exist for the binomial coefficient . k A combinatorial proof is given below. ) n . {\displaystyle ... | 2021-05-09T08:09:04 | {
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"openwebmath_perplexity": 1782.271509811245,
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"lm_q1_score": 0... |
https://math.stackexchange.com/questions/2963069/integers-which-are-squared-norm-of-2-by-2-integer-matrices | Integers which are squared norm of 2 by 2 integer matrices
Question: Which integers are of the form $$\Vert A \Vert^2$$, with $$A \in M_2(\mathbb{Z})$$.
The code below provides the first such integers: $$0, 1, 2, 4, 5, 8, 9, 10, 13, 16, 17, 18, 20, 25, 26$$.
By searching this sequence on OEIS, we find: "Numbers that ... | 2022-07-02T18:33:37 | {
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"lm_q1_score... |
https://www.hopecoalitionboulder.org/brief-history-idsqv/page.php?5bbf8e=aas-congruence-theorem | In this section we will consider two more cases where it is possible to conclude that triangles are congruent with only partial information about their sides and angles. We have enough information to state the triangles are congruent. Now it's time to make use of the Pythagorean Theorem. AAS congruence theorem. CosvoSt... | 2021-04-22T20:07:38 | {
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"lm_q1_score": ... |
http://mathhelpforum.com/calculus/8550-total-dist-traveled.html | 1. ## total dist. traveled
An object moves along a line so that its velocity at time $t$ is $v(t) = 1/2 + sin2t$ feet per second. Find the displacement and the total distance traveled by the object for $0 <= t <= 3pi/2$
i was able to find the displacement which is 3.35619 ft. need help on finding the total distance t... | 2017-10-21T16:26:56 | {
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https://mathhelpboards.com/threads/find-integer-sequences.6621/ | # Find integer sequences
#### hxthanh
##### New member
Define $\{a_n\}$ is integer sequences (all term are integers) satisfy condition
$a_n=a_{n-1}+\left\lfloor\dfrac{n^2-2n+2-a_{n-1}}{n}\right\rfloor$ for $n=1,2,...$
*note: $\left\lfloor x\right\rfloor$ is a greatest integer number less than or equal $x$
Find gene... | 2022-05-19T03:13:16 | {
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"lm_q1_score": 0.9859363717170516,
"lm_q2_score": 0.... |
https://gmatclub.com/forum/if-x-is-a-positive-integer-is-x-1-a-factor-of-126421.html | GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 17 Jul 2018, 12:06
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"domain": "gmatclub.com",
"url": "https://gmatclub.com/forum/if-x-is-a-positive-integer-is-x-1-a-factor-of-126421.html",
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"lm_q1_score": 1,
"lm_q2_score": 0... |
https://gmatclub.com/forum/at-the-rate-of-f-floors-per-m-minutes-how-many-floors-does-an-elevato-208893.html | GMAT Question of the Day - Daily to your Mailbox; hard ones only
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Customize... | 2019-10-19T19:51:04 | {
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"url": "https://gmatclub.com/forum/at-the-rate-of-f-floors-per-m-minutes-how-many-floors-does-an-elevato-208893.html",
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"lm_label": "1. Yes\n2. Yes\n\n",
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http://fluencyuniversity.com/m9o4am/b437h.php?cc98e9=matrix-inverse-properties-addition | The identity matrix is a square matrix that has 1’s along the main diagonal and 0’s for all other entries. What are the Inverse Properties of Addition and Multiplication? Matrix Multiplication Properties 9:02. Properties of Inverse For a matrix A, A −1 is unique, i.e., there is only one inverse of a matrix (A −1 ) −1 =... | 2021-05-12T05:50:20 | {
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"lm_label": "1. Yes\n2. Yes\n\n",
"lm_q1_score": 0.98433... |
https://mathforums.com/threads/how-to-find-the-percentage-of-kinetic-energy-from-the-collision-of-three-spheres-in-tandem.347796/ | # How to find the percentage of kinetic energy from the collision of three spheres in tandem?
#### Chemist116
The problem is as follows:
Three spheres identical in size, shape and mass are situated over a surface as indicated in the picture. Initially, $2$ and $3$ are at rest. Sphere labeled $1$ makes a collision wi... | 2020-02-27T21:28:33 | {
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"openwebmath_perplexity": 500.563210335766,
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"lm_label": "1. YES\n2. Y... |
https://scicomp.stackexchange.com/questions/28753/finite-difference-method-basic-implementation-on-octave | # Finite difference method basic implementation on Octave
Trying to study the error of FDM for a second order derivative versus step size I calculated the coefficients and validated them, but the output has errors for small step sizes.
The function in question is
$$f(x) = e^{\sin(x)}$$
With a derivative of $$f''(x)... | 2020-11-30T07:34:49 | {
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http://mathhelpforum.com/algebra/15069-geometric-sequence.html | # Math Help - Geometric sequence
1. ## Geometric sequence
The fifth term of a geometric series is 5! and the sixth term is 6!. What is the fourth term?
Can someone post their answer and reasoning. I have my answer and think it's right but i really need e.c right now and want to make sure. Thanks!
2. Originally Post... | 2015-05-22T16:06:49 | {
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https://math.stackexchange.com/questions/3738214/is-there-a-geometric-analog-of-absolute-value | # Is there a geometric analog of absolute value?
I'm wondering whether there exists a geometric analog concept of absolute value. In other words, if absolute value can be defined as
$$\text{abs}(x) =\max(x,-x)$$
intuitively the additive distance from $$0$$ to $$x$$, is there a geometric version
$$\text{Geoabs}(x) =... | 2022-07-01T20:07:31 | {
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"lm_q1_score": 0.982823... |
https://math.stackexchange.com/questions/4251809/how-do-you-approach-when-completing-the-square | # How do you approach when completing the square?
If $$M = 3x^2 - 8xy + 9y^2 - 4x + 6y + 13$$, where $$x,y\in\mathbb R$$, then $$M$$ must be:
a) positive $$\qquad$$b) negative $$\qquad$$c) $$0 \qquad$$ d) an integer
I somehow managed to figure it out by completing the square but in order to do so, it took me a lot o... | 2021-10-20T03:22:55 | {
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"lm_q1_score": 0.98866... |
http://mathhelpforum.com/calculus/43609-notation-again-again.html | 1. ## Notation again again
I do not know how to search this but does
$C^{\infty}$ mean that is differentiable any number of times, or something?
Any help appreciated.
2. Originally Posted by Mathstud28
I do not know how to search this but does
$C^{\infty}$ mean that is differentiable any number of times, or someth... | 2017-09-25T05:24:13 | {
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"lm_q1_score": 0.98866824479921,
"lm_q2_score": 0.... |
https://www.physicsforums.com/threads/integrating-the-area-of-a-disc.222062/ | Integrating the area of a disc
1. Mar 14, 2008
Hakins90
1. The problem statement, all variables and given/known data
Finding the area of a disc by integration of rings.
2. Relevant equations
A ring of radius r and thickness dr has an area of $$2 \pi rdr$$.
3. The attempt at a solution
Why isn't it $$\pi (2rdr +... | 2016-10-25T17:28:59 | {
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"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.979976559880137,
"lm_q2... |
http://kinmenhouse.com/pesticides-in-ktvhmwj/how-to-prove-a-function-is-continuous-7db71d | The function is defined at a.In other words, point a is in the domain of f, ; The limit of the function exists at that point, and is equal as x approaches a from both sides, ; The limit of the function, as x approaches a, is the same as the function output (i.e. The Solution: We must show that $\lim_{h \to 0}\cos(a + h... | 2021-07-28T19:54:34 | {
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"url": "http://kinmenhouse.com/pesticides-in-ktvhmwj/how-to-prove-a-function-is-continuous-7db71d",
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"openwebmath_perplexity": 510.3377641586615,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.9840936092... |
https://s7097.gridserver.com/7k6tqu/3a6bd0-decomposition-of-antisymmetric-tensor | The statement in this question is similar to a rule related to linear algebra and matrices: Any square matrix can expressed or represented as the sum of symmetric and skew-symmetric (or antisymmetric) parts. There are many other tensor decompositions, including INDSCAL, PARAFAC2, CANDELINC, DEDICOM, and PARATUCK2 as we... | 2022-06-26T05:56:51 | {
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"url": "https://s7097.gridserver.com/7k6tqu/3a6bd0-decomposition-of-antisymmetric-tensor",
"openwebmath_score": 0.9046940803527832,
"openwebmath_perplexity": 1231.6727965524285,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.9869795075882267,
"lm... |
http://codeforces.com/problemset/problem/1270/C | Please, try EDU on Codeforces! New educational section with videos, subtitles, texts, and problems. ×
C. Make Good
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
Let's call an array $a_1, a_2, \dots, a_m$ of nonnegative integer numbers good if $a_1 + a_2 ... | 2020-07-05T01:35:36 | {
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"lm_q2_score": 0.9046505312448598,
"... |
https://math.stackexchange.com/questions/939280/part-of-a-proof-that-the-product-of-an-odd-and-even-integers-is-even | # Part of a proof that the product of an odd and even integers is even
I'm practicing for a test on Monday and I'm trying to do some proofs - but I'm not entirely sure if this is sufficient enough for the question.
"Prove that for all integers, m and n, if m is odd and n is even, then $m\cdot n$ is even."
These are ... | 2021-01-23T08:34:52 | {
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"openwebmath_perplexity": 81.18333235828224,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"l... |
https://brilliant.org/discussions/thread/how-to-count-squares/ | # How to Count Squares!
Let me go grab a hamburger real quick...
Ok, I'm back.
How many squares are there in the 6$$\times$$4 grid below?
That's a reaallly good question!
Let's start by counting the smallest 1$$\times$$1 squares, this is just the same as counting the number of unit squares in a 6$$\times$$4 grid, ... | 2018-04-25T08:50:58 | {
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"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.9898303413461358,
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https://math.stackexchange.com/questions/2892375/prove-sum-i-0n-1n-i-binomn1i-i1n-n2n | # Prove $\sum_{i=0}^n (-1)^{n-i} \binom{n+1}{i} (i+1)^n = (n+2)^n$
I found through simulations that
$$\sum_{i=0}^n (-1)^{n-i} \binom{n+1}{i} (i+1)^n = (n+2)^n$$
Is there any proof of this? I've tried to solve it by:
• Induction, but it gets too messy.
• Binomial theorem, but I got nowhere.
Any help with this is hi... | 2022-05-16T09:51:24 | {
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9852713852853137... |
http://mathhelpforum.com/statistics/144005-help-svp.html | # Math Help - Help, SVP.
1. ## Help, SVP.
Hey... if you could answer/explain any of the following (even one would be awesome), I'd be forever thankful.
1. A six-member working group to plan a student lounge is to be selected from five teachers and nine students. If the working group is randomly selected, what is the... | 2015-03-05T23:20:37 | {
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"openwebmath_score": 0.5251576900482178,
"openwebmath_perplexity": 2088.989796163547,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9852713870152409,
"lm_q2_score": 0.90465053... |
http://experiential-architecture.com/kushco-holdings-oercf/find-permutation-problem-fd31c5 | This article has been viewed 12,813 times. For example, if you have 10 digits to choose from for a combination lock with 6 numbers to enter, and you're allowed to repeat all the digits, you're looking to find the number of permutations with repetition. If you're seeing this message, it means we're having trouble loadin... | 2021-05-18T16:35:58 | {
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"url": "http://experiential-architecture.com/kushco-holdings-oercf/find-permutation-problem-fd31c5",
"openwebmath_score": 0.5052473545074463,
"openwebmath_perplexity": 587.9953836579109,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes\n\n",
"lm_q1_score... |
https://math.stackexchange.com/questions/2919921/of-all-polygons-inscribed-in-a-given-circle-which-one-has-the-maximum-sum-of-squ | # Of all polygons inscribed in a given circle which one has the maximum sum of squares of side lengths?
My son presented me with an interesting problem:
Of all possible polygons inscribed in a circle of radius $R$, find the one that has the sum $S$ of squared side lengths maximized: $S=a_1^2+a_2^2+\dots+a_n^2$, with ... | 2019-06-16T08:45:09 | {
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"url": "https://math.stackexchange.com/questions/2919921/of-all-polygons-inscribed-in-a-given-circle-which-one-has-the-maximum-sum-of-squ",
"openwebmath_score": 0.9784698486328125,
"openwebmath_perplexity": 224.18168856934906,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\... |
https://math.stackexchange.com/questions/508308/a-definite-integral-int-0-infty-frac2-cos-x-left1x4-right-left5-4 | # A definite integral $\int_0^\infty\frac{2-\cos x}{\left(1+x^4\right)\,\left(5-4\cos x\right)}dx$
I need to find a value of this definite integral: $$\int_0^\infty\frac{2-\cos x}{\left(1+x^4\right)\,\left(5-4\cos x\right)}dx.$$ Its numeric value is approximately $0.7875720991394284$, and lookups in Inverse Symbolic C... | 2019-05-23T21:54:57 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/508308/a-definite-integral-int-0-infty-frac2-cos-x-left1x4-right-left5-4",
"openwebmath_score": 0.9856529831886292,
"openwebmath_perplexity": 645.9097491669671,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q... |
https://www.physicsforums.com/threads/show-that-you-can-distribute-powers-to-commuting-elements.950679/ | # Show that you can distribute powers to commuting elements
## Homework Statement
If ##a## and ##b## are commuting elements of ##G##, prove that ##(ab)^n = a^nb^n## for all ##n \in \mathbb{Z}##.
## The Attempt at a Solution
We prove two lemmas:
1) If ##a## and ##b## commute, then so do their inverses: ##ab=ba \impl... | 2021-04-20T11:12:27 | {
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"url": "https://www.physicsforums.com/threads/show-that-you-can-distribute-powers-to-commuting-elements.950679/",
"openwebmath_score": 0.9905398488044739,
"openwebmath_perplexity": 1939.152515500805,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_scor... |
http://www.southernmines.org/water-pressure-rzyocn/transpose-matrix-definition-d896ca | # transpose matrix definition
A new matrix is obtained the following way: each [i, j] element of the new matrix gets the value of the [j, i] element of the original one. Transpose of a matrix is the interchanging of rows and columns. In practical terms, the matrix transpose is usually thought of as either (a) flipping... | 2021-04-10T18:19:48 | {
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"url": "http://www.southernmines.org/water-pressure-rzyocn/transpose-matrix-definition-d896ca",
"openwebmath_score": 0.6923036575317383,
"openwebmath_perplexity": 714.7809239474072,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.986363162313... |
https://math.stackexchange.com/questions/2217630/proving-the-existence-and-number-of-real-roots-for-x3-3x-2 | # Proving the existence and number of *real* roots for $x^3 - 3x + 2$
I need to find how many real roots this polynomial has and prove there existence. I was wondering if my logic and thought process was correct.
Determine the number of real roots and prove it for $x^3 - 3x + 2$
First, note that $f'(x) = 3x^2 - 3$ a... | 2019-08-20T08:17:00 | {
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"url": "https://math.stackexchange.com/questions/2217630/proving-the-existence-and-number-of-real-roots-for-x3-3x-2",
"openwebmath_score": 0.7924861311912537,
"openwebmath_perplexity": 280.92575364444633,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_sco... |
https://math.stackexchange.com/questions/381243/integral-of-sin-x-cdot-cos-x | # Integral of $\sin x \cdot \cos x$ [duplicate]
I've found 3 different solutions of this integral. Where did I make mistakes? In case there is no errors, could you explain why the results are different?
$\int \sin x \cos x dx$
1) via subsitution $u = \sin x$ $u = \sin x; du = \cos x dx \Rightarrow \int udu = \frac12... | 2019-12-13T09:23:15 | {
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"url": "https://math.stackexchange.com/questions/381243/integral-of-sin-x-cdot-cos-x",
"openwebmath_score": 0.8569950461387634,
"openwebmath_perplexity": 1471.5342871800144,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9664104972521578,
"lm_... |
https://math.stackexchange.com/questions/1113556/how-to-show-that-sum-k-1n-kn1-k-binomn23 | # How to show that $\sum_{k=1}^n k(n+1-k)=\binom{n+2}3$?
While thinking about another question I found out that this equality might be useful there: $$n\cdot 1 + (n-1)\cdot 2 + \dots + 2\cdot (n-1) + 1\cdot n = \frac{n(n+1)(n+2)}6$$ To rewrite it in a more compact way: $$\sum_{k=1}^n k(n+1-k)=\frac{n(n+1)(n+2)}6.$$
T... | 2019-08-24T04:50:17 | {
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"url": "https://math.stackexchange.com/questions/1113556/how-to-show-that-sum-k-1n-kn1-k-binomn23",
"openwebmath_score": 0.9279963970184326,
"openwebmath_perplexity": 260.42070663162303,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.97903576101... |
https://math.stackexchange.com/questions/2916482/probability-with-poker-cards | Probability with Poker cards
You deal 5 cards from a well-shuffled deck of playing cards. What is the probability that the 5th card is the queen of spades?
Just from analysis, P(5th queen spade) = (51*50*49*48*1)/(52*51*50*49*48) = 1/52
However why wont this method of logic thinking incorrect?
P(5th queen spade) = ... | 2019-06-26T04:37:05 | {
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"url": "https://math.stackexchange.com/questions/2916482/probability-with-poker-cards",
"openwebmath_score": 0.6646839380264282,
"openwebmath_perplexity": 520.5258183702905,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.987568347317383,
"... |
http://mathhelpforum.com/algebra/25338-algebra.html | 1. ## Algebra
Q1= show that if x is real, 2(x^2) + 6x + 9 is always positive.
Q2= Solve the simultaneous equations for x,y > 0
2log y = log 2 + log x
2^y = 4^x
cheers
2. for Q1 check the discriminant of the quadratic $b^2 -4ac$
for Q2 using the first equation you should be able to get $\log y^2 = \log 2x \Righta... | 2017-05-23T19:14:15 | {
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"url": "http://mathhelpforum.com/algebra/25338-algebra.html",
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"openwebmath_perplexity": 570.7701804020886,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.9875683476832692,
"lm_q2_score": 0.901920677... |
http://centrosamo.it/fskn/minimize-a-cost-function.html | Minimization and maximization refresher. from Wikipedia. The minimization will be performed by a gradient descent algorithm, whose task is to parse the cost function output until it finds the lowest minimum point. To find the profit maximization levels, other approaches can be taken as well. In place of dJ/dTheta-j you... | 2020-05-27T05:40:05 | {
"domain": "centrosamo.it",
"url": "http://centrosamo.it/fskn/minimize-a-cost-function.html",
"openwebmath_score": 0.5647906064987183,
"openwebmath_perplexity": 1047.402508227663,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.987568346219724,
"lm_q2_score": 0.90192067652954... |
https://math.stackexchange.com/questions/93553/squarefree-polynomials-over-finite-fields | # Squarefree polynomials over finite fields
I'm trying to figure out how many squarefree polynomials there are of a fixed degree over $\mathbb{F}_2$ specifically (and in general, over any finite field). Looking at some low-degree examples seems to suggest that half of the polynomials of any given degree are squarefree... | 2019-05-23T23:26:43 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/93553/squarefree-polynomials-over-finite-fields",
"openwebmath_score": 0.8578269481658936,
"openwebmath_perplexity": 185.26956633017988,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.983085090202... |
https://math.stackexchange.com/questions/509240/different-limits-for-the-alternating-harmonic-series | Different limits for the alternating harmonic series?
Show that the series $$\sum_{n=1}^{\infty} \dfrac{(-1)^n}{n}$$ is not absolutely convergent. Show that by permuting the terms of the series one can obtain series with different limits.
I am able to show that this is not absolutely convergent. I am also able to sho... | 2020-02-22T10:26:14 | {
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"url": "https://math.stackexchange.com/questions/509240/different-limits-for-the-alternating-harmonic-series",
"openwebmath_score": 0.8805743455886841,
"openwebmath_perplexity": 129.12278173750303,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.... |
http://mathhelpforum.com/number-theory/145058-simple-number-theory-print.html | # Simple Number Theory
• May 16th 2010, 07:06 PM
FlacidCelery
Simple Number Theory
Positive integers 30, 72, and N have the property that the product of any two of them is divisible by the third. What is the smallest possible value of N?
Note I have not yet taken a Number Theory course.
I think I have found the solu... | 2017-12-15T01:19:59 | {
"domain": "mathhelpforum.com",
"url": "http://mathhelpforum.com/number-theory/145058-simple-number-theory-print.html",
"openwebmath_score": 0.8534181714057922,
"openwebmath_perplexity": 237.8788061809354,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.984336353126336,
"lm_q... |
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