Search is not available for this dataset
url string | text string | date timestamp[s] | meta dict |
|---|---|---|---|
http://mathhelpforum.com/calculus/60890-need-help-3-calculus-extra-credit-problems.html | # Math Help - Need help with 3 Calculus Extra Credit Problems
1. ## Need help with 3 Calculus Extra Credit Problems
I'm in intro to calculus and I need help setting this equation up:
Newton's Law of cooling: the rate at which the temperature of an object changes is proportional to the difference between its own temp... | 2014-07-24T04:03:59 | {
"domain": "mathhelpforum.com",
"url": "http://mathhelpforum.com/calculus/60890-need-help-3-calculus-extra-credit-problems.html",
"openwebmath_score": 0.5939760208129883,
"openwebmath_perplexity": 1095.9537145538923,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.978712649... |
https://math.stackexchange.com/questions/2746968/the-proof-of-infinitude-of-pythagorean-triples-x-x1-z | # The Proof of Infinitude of Pythagorean Triples $(x,x+1,z)$
Proof that there exists infinity positive integers triple $x^2+y^2=z^2$ that $x,y$ are consecutive integers, then exhibit five of them.
This is a question in my number theory textbook, the given hint is that
"If $x,x+1,z$ is a Pythagorean triple, then so do... | 2019-10-20T19:46:02 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/2746968/the-proof-of-infinitude-of-pythagorean-triples-x-x1-z",
"openwebmath_score": 0.9638389348983765,
"openwebmath_perplexity": 616.9689531284344,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0... |
http://qely.venetoacquaeterme.it/solving-cubic-equations-formula.html | # Solving Cubic Equations Formula
Solving Cubic Equations with the help of Factor Theorem If x – a is indeed a factor of p(x), then the remainder after division by x – a will be zero. It solves cubic, quadratic and linear equations. 2 But it is important to remember van der Waals’ equation for the volume is a cubic an... | 2019-12-13T09:05:27 | {
"domain": "venetoacquaeterme.it",
"url": "http://qely.venetoacquaeterme.it/solving-cubic-equations-formula.html",
"openwebmath_score": 0.7340618371963501,
"openwebmath_perplexity": 460.93382348864924,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.9871787827157819,
"lm_q2_s... |
https://www.physicsforums.com/threads/de-nesting-radicals.777895/ | 1. Oct 23, 2014
### bamajon1974
I want to de-nest the following radical:
(1) $$\sqrt{3+2\sqrt{2}}$$
Into the general simplified form:
(2) $$a+b\sqrt{2}$$
Equating (1) with (2),
(3) $$\sqrt{3+2\sqrt{2}} = a+b\sqrt{2}$$
and squaring both sides:
(4) $$3+2\sqrt{2} = a^2 + 2b^2 + 2ab\sqrt{2}$$
generates a system of two eq... | 2018-07-20T20:41:15 | {
"domain": "physicsforums.com",
"url": "https://www.physicsforums.com/threads/de-nesting-radicals.777895/",
"openwebmath_score": 0.8350215554237366,
"openwebmath_perplexity": 542.9755849662545,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9805806484125338,
"lm_q2_score": 0... |
https://mathhelpboards.com/threads/proof-critique-induction.6248/ | # Proof critique: Induction
#### sweatingbear
##### Member
We wish to show that $3^n > n^3 \, , \ \forall n \geqslant 4$. Base case $n = 4$ yields
$3^4 = 81 > 4^3 = 64$
Assume the inequality holds for $n = p$ i.e. $3^p > p^3$ for $p \geqslant 4$. Then
$3^{p+1} > 3p^3$
$p \geqslant 4$ implies $3p^3 \geq 192$, as w... | 2020-09-26T13:03:45 | {
"domain": "mathhelpboards.com",
"url": "https://mathhelpboards.com/threads/proof-critique-induction.6248/",
"openwebmath_score": 0.9834364652633667,
"openwebmath_perplexity": 977.5917597252328,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9924227591803558,
"lm_q2_score": ... |
https://math.stackexchange.com/questions/2114575/partitions-of-n-that-generate-all-numbers-smaller-than-n | # Partitions of n that generate all numbers smaller than n
Consider a partition $$n=n_1+n_2+\cdots+n_k$$ such that each number $1,\cdots, n$ can be obtained by adding some of the numbers $n_1,n_2,\cdots,n_k$. For example, $$9=4+3+1+1,$$
and every number $1,2,\cdots,9$ be ca written as a sum of some of the numbers $4,... | 2019-04-24T20:35:35 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/2114575/partitions-of-n-that-generate-all-numbers-smaller-than-n",
"openwebmath_score": 0.8674020171165466,
"openwebmath_perplexity": 151.52469035540983,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score... |
http://elespiadigital.org/libs/king-size-lzxvyu/archive.php?13828f=absolute-value-function | The absolute value function is commonly thought of as providing the distance the number is from zero on a number line. The absolute value function is commonly thought of as providing the distance the number is from zero on a number line. Describe all numbers$\,x\,$that are at a distance of 4 from the number 8. Write an... | 2021-06-15T17:12:00 | {
"domain": "elespiadigital.org",
"url": "http://elespiadigital.org/libs/king-size-lzxvyu/archive.php?13828f=absolute-value-function",
"openwebmath_score": 0.6666929721832275,
"openwebmath_perplexity": 666.4102091724513,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.9920620049... |
https://math.stackexchange.com/questions/1922013/are-there-primes-of-every-possible-number-of-digits/1922015 | # Are there primes of every possible number of digits?
That is, is it the case that for every natural number $n$, there is a prime number of $n$ digits? Or, is there some $n$ such that no primes of $n$-digits exist?
I am wondering this because of this Project Euler problem: https://projecteuler.net/problem=37. I find... | 2022-05-17T08:22:26 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/1922013/are-there-primes-of-every-possible-number-of-digits/1922015",
"openwebmath_score": 0.8959529399871826,
"openwebmath_perplexity": 153.28106886512555,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_sc... |
https://math.stackexchange.com/questions/2863671/how-many-poker-hands-have-two-pairs | # How many poker hands have two pairs?
I'm trying to calculate how many poker hands called Two Pair, there are. Such a hand consists of one pair of one rank, another pair of another rank and one card of a third rank. A poker hand consists of 5 cards.
I have two methods that I thought would work equally well. Turns ou... | 2020-05-30T18:51:26 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/2863671/how-many-poker-hands-have-two-pairs",
"openwebmath_score": 0.6769075393676758,
"openwebmath_perplexity": 327.0273536874462,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9934102283369195,... |
https://www.physicsforums.com/threads/integration-problem.158225/ | # Integration Problem
## Homework Statement
$$\int {\frac{sin^{2}x}{1+sin^{2}x}dx}$$
## Homework Equations
Let t = tan x/2, then dx = 2/(1+t^2) and sin x = 2t / (1+t^2)
## The Attempt at a Solution
I got up to the point where $$\int {\frac{8t^{2}}{(1+6t^{2}+t^{4})(1+t^{2})} dt}$$. Not sure if I'm on the right tra... | 2021-04-21T03:09:55 | {
"domain": "physicsforums.com",
"url": "https://www.physicsforums.com/threads/integration-problem.158225/",
"openwebmath_score": 0.8774517774581909,
"openwebmath_perplexity": 777.9312771301906,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes\n\n",
"lm_q1_score": 0.9863631679255076,
"lm_q2_score... |
http://mathhelpforum.com/discrete-math/130610-set-odd-integers-proof-print.html | # set of odd integers proof
• Feb 24th 2010, 02:21 PM
james121515
set of odd integers proof
I am working on a simple set theory proof involving the definition of odd numbers, and so far I've done one containment. I would guess that if thiss is correct, then the other containment would be equally simple. Does this look... | 2017-10-18T00:16:39 | {
"domain": "mathhelpforum.com",
"url": "http://mathhelpforum.com/discrete-math/130610-set-odd-integers-proof-print.html",
"openwebmath_score": 0.957656979560852,
"openwebmath_perplexity": 722.7092434974562,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9890130551025345,
"lm... |
https://math.stackexchange.com/questions/3570010/what-is-the-general-solution-to-the-equation-sin-x-sqrt3-cos-x-sqrt2 | # What is the general solution to the equation $\sin x + \sqrt{3}\cos x = \sqrt2$
I need to find the general solution to the equation
$$\sin(x) + \sqrt3\cos(x)=\sqrt2$$
So I went ahead and divided by $$2$$, thus getting the form
$$\cos(x-\frac{\pi}{6})=\cos(\frac{\pi}{4})$$
Thus the general solution to this would ... | 2021-10-19T06:32:02 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/3570010/what-is-the-general-solution-to-the-equation-sin-x-sqrt3-cos-x-sqrt2",
"openwebmath_score": 0.867301881313324,
"openwebmath_perplexity": 158.98612471699494,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"... |
https://math.stackexchange.com/questions/1277038/why-is-1-i-equal-to-i/1277042 | # Why is $1/i$ equal to $-i$?
When I entered the value $$\frac{1}{i}$$ in my calculator, I received the answer as $-i$ whereas I was expecting the answer as $i^{-1}$. Even google calculator shows the same answer (Click here to check it out).
Is there a fault in my calculator or $\frac{1}{i}$ really equals $-i$? If it... | 2023-03-31T20:02:43 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/1277038/why-is-1-i-equal-to-i/1277042",
"openwebmath_score": 0.9456176161766052,
"openwebmath_perplexity": 257.71496231595404,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9873750477464142,
"l... |
https://brilliant.org/discussions/thread/sum-of-harmonic-series/ | # Sum of Harmonic Series
It is well known that the sum of a harmonic series does not have a closed form. Here is a formula which gives us a good approximation.
We need to find the sum of the following series
$\dfrac{1}{a}+\dfrac{1}{a+d}+\dfrac{1}{a+2d}+\ldots+\dfrac{1}{a+(n-1)d}$
Consider the function $$f(x)=\frac{... | 2018-04-20T07:07:02 | {
"domain": "brilliant.org",
"url": "https://brilliant.org/discussions/thread/sum-of-harmonic-series/",
"openwebmath_score": 0.9984549880027771,
"openwebmath_perplexity": 2927.9678096791167,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.9748211626883622,
"lm_q2_score": 0.924... |
https://math.stackexchange.com/questions/1398083/are-there-many-different-power-series-representation-for-a-given-function | # Are there many different power series representation for a given function?
So I have to find the power series representation for $f(x) = \ln (3-x)$.
I attempted the following:
$$\ln(3-x) = \int {- \frac{1}{3-x} dx}$$ $$= - \int { \frac{1}{1-(x-2)} dx}$$ $$= - \int {\sum_{n=0}^{\infty}{(x-2)^n} dx}$$ $$= \sum_{n=0}... | 2021-08-02T13:48:36 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/1398083/are-there-many-different-power-series-representation-for-a-given-function",
"openwebmath_score": 0.944172739982605,
"openwebmath_perplexity": 396.303447041935,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
... |
https://math.stackexchange.com/questions/4257386/given-the-gcd-and-lcm-of-n-positive-integers-how-many-solutions-are-there | Given the GCD and LCM of n positive integers, how many solutions are there?
Question: Suppose you know $$G:=\gcd$$ (greatest common divisor) and $$L:=\text{lcm}$$ (least common multiple) of $$n$$ positive integers; how many solution sets exist?
In the case of $$n = 2$$, one finds that for the $$k$$ distinct primes di... | 2022-01-23T03:00:56 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/4257386/given-the-gcd-and-lcm-of-n-positive-integers-how-many-solutions-are-there",
"openwebmath_score": 0.8209962248802185,
"openwebmath_perplexity": 224.42383233340095,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES... |
https://math.stackexchange.com/questions/618091/inferential-logic-in-a-simple-life-situation | # Inferential logic in a simple-life situation.
Here's a little situation I want math to resolve for me :
1. If I study, I make the exam ,
2. If I do not play tennis, I study ,
3. I didn't make the exam
Can I conclude that was playing tennis ?
Trying to put this into the symbology of inference logic and proposition... | 2019-10-18T03:50:24 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/618091/inferential-logic-in-a-simple-life-situation",
"openwebmath_score": 0.7437729239463806,
"openwebmath_perplexity": 1069.2030222676608,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.97023990... |
https://math.stackexchange.com/questions/3607102/calculating-total-number-of-allowable-paths/3607174 | # calculating total number of allowable paths
I seem to be struggling with the following type of path questions
Consider paths starting at $$(0, 0)$$ with allowable steps
(i) from $$(x,y)$$ to $$(x+1,y+2)$$,
(ii) from $$(x,y)$$ to $$(x+2,y+1)$$,
(iii)from $$(x,y)$$ to $$(x+1,y)$$
Determine the total number of all... | 2022-08-08T03:39:36 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/3607102/calculating-total-number-of-allowable-paths/3607174",
"openwebmath_score": 0.8159676790237427,
"openwebmath_perplexity": 262.8508306791505,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9... |
https://gmatclub.com/forum/m-is-a-positive-integer-less-than-100-when-m-is-raised-to-the-third-226775.html | It is currently 19 Feb 2018, 04:06
### 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.
Customized
for You
we will pick new questions that match your level based o... | 2018-02-19T12:06:00 | {
"domain": "gmatclub.com",
"url": "https://gmatclub.com/forum/m-is-a-positive-integer-less-than-100-when-m-is-raised-to-the-third-226775.html",
"openwebmath_score": 0.7223361730575562,
"openwebmath_perplexity": 1336.469105695326,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes\n",
"lm_q1_score": ... |
https://gmatclub.com/forum/if-p-x-and-y-are-positive-integers-y-is-odd-and-p-x-82399.html?kudos=1 | It is currently 18 Oct 2017, 22:56
### 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.
Customized
for You
we will pick new questions that match your level based o... | 2017-10-19T05:56:09 | {
"domain": "gmatclub.com",
"url": "https://gmatclub.com/forum/if-p-x-and-y-are-positive-integers-y-is-odd-and-p-x-82399.html?kudos=1",
"openwebmath_score": 0.5733380317687988,
"openwebmath_perplexity": 2726.3281205360695,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes\n\n",
"lm_q1_score": 1,
"... |
https://math.stackexchange.com/questions/669085/what-does-curly-curved-less-than-sign-succcurlyeq-mean/669115 | # What does "curly (curved) less than" sign $\succcurlyeq$ mean?
I am reading Boyd & Vandenberghe's Convex Optimization. The authors use curved greater than or equal to (\succcurlyeq)
$$f(x^*) \succcurlyeq \alpha$$
and curved less than or equal to (\preccurlyeq)
$$f(x^*) \preccurlyeq \alpha$$
Can someone explain w... | 2022-05-22T17:49:09 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/669085/what-does-curly-curved-less-than-sign-succcurlyeq-mean/669115",
"openwebmath_score": 0.8520500659942627,
"openwebmath_perplexity": 663.221938754306,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_sco... |
http://mathhelpforum.com/pre-calculus/10298-piecewise-defined-function.html | # Math Help - Piecewise-Defined Function
1. ## Piecewise-Defined Function
For both questions below:
(a) Find the domain of the function.
(b) Locate any intercepts.
(1)
.....{3 + x......if -3 <or= to x < 0
f(x){3...........if......x = 0
.....{Sqrt{x}..if......x > 0
=======================
(2)
..........{1/x....... | 2015-01-29T16:41:51 | {
"domain": "mathhelpforum.com",
"url": "http://mathhelpforum.com/pre-calculus/10298-piecewise-defined-function.html",
"openwebmath_score": 0.6340510845184326,
"openwebmath_perplexity": 2681.056311776446,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9653811641488385,
"lm_q2... |
https://mathematica.stackexchange.com/questions/151050/mellin-transform-of-xp-seems-to-miss-a-factor-of-2-pi/170579 | # Mellin transform of $x^p$ seems to miss a factor of $2\pi$
Bug introduced in 11.1 or earlier and fixed in 11.3
On Mathematica 11.1.1.0 the Mellin transform of $x^p$ is evaluated as $\delta(p+s)$, while I think it should be $2\pi\,\delta(p+s)$:
In:= MellinTransform[x^p, x, s, GenerateConditions -> True]
Out:= Dirac... | 2020-07-15T02:22:58 | {
"domain": "stackexchange.com",
"url": "https://mathematica.stackexchange.com/questions/151050/mellin-transform-of-xp-seems-to-miss-a-factor-of-2-pi/170579",
"openwebmath_score": 0.45609450340270996,
"openwebmath_perplexity": 1455.502810609982,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"l... |
https://www.physicsforums.com/threads/finding-horizontal-tangent-planes-on-s.556301/ | # Finding Horizontal Tangent Planes on S
1. Dec 2, 2011
### TranscendArcu
1. The problem statement, all variables and given/known data
S is the surface with equation $$z = x^2 +2xy+2y$$a) Find an equation for the tangent plane to S at the point (1,2,9).
b) At what points on S, in any, does S have a horizontal tangen... | 2017-09-20T22:38:11 | {
"domain": "physicsforums.com",
"url": "https://www.physicsforums.com/threads/finding-horizontal-tangent-planes-on-s.556301/",
"openwebmath_score": 0.638455867767334,
"openwebmath_perplexity": 1154.9442875848038,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9811668728630677,... |
http://kkul.mascali1928.it/solving-quadratic-equations-pure-imaginary-numbers.html | # Solving Quadratic Equations Pure Imaginary Numbers
For y = x 2 , as you move one unit right or left, the curve moves one unit up. So, thinking of numbers in this light we can see that the real numbers are simply a subset of the complex numbers. In our recent paper we gave an efficient algorithm to calculate "small" ... | 2020-10-25T08:25:48 | {
"domain": "mascali1928.it",
"url": "http://kkul.mascali1928.it/solving-quadratic-equations-pure-imaginary-numbers.html",
"openwebmath_score": 0.7229335308074951,
"openwebmath_perplexity": 546.7770577462251,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.9919380075184121,
"l... |
http://math.stackexchange.com/questions/66443/a-square-matrix-has-the-same-minimal-polynomial-over-its-base-field-as-it-has-ov | # A square matrix has the same minimal polynomial over its base field as it has over an extension field
I think I have heard that the following is true before, but I don't know how to prove it:
Let $A$ be a matrix with real entries. Then the minimal polynomial of $A$ over $\mathbb{C}$ is the same as the minimal polyn... | 2015-10-09T11:03:38 | {
"domain": "stackexchange.com",
"url": "http://math.stackexchange.com/questions/66443/a-square-matrix-has-the-same-minimal-polynomial-over-its-base-field-as-it-has-ov",
"openwebmath_score": 0.9426719546318054,
"openwebmath_perplexity": 105.42503669789473,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2.... |
https://math.stackexchange.com/questions/769366/how-many-non-empty-subsets-of-1-2-n-satisfy-that-the-sum-of-their-eleme | # How many non empty subsets of {1, 2, …, n} satisfy that the sum of their elements is even?
The question I am working on is the case for $n$ = 9. How many non-empty subsets of $\{1,2,...,9\}$ have that the sum of their elements is even?
My solution is that the sum of elements is even if and only if the subset contai... | 2019-07-22T04:28:47 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/769366/how-many-non-empty-subsets-of-1-2-n-satisfy-that-the-sum-of-their-eleme",
"openwebmath_score": 0.968389093875885,
"openwebmath_perplexity": 56.11930097272193,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
... |
https://math.stackexchange.com/questions/2886048/two-alternate-proofs-that-x-neq-0-wedge-xy-xz-implies-y-z | # Two Alternate Proofs that $x \neq 0 \wedge xy = xz \implies y = z$.
I believe I have been able to construct in two ways, using the field axioms, that if $x \neq 0$ and $xy = xz$, then $y = z$. However, I've seen similar proofs like this assume that we can perform arithmetic operations, such as multiplying both sides... | 2019-08-25T10:04:23 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/2886048/two-alternate-proofs-that-x-neq-0-wedge-xy-xz-implies-y-z",
"openwebmath_score": 0.9999711513519287,
"openwebmath_perplexity": 830.331103338256,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score"... |
https://physics.stackexchange.com/questions/701918/does-this-question-have-two-answers-correct | Does this question have two answers correct?
A simple pendulum (whose length is less than that of a second's pendulum) and a second's pendulum start swinging in phase. They again swing in phase after an interval of $$18$$ seconds from the start. The period of the simple pendulum is
(A) $$0.9$$ sec
(B) $$1.8$$ sec
(... | 2022-08-12T18:16:36 | {
"domain": "stackexchange.com",
"url": "https://physics.stackexchange.com/questions/701918/does-this-question-have-two-answers-correct",
"openwebmath_score": 0.7544134855270386,
"openwebmath_perplexity": 462.6578848021551,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.9808759... |
https://wiki.documentfoundation.org/Documentation/Calc_Functions/MOD | # Documentation/Calc Functions/MOD
Other languages:
English • Nederlands • dansk • español • עברית
MOD
Mathematical
## Summary:
Calculates the remainder when one number (the dividend or numerator) is divided by another number (the divisor or denominator). This is known as the modulo operation.
Often the divid... | 2022-08-13T03:28:23 | {
"domain": "documentfoundation.org",
"url": "https://wiki.documentfoundation.org/Documentation/Calc_Functions/MOD",
"openwebmath_score": 0.6802622079849243,
"openwebmath_perplexity": 643.7915554568802,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9888419674366167,
"lm_q2_s... |
https://niejeden.pl/sub-zero-iduju/450445-properties-of-matrix-addition | # properties of matrix addition
To understand the properties of transpose matrix, we will take two matrices A and B which have equal order. Question 1 : then, verify that A + (B + C) = (A + B) + C. Question 2 : then verify: (i) A + B = B + A (ii) A + (- A) = O = (- A) + A. For any natural number n > 0, the set of n-by... | 2021-07-25T19:24:18 | {
"domain": "niejeden.pl",
"url": "https://niejeden.pl/sub-zero-iduju/450445-properties-of-matrix-addition",
"openwebmath_score": 0.757469117641449,
"openwebmath_perplexity": 377.20628639766676,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.9888419661213173,
"lm_q2_score": 0... |
https://math.stackexchange.com/questions/2280376/find-the-sum-of-a-sequence/2280381 | # Find the sum of a sequence [duplicate]
Based on: $\frac{1}{n*(n+1)}=\frac{1}{n}-\frac{1}{n+1}$ where n is element of N find the sum of the following:
$\frac{1}{1*2}+\frac{1}{2*3}+\frac{1}{3*4}+ ... +\frac{1}{38*39}+\frac{1}{39*40}$
How should one deal with this kind of problem? Is this a mathematical induction, ar... | 2019-08-25T08:58:56 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/2280376/find-the-sum-of-a-sequence/2280381",
"openwebmath_score": 0.19018863141536713,
"openwebmath_perplexity": 2584.9566510886048,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9871787876194205... |
http://bootmath.com/is-this-induction-procedure-correct-2nn.html | # Is this induction procedure correct? ($2^n<n!$)
I am rather new to mathematical induction. Specially inequalities, as seen here How to use mathematical induction with inequalities?. Thanks to that question, I’ve been able to solve some of the form $1 + \frac{1}{2} + \frac{1}{3} + \cdots + \frac{1}{n} \leq \frac{n}{2... | 2018-08-16T16:32:10 | {
"domain": "bootmath.com",
"url": "http://bootmath.com/is-this-induction-procedure-correct-2nn.html",
"openwebmath_score": 0.8984649777412415,
"openwebmath_perplexity": 174.6526703021361,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9927672376944796,
"lm_q2_score": 0.90598... |
http://math.stackexchange.com/questions/801505/shall-remainder-always-be-positive | Shall remainder always be positive?
My cousin in grade 10, was told by his teacher that remainders are never negative. In a specific example,
$$-48\mod{5} = 2$$
I kinda agree.
But my grandpa insists that
$$-48 \mod{5} = -3$$
Which is true? Why?
-
$2$ and $-3$ are just two names for the same element in $\mathbb{Z... | 2016-05-03T09:12:33 | {
"domain": "stackexchange.com",
"url": "http://math.stackexchange.com/questions/801505/shall-remainder-always-be-positive",
"openwebmath_score": 0.8304064869880676,
"openwebmath_perplexity": 505.23722140379584,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.983085089706734... |
https://math.stackexchange.com/questions/3301854/finding-int-sec2-x-tan-x-dx-i-get-frac12-sec2xc-but-an-online-ca | # Finding $\int \sec^2 x \tan x \, dx$, I get $\frac12\sec^2x+C$, but an online calculator gets $\frac12\tan^2x+C$.
I tried to find a generic antiderivative for
$$\displaystyle \int \sec^2x \tan x \mathop{dx}$$
but I think there is something wrong with my solution because it doesn't match what I got through an onlin... | 2019-10-20T08:37:44 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/3301854/finding-int-sec2-x-tan-x-dx-i-get-frac12-sec2xc-but-an-online-ca",
"openwebmath_score": 0.7937160730361938,
"openwebmath_perplexity": 319.5936317607945,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q... |
https://math.stackexchange.com/questions/2764985/intuition-for-why-the-difference-between-frac2x2-xx2-x1-and-fracx-2/2765019 | # Intuition for why the difference between $\frac{2x^2-x}{x^2-x+1}$ and $\frac{x-2}{x^2-x+1}$ is a constant?
Why is the difference between these two functions a constant?
$$f(x)=\frac{2x^2-x}{x^2-x+1}$$ $$g(x)=\frac{x-2}{x^2-x+1}$$
Since the denominators are equal and the numerators differ in degree I would never ha... | 2022-05-29T09:27:13 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/2764985/intuition-for-why-the-difference-between-frac2x2-xx2-x1-and-fracx-2/2765019",
"openwebmath_score": 0.793973982334137,
"openwebmath_perplexity": 346.3680785891427,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES... |
http://mathhelpforum.com/geometry/143843-solved-finding-co-ordinates-rectangle.html | # Thread: [SOLVED] Finding Co-Ordinates of a Rectangle
1. ## [SOLVED] Finding Co-Ordinates of a Rectangle
Here's a question from a past paper which I have successfully attempted. My question is regarding part (iii). I have successfully figured out the co-ordinates by the following method:
Is my method correct, consi... | 2018-06-20T14:11:27 | {
"domain": "mathhelpforum.com",
"url": "http://mathhelpforum.com/geometry/143843-solved-finding-co-ordinates-rectangle.html",
"openwebmath_score": 0.844447135925293,
"openwebmath_perplexity": 646.5633322110568,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.984336353585837,
... |
https://lotusmc.org/ii5sh61n/archive.php?id=6a0ed8-system-of-linear-equations-problems | Below is an example that shows how to use the gradient descent to solve for three unknown variables, x 1, x 2, and x 3. Solution: Rewrite in order to align the x and y terms. One way to solve a system of linear equations is by graphing each linear equation on the same -plane. ... Systems of equations word problems (wit... | 2021-09-23T22:03:28 | {
"domain": "lotusmc.org",
"url": "https://lotusmc.org/ii5sh61n/archive.php?id=6a0ed8-system-of-linear-equations-problems",
"openwebmath_score": 0.4137629270553589,
"openwebmath_perplexity": 474.14805537072425,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.9869795091201805,
... |
https://math.stackexchange.com/questions/2398684/average-number-of-selections-before-duplicate-picked | # Average number of selections before duplicate picked
I have a dataset of 1296 unique codes which can be numbered 1 through 1296. If numbers are selected at random, one at a time, with replacement. On average, how many iterations will it take to select a number that has already been selected?
Experimentally, (loopin... | 2019-05-25T03:14:54 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/2398684/average-number-of-selections-before-duplicate-picked",
"openwebmath_score": 0.7660864591598511,
"openwebmath_perplexity": 279.07212059651675,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0... |
https://math.stackexchange.com/questions/2287316/find-relationship-between-a-b-c-f-g-h | # Find relationship between $a, b, c, f, g, h$
Given that - $$a=a_1 a_2$$ $$b=b_1 b_2$$ $$c=c_1 c_2$$ $$h=a_2 b_1 + b_2 a_1$$ $$g=a_1 c_2 + a_2 c_1$$ $$f=b_1 c_2 + b_2 c_1$$
Find the relationship between $a, b, c, f, g, h$
My Attempt: I could not see how I could exploit the symmetry of the equations to directly get ... | 2019-08-26T00:38:12 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/2287316/find-relationship-between-a-b-c-f-g-h",
"openwebmath_score": 0.8017062544822693,
"openwebmath_perplexity": 294.01646413254554,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.98282329249702... |
https://www.freemathhelp.com/forum/threads/find-the-numbers.115989/ | # Find the Numbers
Status
Not open for further replies.
##### Full Member
There are two numbers whose sum is 53. Three times the smaller number is equal to 19 more than the larger number. What are the numbers?
Set up:
Let x = large number
Let y = small number
x + y = 53...Equation A
3y = x + 19....Equation B
x + ... | 2019-05-25T11:46:25 | {
"domain": "freemathhelp.com",
"url": "https://www.freemathhelp.com/forum/threads/find-the-numbers.115989/",
"openwebmath_score": 0.5126290917396545,
"openwebmath_perplexity": 1169.4730670751283,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.9828232879690035,
"lm_q2_score":... |
http://winbytes.org/help/standard-error/proportion-standard-error.html | Home > standard error > proportion standard error
# Proportion Standard Error
## Contents
repeatedly randomly drawn from a population, and the proportion of successes in each sample is recorded ($$\widehat{p}$$),the distribution of the sample
## Standard Error Of Proportion Formula
proportions (i.e., the sampling ... | 2019-04-25T14:21:47 | {
"domain": "winbytes.org",
"url": "http://winbytes.org/help/standard-error/proportion-standard-error.html",
"openwebmath_score": 0.3121330142021179,
"openwebmath_perplexity": 10404.382160598483,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9840936068886641,
"lm_q2_score": ... |
https://math.stackexchange.com/questions/1457701/spectral-decomposition-of-a-and-b | # Spectral Decomposition of A and B.
I was given the following question in my linear algebra course.
Let $A$ be a symmetric matrix, $c >0$, and $B=cA$, find the relationship between the spectral decompositions of $A$ and $B$.
From what I understand. If $A$ is a symmetric matrix, then $A=A^T$. A symmetric matrix has ... | 2022-07-02T12:28:59 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/1457701/spectral-decomposition-of-a-and-b",
"openwebmath_score": 0.9967987537384033,
"openwebmath_perplexity": 98.99838089290482,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.9867771782476948,
... |
http://math.stackexchange.com/questions/110667/why-binomial-distribution-formula-includes-the-not-happening-probability | # Why Binomial Distribution formula includes the “not-happening” probability?
Suppose I have a dice with 6 sides, and I let a random variable $X$ be the number of times I get 3 points when I throw the dice.
So I throw the dice for $10$ times, I want to find the probability of getting 3 points from the dice for $4$ ti... | 2016-05-31T02:20:02 | {
"domain": "stackexchange.com",
"url": "http://math.stackexchange.com/questions/110667/why-binomial-distribution-formula-includes-the-not-happening-probability",
"openwebmath_score": 0.8770877122879028,
"openwebmath_perplexity": 221.62111013827325,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
... |
https://www.physicsforums.com/threads/give-a-big-o-estimate-of-the-product-of-the-first-n-odd-positive-integers.514750/ | # Homework Help: Give a big-O estimate of the product of the first n odd positive integers
1. Jul 17, 2011
### pc2-brazil
1. The problem statement, all variables and given/known data
Give a big-O estimate of the product of the first n odd
positive integers.
2. Relevant equations
Big-O notation:
f(x) is O(g(x)) if t... | 2018-05-22T16:25:07 | {
"domain": "physicsforums.com",
"url": "https://www.physicsforums.com/threads/give-a-big-o-estimate-of-the-product-of-the-first-n-odd-positive-integers.514750/",
"openwebmath_score": 0.8235124945640564,
"openwebmath_perplexity": 2055.7448349221136,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
... |
https://calspasblog.com/z6oue/viewtopic.php?page=67a3e4-rational-numbers-symbol | rational numbers symbol
# rational numbers symbol
The real line consists of the union of the rational and irrational numbers. We have seen that all counting numbers are whole numbers, all whole numbers are integers, and all integers are rational numbers. Formally, rational numbers are the set of all real numbers that... | 2021-05-12T15:11:26 | {
"domain": "calspasblog.com",
"url": "https://calspasblog.com/z6oue/viewtopic.php?page=67a3e4-rational-numbers-symbol",
"openwebmath_score": 0.8266318440437317,
"openwebmath_perplexity": 321.2912625395907,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.9935117296348998,
"lm_... |
https://math.stackexchange.com/questions/2119158/conditional-probability-exercise-apples-and-oranges/2119210 | # Conditional probability exercise - apples and oranges
We have two crates, crate 1 and crate 2. Crate 1 has 2 oranges and 4 apples, and crate 2 has 1 orange and 1 apple. We take 1 fruit from crate 1 and put it in crate 2, and then we take a fruit from crate 2.
The first point of this exercise asks me to calculate th... | 2020-12-02T09:59:58 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/2119158/conditional-probability-exercise-apples-and-oranges/2119210",
"openwebmath_score": 0.6868855953216553,
"openwebmath_perplexity": 136.17207693072405,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_sc... |
https://math.stackexchange.com/questions/2844980/general-solution-for-a-recurrence-relation | # general solution for a recurrence relation
I have the following recurrence relation: $$x_1=1, x_2=a, x_{n+2}=ax_{n+1}-x_n\hspace{1cm}(*)$$
If we assume that $x_n=r^n$ is a solution for the relation $x_{n+2}=ax_{n+1}-x_n$, then I can deduce that $r=\frac{a+\sqrt{a^2-4}}{2}$ or $r=\frac{a-\sqrt{a^2-4}}{2}$.
By using... | 2019-05-26T21:42:49 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/2844980/general-solution-for-a-recurrence-relation",
"openwebmath_score": 0.8752542734146118,
"openwebmath_perplexity": 176.84608042968154,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.986363167... |
https://afd-hamburg-nord.de/forum/archive.php?53e5c2=block-triangular-matrix-eigenvalues | Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share ⦠In mathematics, a block matrix or a partitioned matrix is a matrix that is interpreted as having been broken into sections called blocks or submatrices. If P A A... | 2021-04-11T06:33:15 | {
"domain": "afd-hamburg-nord.de",
"url": "https://afd-hamburg-nord.de/forum/archive.php?53e5c2=block-triangular-matrix-eigenvalues",
"openwebmath_score": 0.786680281162262,
"openwebmath_perplexity": 430.25903240845196,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.99493966886... |
https://brilliant.org/discussions/thread/a-seemingly-impossible-problem/ | # A Seemingly Impossible Problem
Given that $w, x, y, z$ take on values $0$ and $1$ with equal probability, what is the probability that $w+x+y+z$ is odd?
Which of the following arguments is correct?
Furthermore, can you generalize this result?
Argument 1:
If all 4 numbers are even, the sum is even.
If 3 numbers ar... | 2019-10-19T00:53:07 | {
"domain": "brilliant.org",
"url": "https://brilliant.org/discussions/thread/a-seemingly-impossible-problem/",
"openwebmath_score": 0.968029260635376,
"openwebmath_perplexity": 1416.1759739498716,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.9759464485047916,
"lm_q2_sc... |
http://math.stackexchange.com/questions/79446/what-is-the-remainder-of-1420101-div-6 | What is the remainder of $(14^{2010}+1) \div 6$?
What is the remainder of $(14^{2010}+1) \div 6$?
Someone showed me a way to do this by finding a pattern, i.e.:
$14^1\div6$ has remainder 2
$14^2\div6$ has remainder 4
$14^3\div6$ has remainder 2
$14^4\div6$ has remainder 4
And it seems that when the power is odd, th... | 2015-04-27T02:07:07 | {
"domain": "stackexchange.com",
"url": "http://math.stackexchange.com/questions/79446/what-is-the-remainder-of-1420101-div-6",
"openwebmath_score": 0.782090425491333,
"openwebmath_perplexity": 175.36066282774567,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.980875959894864,
... |
https://math.stackexchange.com/questions/72589/whats-the-probability-of-at-least-and-exactly-one-event-occurring | # What's the probability of “at least” and “exactly” one event occurring?
If I know the probability of event $A$ occurring and I also know the probability of $B$ occurring, how can I calculate the probability of "at least one of them" occurring?
I was thinking that this is $P(A \text{ or } B) = P(A) + P(B) - P(A \tex... | 2020-02-19T04:44:22 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/72589/whats-the-probability-of-at-least-and-exactly-one-event-occurring",
"openwebmath_score": 0.819298505783081,
"openwebmath_perplexity": 273.2812882762553,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_... |
https://charlottegroutars.nl/f960gm/9a14f6-matrix-multiplied-by-its-conjugate-transpose | One property I am aware of is that $AA^H$ is Hermitian, i.e. An matrix can be multiplied on the right by an matrix, where is any positive integer. If you want to discuss contents of this page - this is the easiest way to do it. It only takes a minute to sign up. To learn more, see our tips on writing great answers. The... | 2021-04-15T18:15:34 | {
"domain": "charlottegroutars.nl",
"url": "https://charlottegroutars.nl/f960gm/9a14f6-matrix-multiplied-by-its-conjugate-transpose",
"openwebmath_score": 0.5960926413536072,
"openwebmath_perplexity": 714.0621717159065,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes\n\n",
"lm_q1_score": 0.9886682... |
http://incommunity.it/ulik/coin-change-problem-greedy.html | So, I gave Rs. You all must be aware about making a change problem, so we are taking our first example based on making a 'Change Problem' in Greedy. Let a m be an activity in S k with the earliest nish time. Write a function to compute the fewest number of coins that you need to make up that amount. There are many poss... | 2020-05-30T02:52:41 | {
"domain": "incommunity.it",
"url": "http://incommunity.it/ulik/coin-change-problem-greedy.html",
"openwebmath_score": 0.6997814178466797,
"openwebmath_perplexity": 631.4589835219829,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.9886682458008671,
"lm_q2_score": 0.90861... |
https://math.stackexchange.com/questions/2335051/determine-all-convex-polyhedra-with-6-faces | # Determine all convex polyhedra with $6$ faces
I want to determine all convex polyhedra with 6 faces (not necessarily regular). Based on the Euler characteristic, $v-e+f=2$, we know that $v-e+6=2$, or $v+4=e$. Let $n_i$ be the number of edges on the $i$th face. Then $\sum n_i=2e$. Each face has at least $3$ edges, so... | 2022-08-07T22:19:41 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/2335051/determine-all-convex-polyhedra-with-6-faces",
"openwebmath_score": 0.6178984642028809,
"openwebmath_perplexity": 420.85012306234296,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.98717878... |
http://happinessconnection.newmedia1.net/uuqb0/b5f281-distance-formula-real-life-problems | distance formula real life problems
Distance is the total movement of an object without any regard to direction. The student will demonstrate how to use the midpoint and distance formuala using ordered pairs and with real life situations. Distance Formula. For example, the formula for calculating speed is speed = dist... | 2021-09-22T08:12:14 | {
"domain": "newmedia1.net",
"url": "http://happinessconnection.newmedia1.net/uuqb0/b5f281-distance-formula-real-life-problems",
"openwebmath_score": 0.45044904947280884,
"openwebmath_perplexity": 1134.5942273666617,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes\n\n",
"lm_q1_score": 0.9830850832... |
http://dreams.grecotel.com/v1g8jvh/third-fundamental-theorem-of-calculus-0d5f9d | Using the first fundamental theorem of calculus vs the second. The Mean Value Theorem for Integrals and the first and second forms of the Fundamental Theorem of Calculus are then proven. The course develops the following big ideas of calculus: limits, derivatives, integrals and the Fundamental Theorem of Calculus, and ... | 2021-05-15T02:13:30 | {
"domain": "grecotel.com",
"url": "http://dreams.grecotel.com/v1g8jvh/third-fundamental-theorem-of-calculus-0d5f9d",
"openwebmath_score": 0.8412231802940369,
"openwebmath_perplexity": 578.4206299133635,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes\n\n",
"lm_q1_score": 0.9914225125587971,
"lm... |
http://mathhelpforum.com/math-challenge-problems/16249-problem-28-a.html | # Math Help - Problem 28
1. ## Problem 28
Proposition 1: If $x+y+z=1$ then $xy+yz+xz<1/2$
Q1. Prove Proposition 1 is true
Q2. Prove Proposition 1 is false
There is a Q3 for when Q1 and Q2 have been settled.
RonL
2. If $x,y,z\in\mathbf{R}$ then
$1=(x+y+z)^2=x^2+y^2+z^2+2(xy+xz+yz)\Rightarrow$
$\Rightarrow 2(xy+xz... | 2016-05-05T09:28:59 | {
"domain": "mathhelpforum.com",
"url": "http://mathhelpforum.com/math-challenge-problems/16249-problem-28-a.html",
"openwebmath_score": 0.953863799571991,
"openwebmath_perplexity": 904.2671845181916,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9928785702006464,
"lm_q2_sco... |
https://math.stackexchange.com/questions/3253020/composite-simpsons-rule-vs-trapezoidal-on-integrating-int-02-pi-sin2x-dx | # Composite Simpson's rule vs Trapezoidal on integrating $\int_0^{2\pi}\sin^2x dx$
A simple question comparing both methods for numerical integration for a very specific case. We expect the Simpsons rule to have a smaller error than the trapezoidal method, but if we want to calculate
$$\int_0^{2\pi}\sin^2x dx$$
with... | 2022-01-22T21:22:36 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/3253020/composite-simpsons-rule-vs-trapezoidal-on-integrating-int-02-pi-sin2x-dx",
"openwebmath_score": 0.7842830419540405,
"openwebmath_perplexity": 1170.837746442434,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",... |
https://mathhelpboards.com/threads/compute-a-b-a-c-b-c.6615/ | # Compute (a + b)(a + c)(b + c)
#### anemone
##### MHB POTW Director
Staff member
Let $a, b, c$ be the roots of $x^3-7x^2-6x+5=0$.
Compute $(a+b)(a+c)(b+c)$.
##### Well-known member
Re: Compute (a+b)(a+c)(b+c)
Let $a, b, c$ be the roots of $x^3-7x^2-6x+5=0$.
Compute $(a+b)(a+c)(b+c)$.
F(x) = x^3- 7x^2 – 6x + 5
no... | 2022-01-28T20:12:34 | {
"domain": "mathhelpboards.com",
"url": "https://mathhelpboards.com/threads/compute-a-b-a-c-b-c.6615/",
"openwebmath_score": 0.7596861124038696,
"openwebmath_perplexity": 5761.7894840643485,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9912886142555052,
"lm_q2_score": 0.90... |
https://analyzehashtags.com/lw6ql/47d182-heat-equation-separation-of-variables | Together with a PDE, we usually have specified some boundary conditions, where the value of the solution or its derivatives is specified along the boundary of a region, and/or someinitial conditions where the value of the solution or its derivatives is specified for some initial time. Up: Heat equation. The LibreTexts ... | 2021-07-28T19:09:19 | {
"domain": "analyzehashtags.com",
"url": "https://analyzehashtags.com/lw6ql/47d182-heat-equation-separation-of-variables",
"openwebmath_score": 0.8415722250938416,
"openwebmath_perplexity": 976.8539394173508,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9869795075882268,
"... |
https://mathhelpboards.com/threads/show-that-a-linear-function-is-convex.8538/ | # Show that a linear function is convex
#### mathmari
##### Well-known member
MHB Site Helper
Hey!
To show that a two-variable function is convex, we can use the hessiam matrix and the determinants. But the function is linear the matrix is the zero matrix. What can I do in this case?
#### Klaas van Aarsen
##### MHB... | 2021-01-21T06:07:39 | {
"domain": "mathhelpboards.com",
"url": "https://mathhelpboards.com/threads/show-that-a-linear-function-is-convex.8538/",
"openwebmath_score": 0.8647732138633728,
"openwebmath_perplexity": 870.4838594312288,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.9802808753491772,
... |
https://math.stackexchange.com/questions/3154699/how-many-possible-factorizations-are-there-for-a-square-matrix-and-how-can-we-k/3154706 | # How many possible factorizations are there for a square matrix, and how can we know?
Given a square matrix A, how many possible factorization CB=A is there, and how can this number be calculated? I understand that there are many ways of decomposing a matrix that yields matrix multiplications with special properties ... | 2019-05-26T22:57:36 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/3154699/how-many-possible-factorizations-are-there-for-a-square-matrix-and-how-can-we-k/3154706",
"openwebmath_score": 0.8687286972999573,
"openwebmath_perplexity": 152.27285034033238,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "... |
https://cs.stackexchange.com/questions/121735/conditions-for-applying-case-3-of-master-theorem | Conditions for applying Case 3 of Master theorem
In Introduction to Algorithms, Lemma 4.4 of the proof of the master theorem goes like this. $$a\geq1$$, $$b>1$$, $$f$$ is a nonnegative function defined on exact powers of b. The recurrence relation for $$T$$ is $$T(n) = a T(n/b) + f(n)$$ for $$n=b^i$$, $$i>0$$.
For th... | 2022-05-19T03:14:36 | {
"domain": "stackexchange.com",
"url": "https://cs.stackexchange.com/questions/121735/conditions-for-applying-case-3-of-master-theorem",
"openwebmath_score": 0.9641386866569519,
"openwebmath_perplexity": 130.1558069180877,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.9777138... |
https://avenuewebmedia.com/jam-strain-mmerms/c7e472-area-of-a-polygon | Area of a square. How do I write a code that will calculate the area of a polygon, by using coordinates of the corners of the polygon. Polygon Calculator. Area. Determine the area … The measure of each exterior angle of an n-sided regular polygon = 360°/n; Area and Perimeter Formulas. One hectare is about $$\text{0,01}... | 2021-06-14T18:21:23 | {
"domain": "avenuewebmedia.com",
"url": "https://avenuewebmedia.com/jam-strain-mmerms/c7e472-area-of-a-polygon",
"openwebmath_score": 0.6473884582519531,
"openwebmath_perplexity": 495.3903390611758,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.9883127423485422,
"lm_q2_scor... |
https://math.stackexchange.com/questions/3054472/solving-an-equation-involving-complex-conjugates/3054475 | # Solving an equation involving complex conjugates
I have the following question and cannot seem to overcome how to contend with equations using $$z$$ and $$\bar z$$ together. For example, the below problem:
Find the value of $$z \in \Bbb C$$ that verifies the equation: $$3z+i\bar z=4+i$$
For other operations that d... | 2019-07-16T22:41:27 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/3054472/solving-an-equation-involving-complex-conjugates/3054475",
"openwebmath_score": 0.9862595796585083,
"openwebmath_perplexity": 272.7966326062529,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score"... |
http://aimath.org/textbooks/beezer/Ssection.html | A subspace is a vector space that is contained within another vector space. So every subspace is a vector space in its own right, but it is also defined relative to some other (larger) vector space. We will discover shortly that we are already familiar with a wide variety of subspaces from previous sections. Here's the... | 2013-05-21T15:59:34 | {
"domain": "aimath.org",
"url": "http://aimath.org/textbooks/beezer/Ssection.html",
"openwebmath_score": 0.8992156982421875,
"openwebmath_perplexity": 207.62701633078964,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9923043537319405,
"lm_q2_score": 0.9046505428129514,
"l... |
https://math.stackexchange.com/questions/4455035/does-the-set-of-convex-combination-of-points-in-cantor-set-contains-a-non-empty | # Does the set of convex combination of points in Cantor set contains a non empty open interval?
$$\mathcal{C}$$ denote the cantor middle third set.
$$\mathcal{C}_t=\{(1-t)x+ty : x, y\in \mathcal{C} \}$$
$$\mathcal{C}_0=\mathcal{C}_1=\mathcal{C}$$ and we can prove that that $$\mathcal{C}$$ contains no non empty open... | 2022-06-26T10:23:27 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/4455035/does-the-set-of-convex-combination-of-points-in-cantor-set-contains-a-non-empty",
"openwebmath_score": 0.9852447509765625,
"openwebmath_perplexity": 146.98010200419125,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n... |
https://kokecacao.me/page/Course/F20/21-127/Lecture_018.md | # Lecture 018
## Surjection - horizontal line test at least once
Surjection(surjectivity): everything in the codomain gets hit by something
• Definition Let A and B be sets and $f: A \rightarrow B$ be a function. f is surjective (or onto) iff $Im_f(A) = B$.
• $(\forall b \in B)(\exists a \in A)(f(a) = b)$
• $f:A \... | 2022-11-30T16:33:28 | {
"domain": "kokecacao.me",
"url": "https://kokecacao.me/page/Course/F20/21-127/Lecture_018.md",
"openwebmath_score": 0.9775453209877014,
"openwebmath_perplexity": 1577.3892278433505,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9967775151494933,
"lm_q2_score": 0.9005297787... |
https://math.stackexchange.com/questions/2463421/diophantine-equation-with-three-variables | # Diophantine equation with three variables
The question is:
Nadir Airways offers three types of tickets on their Boston-New York flights. First-class tickets are \$140, second-class tickets are \$110, and stand-by tickets are \$78. If 69 passengers pay a total of$6548 for their tickets on a particular flight, how ma... | 2020-07-13T01:59:17 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/2463421/diophantine-equation-with-three-variables",
"openwebmath_score": 0.22486960887908936,
"openwebmath_perplexity": 543.1489795863957,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9863631639... |
http://mathhelpforum.com/pre-calculus/10920-calculating-position-circumference.html | # Math Help - Calculating position on a circumference
1. ## Calculating position on a circumference
Hello all, I hope someone is able to help me get my head round this little problem.
If I have a circle that is centered at (200,200) and its radius is 150, how do I calculate the point at any given angle? For example,... | 2015-08-29T20:03:45 | {
"domain": "mathhelpforum.com",
"url": "http://mathhelpforum.com/pre-calculus/10920-calculating-position-circumference.html",
"openwebmath_score": 0.6894080638885498,
"openwebmath_perplexity": 2250.523898078114,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9822876997410348,
... |
https://math.stackexchange.com/questions/2921270/determining-linearly-dependent-vectors | # Determining Linearly Dependent Vectors
I am learning about Linear dependent vector from here
But I am unable to grasp the following equation:
If no such scalars exist, then the vectors are to be linearly independent.
$$c_1\begin{bmatrix}x_{11}\\x_{21}\\\vdots\\x_{n1}\\ \end{bmatrix}+c_2\begin{bmatrix}x_{12}\\x_{2... | 2020-02-23T02:56:30 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/2921270/determining-linearly-dependent-vectors",
"openwebmath_score": 0.9722394943237305,
"openwebmath_perplexity": 561.0961631677354,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.97935406986337... |
http://zttj.couponit.de/plot-transfer-function-matlab.html | # Plot Transfer Function Matlab
Matlab also o ers w a ys to turn a sequence of graphs in toamo vie, con. You need to use the tf (link) function to produce a system object from your transfer function, and the lsim (link) function to do the simulation. Yes, i have Control System Toolbox. Bode Plot Example of First-Order... | 2020-02-24T20:00:20 | {
"domain": "couponit.de",
"url": "http://zttj.couponit.de/plot-transfer-function-matlab.html",
"openwebmath_score": 0.6140795350074768,
"openwebmath_perplexity": 762.446803438893,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.9755769099458929,
"lm_q2_score": 0.9196425295259... |
https://math.stackexchange.com/questions/2333306/for-any-two-sets-a-b-b-a-implies-a-b/2333309 | # For any two sets, $A - B = B - A$ implies $A = B$
Is the following statement True or False:
For any two sets $A$ and $B$: If $A - B = B - A$ then $A = B$.
If it is true, prove it, otherwise provide a counterexample.
I am unable to come up with a counter example. I think the statement is true but how do I prove it... | 2021-02-28T22:29:56 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/2333306/for-any-two-sets-a-b-b-a-implies-a-b/2333309",
"openwebmath_score": 1.0000100135803223,
"openwebmath_perplexity": 228.78163934148245,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9916842... |
http://mathhelpforum.com/geometry/225764-rhombus-problem.html | # Math Help - Rhombus Problem
1. ## Rhombus Problem
Given Rhombus ABCD (not shown) AB = 10 and AC = 12. Find AD and BD
I know that AD = 10 because the sides of a rhombus are all congruent. I cannot find what BD equals though. I thought it was 12 but I don't think the diagonals of a rhombus are congruent.
2. ## Re: ... | 2015-10-09T10:49:55 | {
"domain": "mathhelpforum.com",
"url": "http://mathhelpforum.com/geometry/225764-rhombus-problem.html",
"openwebmath_score": 0.7661396861076355,
"openwebmath_perplexity": 1618.3267976628933,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.993096162337438,
"lm_q2_score": 0.903... |
http://s141453.gridserver.com/do-index-yxivp/a139c0-simplify-radical-expressions | Categorías
In order to simplify radical expressions, you need to be aware of the following rules and properties of radicals 1) From definition of n th root(s) and principal root Examples More examples on Roots of Real Numbers and Radicals. Random: Simplify . smaller If you like this Page, please click that +1 button, ... | 2023-03-27T19:45:17 | {
"domain": "gridserver.com",
"url": "http://s141453.gridserver.com/do-index-yxivp/a139c0-simplify-radical-expressions",
"openwebmath_score": 0.7425239682197571,
"openwebmath_perplexity": 1347.4324661967407,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9766692332287863,
"lm... |
https://math.stackexchange.com/questions/1340632/solve-this-functional-equation | # Solve this functional equation:
Functional equations such as this one appear only once every several years on exams, so I feel it's hard to have a sure-fire way to approach the problem, unlike, say, solving a series convergence problem, multiple variable integration, or proving some results using basic Fourier serie... | 2019-09-22T22:50:53 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/1340632/solve-this-functional-equation",
"openwebmath_score": 0.9482557773590088,
"openwebmath_perplexity": 214.29778855004562,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9830850827686585,
"... |
http://www.danaetobajas.com/furniture-manufacturers-auh/9e2609-standard-form-of-a-quadratic-function-examples | standard form of a quadratic function examples
23303
The functions above are examples of quadratic functions in standard quadratic form. How to Graph Quadratic Functions given in Vertex Form? The standard form of a quadratic function. Sometimes, a quadratic function is not written in its standard form, $$f(x)=ax^2+bx+c... | 2021-04-16T11:33:25 | {
"domain": "danaetobajas.com",
"url": "http://www.danaetobajas.com/furniture-manufacturers-auh/9e2609-standard-form-of-a-quadratic-function-examples",
"openwebmath_score": 0.5181556940078735,
"openwebmath_perplexity": 372.4999742792435,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_sco... |
http://clay6.com/qa/55480/at-3-40-the-hour-hand-and-the-minute-hand-of-a-clock-form-an-angle-of | Comment
Share
Q)
# At 3.40, the hour hand and the minute hand of a clock form an angle of
( A ) 120
( B ) 135
( C ) 130
( D ) 125
Comment
A)
Comment
A)
130 is correct answer or not
Yes, that is correct
Comment
A)
Solution :
Angle traced by hour hand in 12 hrs $=360^{\circ}$
Angle traced by 1t in $\large\frac{11}{3... | 2019-10-18T13:30:40 | {
"domain": "clay6.com",
"url": "http://clay6.com/qa/55480/at-3-40-the-hour-hand-and-the-minute-hand-of-a-clock-form-an-angle-of",
"openwebmath_score": 0.9463309645652771,
"openwebmath_perplexity": 6261.202688168834,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.98433634945032... |
https://brilliant.org/discussions/thread/show-why-the-value-converges-to-pi/ | # Show why the value converges to $\pi$
$a_0=1$
$a_{n+1}=a_n+\sin{(a_n)}$
Explain why the following occurs:
$a_0=1$
$a_1=1+\sin{(1)}\approx 1.841470985$
$a_2=1+\sin{(1)}+\sin{(1+\sin{(1)})}\approx 2.805061709$
$a_3=1+\sin{(1)}+\sin{(1+\sin{(1)})}+\sin{(1+\sin{(1)}+\sin{(1+\sin{(1)})})}\approx 3.135276333$
$a_4\... | 2020-02-27T14:48:20 | {
"domain": "brilliant.org",
"url": "https://brilliant.org/discussions/thread/show-why-the-value-converges-to-pi/",
"openwebmath_score": 0.9868111610412598,
"openwebmath_perplexity": 899.8362535967503,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes\n\n",
"lm_q1_score": 0.9884918533088547,
"lm_q... |
https://math.stackexchange.com/questions/2399770/in-how-many-ways-can-we-permute-the-digits-2-3-4-5-2-3-4-5-if-identical-digits | # In how many ways can we permute the digits $2,3,4,5,2,3,4,5$ if identical digits must not be adjacent?
In how many ways can we permute the digits $2,3,4,5,2,3,4,5$ if identical digit must not be adjacent?
I tried this by first taking total permutation as $\dfrac{8!}{2^4}$
Now $n_1$ as $22$ or $33$ or $44$ or $55$ o... | 2021-10-25T15:12:25 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/2399770/in-how-many-ways-can-we-permute-the-digits-2-3-4-5-2-3-4-5-if-identical-digits",
"openwebmath_score": 0.8166680335998535,
"openwebmath_perplexity": 242.0459981845183,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2.... |
https://math.stackexchange.com/questions/1506871/with-4-rooks-on-a-4-times4-chessboard-such-that-no-rook-can-attack-another-wh | # With 4 rooks on a $4\times4$ chessboard such that no rook can attack another, what is the probability there are no rooks on the diagonal?
Four rooks are randomly placed on a $4 \times 4$ chessboard. Suppose no rook can attack another. Under this condition, what is the probability that the leading diagonal of the che... | 2021-09-19T07:49:14 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/1506871/with-4-rooks-on-a-4-times4-chessboard-such-that-no-rook-can-attack-another-wh",
"openwebmath_score": 0.9933604598045349,
"openwebmath_perplexity": 361.6331018287296,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. ... |
https://tringham.net/h06rim/5a3ef8-how-to-graph-a-horizontal-stretch | This video explains to graph graph horizontal and vertical stretches and compressions in the A point on the object gets further away from the vertical axis on the image. J. JonathanEyoon. x). 1. This problem has been solved! Embedded content, if any, are copyrights of their respective owners. Horizontal And Vertical Gr... | 2021-07-30T01:55:34 | {
"domain": "tringham.net",
"url": "https://tringham.net/h06rim/5a3ef8-how-to-graph-a-horizontal-stretch",
"openwebmath_score": 0.5198330879211426,
"openwebmath_perplexity": 739.5238033094421,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.9840936101542133,
"lm_q2_score": 0.9... |
https://math.stackexchange.com/questions/1724731/if-i-flip-1-of-3-modified-coins-3-times-whats-the-probability-that-i-wil | # If I flip $1$ of $3$ modified coins $3$ times, what's the probability that I will get tails?
We have $3$ modified coins: $M_1$ which has tails on the both sides, $M_2$ which has heads on the both sides and $M_3$ which is a fair coin. We extract a coin from the urn and we flip it $3$ times.
1. What is the probabilit... | 2022-05-21T10:10:37 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/1724731/if-i-flip-1-of-3-modified-coins-3-times-whats-the-probability-that-i-wil",
"openwebmath_score": 0.950875461101532,
"openwebmath_perplexity": 292.10920648775226,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",... |
http://stewswebsolutions.co.uk/journal/gz9p0.php?b2be3c=how-to-find-arc-length-of-a-circle | The lack of closed form solution for the arc length of an elliptic arc led to the development of the elliptic integrals. Measurement by arc length Definition of arc length and formula to calculate it from the radius and central angle of the arc. Improve your skills with free problems in 'Arc measure and arc length' and... | 2018-10-17T03:35:49 | {
"domain": "co.uk",
"url": "http://stewswebsolutions.co.uk/journal/gz9p0.php?b2be3c=how-to-find-arc-length-of-a-circle",
"openwebmath_score": 0.90330970287323,
"openwebmath_perplexity": 291.45016114516045,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.9865717452580314,
"lm_... |
https://www.hpmuseum.org/forum/thread-14070-post-124365.html | Looking for more algorithms for quasi-random numbers
11-29-2019, 01:06 PM (This post was last modified: 11-30-2019 06:16 AM by Namir.)
Post: #1
Namir Senior Member Posts: 690 Joined: Dec 2013
Looking for more algorithms for quasi-random numbers
Hi All Math Lovers,
In another thread of mine, ttw mentions quasi-random ... | 2020-02-17T09:29:34 | {
"domain": "hpmuseum.org",
"url": "https://www.hpmuseum.org/forum/thread-14070-post-124365.html",
"openwebmath_score": 0.6563873291015625,
"openwebmath_perplexity": 2756.027968051556,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.986571747626947,
"lm_q2_score": 0.9086178944... |
http://lampedusasiamonoi.it/yvgr/max-sum-of-2-arrays.html | # Max Sum Of 2 Arrays
Reductions. It also prints the location or index at which maximum element occurs in array. int [] A = {−2, 1, −3, 4, −1, 2, 1, −5, 4}; Output: contiguous subarray with the largest sum is 4, −1, 2, 1, with sum 6. Array is an arranged set of values of one-type variables that have a common name. Yes... | 2020-05-26T21:19:42 | {
"domain": "lampedusasiamonoi.it",
"url": "http://lampedusasiamonoi.it/yvgr/max-sum-of-2-arrays.html",
"openwebmath_score": 0.3012574017047882,
"openwebmath_perplexity": 681.2426012969111,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.97594644290792,
"lm_q2_score": 0.918480... |
https://math.stackexchange.com/questions/2921700/how-to-simplify-or-upperbound-this-summation | # How to simplify or upperbound this summation?
I am not a mathematician, so sorry for this trivial question. Is there a way to simplify or to upperbound the following summation:
$$\sum_{i=1}^n{\exp{\left(-\frac{i^2}{\sigma^2}\right)}}.$$
Can I use geometric series?
EDIT: I have difficulty because of the power $2$,... | 2018-10-19T06:23:28 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/2921700/how-to-simplify-or-upperbound-this-summation",
"openwebmath_score": 0.9999333620071411,
"openwebmath_perplexity": 522.4824194582968,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.98228769... |
https://casmusings.wordpress.com/tag/polynomial/ | # Tag Archives: polynomial
## 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 ... | 2020-03-31T23:17:44 | {
"domain": "wordpress.com",
"url": "https://casmusings.wordpress.com/tag/polynomial/",
"openwebmath_score": 0.803494930267334,
"openwebmath_perplexity": 980.6773426566747,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9907319878505035,
"lm_q2_score": 0.9046505376715775,
"... |
https://gmatclub.com/forum/what-is-the-greatest-value-of-y-such-that-4-y-is-a-factor-of-230289.html | GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video
It is currently 22 Feb 2020, 18:16
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 Questi... | 2020-02-23T02:16:06 | {
"domain": "gmatclub.com",
"url": "https://gmatclub.com/forum/what-is-the-greatest-value-of-y-such-that-4-y-is-a-factor-of-230289.html",
"openwebmath_score": 0.7827305197715759,
"openwebmath_perplexity": 2563.270617579204,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 1,
"lm_... |
https://brilliant.org/discussions/thread/on-recurring-decimals/ | # On Recurring decimals
$\large{0\red{.}\overline{x_1x_2x_3...x_n}=\dfrac{x_1x_2x_3...x_n}{10^n-1}}$
Proof of the above statement
Let $l=0\red{.}\overline{x_1x_2x_3...x_n}$ $10^nl=x_1x_2x_3...x_n\red{.}\overline{x_1x_2x_3...x_n}$ $\Rightarrow 10^nl-l={x_1x_2x_3...x_n}$ $(10^n-1)l=x_1x_2x_3...x_n$ ${l=\dfrac{x_1x_2x_... | 2021-01-16T00:31:31 | {
"domain": "brilliant.org",
"url": "https://brilliant.org/discussions/thread/on-recurring-decimals/",
"openwebmath_score": 0.9654994010925293,
"openwebmath_perplexity": 2703.0319096444596,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes\n\n",
"lm_q1_score": 0.9664104885453715,
"lm_q2_score": 0.... |
https://zong-music.com/ha2ten/greater-than-or-equal-to-sign-9b504e | # greater than or equal to sign
For example, x ≥ -3 is the solution of a certain expression in variable x. Select Symbol and then More Symbols. For example, the symbol is used below to express the less-than-or-equal relationship between two variables: ≥. "Greater than or equal to", as the suggests, means something is ... | 2021-06-22T19:08:26 | {
"domain": "zong-music.com",
"url": "https://zong-music.com/ha2ten/greater-than-or-equal-to-sign-9b504e",
"openwebmath_score": 0.5518640279769897,
"openwebmath_perplexity": 948.9165942980742,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9621075722839015,
"lm_q2_score": 0.9... |
http://math.stackexchange.com/questions/219329/for-t-in-0-1-is-fracxetxex-1-integrable-over-x-in-0-in/219347 | # For $t\in [ 0, 1 )$ is $\frac{xe^{tx}}{e^{x}-1}$ integrable over $x\in (0 , \infty )$?
For $t\in [ 0, 1 )$ is $$\frac{xe^{tx}}{e^{x}-1}$$ integrable over $x\in (0 , \infty )$? I.e., $$\int_{0}^{\infty} \frac{xe^{tx}}{e^{x}-1} dx < \infty?$$ How do I show this?
-
As $x\to0$, $x/(e^x-1)$ approaches a finite limit. A... | 2015-05-30T09:16:25 | {
"domain": "stackexchange.com",
"url": "http://math.stackexchange.com/questions/219329/for-t-in-0-1-is-fracxetxex-1-integrable-over-x-in-0-in/219347",
"openwebmath_score": 0.9804616570472717,
"openwebmath_perplexity": 161.082132305399,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_scor... |
https://gmatclub.com/forum/the-price-of-a-consumer-good-increased-by-p-228709.html | GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 17 Jun 2019, 08:03
### 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... | 2019-06-17T15:03:43 | {
"domain": "gmatclub.com",
"url": "https://gmatclub.com/forum/the-price-of-a-consumer-good-increased-by-p-228709.html",
"openwebmath_score": 0.7690556645393372,
"openwebmath_perplexity": 1808.9536375803552,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.9744347905312774,
"lm... |
http://centrallab.msu.ac.th/2f1iaj16/lhcbx.php?aea000=least-square-approximation-of-a-function | The idea is to minimize the norm of the difference between the given function and the approximation. Picture: geometry of a least-squares solution. As a result we should get a formula y=F(x), named the empirical formula (regression equation, function approximation), which allows us to calculate y for x's not present in... | 2022-01-23T08:53:20 | {
"domain": "ac.th",
"url": "http://centrallab.msu.ac.th/2f1iaj16/lhcbx.php?aea000=least-square-approximation-of-a-function",
"openwebmath_score": 0.710901141166687,
"openwebmath_perplexity": 896.7067055485361,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9875683498785867,
... |
https://abigail.github.io/HTML/Perl-Weekly-Challenge/week-108-2.html | Perl Weekly Challenge 108: Bell Numbers
by Abigail
Challenge
Example
• $$B_0$$: 1 as you can only have one partition of zero element set.
• $$B_1$$: 1 as you can only have one partition of one element set $$\{a\}$$.
• $$B_2$$: 2
• $$\{a\}\{b\}$$
• $$\{a,b\}$$
• $$B_3$$: 5
• $$\{a\}\{b\}\{c\}$$
• $$\{a,b\}\{c\}$$
• ... | 2021-06-19T22:09:03 | {
"domain": "github.io",
"url": "https://abigail.github.io/HTML/Perl-Weekly-Challenge/week-108-2.html",
"openwebmath_score": 0.41870564222335815,
"openwebmath_perplexity": 4312.791664273166,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9780517437261226,
"lm_q2_score": 0.916... |
https://forum.math.toronto.edu/index.php?PHPSESSID=e02qs82rtho6ihd22c4oep6c21&action=printpage;topic=259.0 | # Toronto Math Forum
## MAT244-2013S => MAT244 Math--Tests => MidTerm => Topic started by: Victor Ivrii on March 06, 2013, 09:08:26 PM
Title: MT Problem 3
Post by: Victor Ivrii on March 06, 2013, 09:08:26 PM
Find a particular solution of equation
\begin{equation*}
t^2 y''-2t y' +2y=t^3 e^t.
\end{equation*}
[BONUS] E... | 2022-06-28T17:47:55 | {
"domain": "toronto.edu",
"url": "https://forum.math.toronto.edu/index.php?PHPSESSID=e02qs82rtho6ihd22c4oep6c21&action=printpage;topic=259.0",
"openwebmath_score": 0.7391995191574097,
"openwebmath_perplexity": 1912.7939147305165,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.... |
https://math.stackexchange.com/questions/2720043/null-space-and-kernel-of-matrix-representation | # Null space and kernel of matrix representation
Let $P_3(\mathbb{C})$ be the complex vector space of complex polynomials of degree $2$ or less. Let $\alpha,\beta\in\mathbb{C}, \alpha\neq\beta$. Consider the function $L:P_3(\mathbb{C}) \mapsto \mathbb{C}^2$ given by
$$L(p)=\begin{bmatrix} p(\alpha) \\ p(\beta)\\ \end... | 2019-09-15T20:12:01 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/2720043/null-space-and-kernel-of-matrix-representation",
"openwebmath_score": 0.9005959630012512,
"openwebmath_perplexity": 97.26763139394704,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.970687... |
https://www.physicsforums.com/threads/antiderivative-of-1-x.841263/ | # Antiderivative of 1/x
1. Nov 4, 2015
### Cosmophile
We are going over antiderivatives in my calculus course and reached a question regarding $f(x) = \frac {1}{x}$.
My instructor went on to say that $\int \frac {1}{x}dx = \ln |x| + C$. This makes sense to me, but only to a certain point. For $f(x) = \frac {1}{x}$,... | 2018-02-20T00:06:44 | {
"domain": "physicsforums.com",
"url": "https://www.physicsforums.com/threads/antiderivative-of-1-x.841263/",
"openwebmath_score": 0.9127521514892578,
"openwebmath_perplexity": 344.04818064506895,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.981735721648143,
"lm_q2_score":... |
http://mathhelpforum.com/trigonometry/88387-bearings-question-trig.html | # Thread: Bearings question with trig.
1. ## Bearings question with trig.
Hey Im really not sure how to do bearings at all.
For homework i have this question:
A ship leaves at port A and travels for 30km on bearing of 120degrees
It then changes course and travels for 50km on bearing of 080degrees arriving at port B.... | 2017-02-25T19:42:25 | {
"domain": "mathhelpforum.com",
"url": "http://mathhelpforum.com/trigonometry/88387-bearings-question-trig.html",
"openwebmath_score": 0.8599735498428345,
"openwebmath_perplexity": 2792.661359215432,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9830850832642353,
"lm_q2_sco... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.