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url string | text string | date timestamp[s] | meta dict |
|---|---|---|---|
https://www.physicsforums.com/threads/need-to-determine-function-based-on-graph.776914/ | # Need to determine function based on graph
1. Oct 18, 2014
### TheExibo
There is this graph: http://i.imgur.com/BdwhN3b.jpg where the equation of the function must be determined. Down below is some thinking I've done, where I've found that the oblique asymptote is -0.5x+2, and the v-asymptote=6. I know how to solve... | 2017-10-20T09:02:52 | {
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"lm_q1_score": 0.97283076925202... |
https://math.stackexchange.com/questions/128538/does-the-intersection-of-two-finite-index-subgroups-have-finite-index | # Does the intersection of two finite index subgroups have finite index?
Let $(G,*)$ be a group and $H,K$ be two subgroups of $G$ of finite index (the number of left cosets of $H$ and $K$ in $G$). Is the set $H\cap K$ also a subgroup of finite index? I feel like need that $[G\colon(H\cap K)]$ is a divisor of $[G\colon... | 2021-01-18T05:20:16 | {
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"openwebmath_perplexity": 115.98408916788723,
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"lm_label": "1. YES\n2. YES",
... |
https://math.stackexchange.com/questions/397035/how-to-graph-the-equation-y-frac-x-2x1 | # How to graph the equation: $y=\frac {x-2}{x+1}$?
the title says it all. I'm pretty sure this is a hyperbola, but is there an alternative way of doing this besides a table of values?
"Graph the equation $y=\frac {x-2}{x+1}$"
I know that $x$ cannot equal $-1$ but I'm not sure how to carry on from there.
Any help wo... | 2019-06-17T12:33:07 | {
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.97443479053127... |
https://math.stackexchange.com/questions/2066004/big-o-notation-is-element-of-or-is-equal?noredirect=1 | # Big O Notation “is element of” or “is equal”
People are always having trouble with "big $O$" notation when it comes to how to write it down in a mathematically correct way.
Example: you have two functions $n\mapsto f(n) = n^3$ and $n\mapsto g(n) = n^2$
Obviously $f$ is asymptotically faster than $g$. Is it $f(n) =... | 2019-10-15T17:35:27 | {
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"url": "https://math.stackexchange.com/questions/2066004/big-o-notation-is-element-of-or-is-equal?noredirect=1",
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"openwebmath_perplexity": 284.42606210262255,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": ... |
https://math.stackexchange.com/questions/2663663/finding-the-sin-inverse | # Finding the sin inverse
Well, so I was finding the value of $\sin 15^{\circ}$. I used the identity $2 \sin x \cos x = \sin 2x$. So solving the quadratic equation and picking the right values simply gave me:
$$\sin 15^{\circ} = \frac {\sqrt {2 - \sqrt {3}}} {2}$$
That was pretty much simple. But I thought what if I... | 2019-10-23T01:10:22 | {
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"url": "https://math.stackexchange.com/questions/2663663/finding-the-sin-inverse",
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9777138190064204,
"lm_q2_sc... |
http://physics.stackexchange.com/questions/78696/angle-needed-for-object-a-to-intercept-with-object-b | # Angle needed for object A to intercept with object B
Object B is 15 degrees East of North at a distance of 20km/h. Object B is moving at an average speed of 30km/h in the direction 40 degrees East of North. If object A is capable of moving at 100km/h, at what angle does it need to move to intercept object B?
I've t... | 2016-07-02T03:48:43 | {
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0... |
https://mathhelpboards.com/threads/captainblacks-occasional-problem-3.857/ | # CaptainBlacks Occasional Problem #3
#### CaptainBlack
##### Well-known member
Prove that the polynomials:
$P_n(x)=x^{2n}-2x^{2n-1}+3x^{2n-2}- ... -2nx + (2n+1),\ \ \ (n=1,2...)$
have no real roots.
CB
Last edited:
#### Opalg
##### MHB Oldtimer
Staff member
Still no replies to this one? I started by graphing $... | 2020-09-19T05:41:56 | {
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"lm_q2_... |
https://math.stackexchange.com/questions/1471987/drawing-without-replacement-prob-for-an-ace-followed-by-an-ace | Drawing without replacement - prob. for an Ace followed by an Ace?
Given a standard 52-cards deck:
You are extracting cards from the deck without replacement, until you get an "Ace" for the first time. What is the probability that the next card will be "Ace" too?
I've already seen the following Q&A: Probability of dr... | 2019-10-23T20:58:45 | {
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"openwebmath_perplexity": 498.98088716848855,
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"lm_label": "1. YES\n2. YES",
"lm_q1_... |
http://math.stackexchange.com/questions/157610/is-there-a-differential-limit | Is there a differential limit?
I'm wondering if there's such a concept as a "differential limit". Let me give an example because my nomenclature is my own and unofficial, but hopefully indicative of the concept.
For some function f(x), there may exist a derivative of that function f'(x) which we call a first order di... | 2016-07-27T03:51:55 | {
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"url": "http://math.stackexchange.com/questions/157610/is-there-a-differential-limit",
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"lm_label": "1. YES\n2. YES",
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"lm_q... |
https://math.stackexchange.com/questions/3488138/evaluating-int-sqrt-frac5-xx-2-dx-with-two-different-methods-and-gett | # Evaluating $\int \sqrt{\frac{5-x}{x-2}}\,dx$ with two different methods and getting two different results [duplicate]
I tried Evaluating $$\int \sqrt{\dfrac{5-x}{x-2}}dx$$ using two different methods and got two different results.
Getting two different answers when tried using two different methods:-
M-$$1$$:
$$\... | 2021-07-28T04:22:26 | {
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"openwebmath_perplexity": 479.26202810304346,
"lm_name": "Qwen/Qwen-72B",
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... |
https://www.gradesaver.com/textbooks/math/calculus/calculus-early-transcendentals-8th-edition/chapter-2-section-2-2-the-limit-of-a-function-2-2-exercises-page-92/1 | ## Calculus: Early Transcendentals 8th Edition
As $x$ approaches 2, $f(x)$ approaches 5. Yes, it is possible for this to be true and for $f(2)=3$.
It means that $f(x)$ becomes arbitrarily close to $3$ as we take $x$ close enough to $2$, but $x\ne2$. It is possible for $f(2)$ to equal $3$ because the limit only relies ... | 2018-10-20T16:42:43 | {
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"openwebmath_score": 0.9688237309455872,
"openwebmath_perplexity": 54.01622114607981,
"lm_name": "Qwen/Qwe... |
http://mathhelpforum.com/calculus/125089-piecewise-function-problem.html | # Math Help - Piecewise Function problem
1. ## Piecewise Function problem
Let f(x) =
(0) if x< 0
(x) if 0 <= x <= 1
(2 - x) if 1 < x <= 2
(0) if x > 2
and g(x) = [integrate] f(t)dt on [0, x]
i) Find an expression for g(x) similar to the one for f(x).
ii) Where is f differentiable? Where is g differentiable?
I'm ... | 2015-02-01T23:13:09 | {
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"lm_label": "1. YES\n2. YES\n\n",
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"lm_q2... |
https://math.stackexchange.com/questions/1404431/a-proof-in-elementary-set-theory | # A Proof in Elementary Set Theory
I apologize in advance for any lack of clarity in my mathematical symbols; I'm beginning to learn how to use this site.
I'm working through "Introduction to Analysis" by Rosenlicht and he presents an exercise
Prove that if $X\subset S$, $Y\subset S$, then $\complement X\cap\complem... | 2019-08-23T11:46:13 | {
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"openwebmath_perplexity": 532.8436017226247,
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9845754504074421,
... |
http://math.stackexchange.com/questions/163070/the-most-efficient-way-to-tile-a-rectangle-with-squares | # The most efficient way to tile a rectangle with squares?
I was writing up a description of the Euclidean algorithm for a set of course notes and was playing around with one geometric intuition for the algorithm that involves tiling an $m \times n$ rectangle with progressively smaller squares, as seen in this animati... | 2016-05-26T12:56:10 | {
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"openwebmath_score": 0.744117021560669,
"openwebmath_perplexity": 364.88121222011256,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0... |
http://gmatclub.com/forum/number-properties-tips-and-hints-174996.html | Find all School-related info fast with the new School-Specific MBA Forum
It is currently 01 Jul 2015, 17:50
### 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.
C... | 2015-07-02T01:50:19 | {
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"lm_q1_score": 0.9579122720843812,
"lm_q2_score": ... |
http://math.stackexchange.com/questions/114453/solve-xy-yx/114476 | # Solve $x^y \, = \, y^x$ [duplicate]
Possible Duplicate:
$x^y = y^x$ for integers $x$ and $y$
I obtained a question asking for how to solve $\large x^y = y^x$. The given restraints was that $x$ and $y$ were both positive integers. By a bit of error an trial we quickly see that $x=2$ and $y=4$ is one solution.
• My ... | 2014-12-18T09:01:00 | {
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https://math.stackexchange.com/questions/3331450/points-in-bbb-r2-that-can-be-reached-via-steps-which-are-1-5-of-a-unit-c | # Points in $\Bbb {R}^2$ that can be reached via steps which are $1/5$ of a unit circle.
I was playing around with this demo of Project Euler Problem 208 which allows you to take steps which are "left" or "right" arcs of $$1/5$$ of a unit circle.
Here's an example walk, which starts at the blue dot pointing verticall... | 2021-01-23T04:21:46 | {
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"openwebmath_score": 0.9381072521209717,
"openwebmath_perplexity": 523.3560065751179,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",... |
http://cqcourseworklruw.vatsa.info/an-analysis-of-the-buffons-needle-a-method-for-the-estimation-of-the-value-of-pi.html | # An analysis of the buffons needle a method for the estimation of the value of pi
Buffon 's needle problem if vou drop any needle, short or long, then the expected number of crossings will be where pi is the probability that the needle will come to lie with exactly one. Buffon's needle refers to a simple monte carlo ... | 2018-10-22T01:30:23 | {
"domain": "vatsa.info",
"url": "http://cqcourseworklruw.vatsa.info/an-analysis-of-the-buffons-needle-a-method-for-the-estimation-of-the-value-of-pi.html",
"openwebmath_score": 0.7109445333480835,
"openwebmath_perplexity": 1603.7392917532973,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_... |
https://math.stackexchange.com/questions/1338411/why-doesnt-using-the-approximation-sin-x-approx-x-near-0-work-for-computin | # Why doesn't using the approximation $\sin x\approx x$ near $0$ work for computing this limit?
The limit is $$\lim_{x\to0}\left(\frac{1}{\sin^2x}-\frac{1}{x^2}\right)$$ which I'm aware can be rearranged to obtain the indeterminate $\dfrac{0}{0}$, but in an attempt to avoid L'Hopital's rule (just for fun) I tried usin... | 2019-11-19T22:54:15 | {
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"openwebmath_score": 0.9807103872299194,
"openwebmath_perplexity": 355.4858753777299,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES... |
https://mathematica.stackexchange.com/questions/133098/derivative-of-the-inverse-of-a-certain-variable | # Derivative of the inverse of a certain variable
I want to take a derivative of the inverse of a certain variable, e.g., being the function:
f[x_, a_, T_] := (a x^3)/T
I want the derivative with respect to $1/T$:
$$\frac{\partial f}{\partial \left(\frac{1}{T}\right)}=ax^3$$
It doesn't work with:
D[f[x, a, T], 1... | 2020-03-29T01:01:13 | {
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"openwebmath_perplexity": 1978.1912545975795,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": ... |
https://mathhelpboards.com/threads/2-1-5-find-the-general-solution-of-the-given-differential-equation.24499/ | # [SOLVED]2.1.5 Find the general solution of the given differential equation
#### karush
##### Well-known member
Find the general solution of the given differential equation
$\displaystyle y^\prime - 2y =3te^t, \\$
Obtain $u(t)$
$\displaystyle u(t)=\exp\int -2 \, dx =e^{-2t} \\$
Multiply thru with $e^{-2t}$
$e^{-2t}... | 2021-06-19T09:23:37 | {
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"lm_label": "1. YES\n2. YES\n\n",
"lm_... |
http://wjxu.grafikohnegrenzen.de/differential-equation-eigenvalue-problem.html | ## Differential Equation Eigenvalue Problem
Apply matrix techniques to solve systems of linear ordinary differential equations with constant coefficients. n first order equations that we can solve separately. Find the eigenvalues and Eigen functions for the boundary value problem, x^{2}{y} for Teachers for Schools for... | 2020-02-26T17:36:38 | {
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"openwebmath_perplexity": 441.5730259174707,
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9956005869677995,
... |
https://nbhmcsirgate.theindianmathematician.com/2020/04/csir-june-2011-part-c-question-63.html | ### CSIR JUNE 2011 PART C QUESTION 63 SOLUTION (When $d(x,y) = |f(x) - f(y)|$ defines a metric)
Which of the following is/are metric on $\Bbb R$?
1)$d(x,y) = min\{x,y\}$,
2)$d(x,y) = |x-y|$,
3) $d(x,y) = |x^2 - y^2|$,
4)$d(x,y) = |x^3 - y^3|$.
Solution
option (1): NO. $d(-1,0) = -1$ which is negative.
option (2): YES... | 2022-05-27T03:48:00 | {
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https://math.stackexchange.com/questions/2816791/how-many-ways-are-there-to-choose-strings-of-length-3-from-s-1-2-3-4-for | # How many ways are there to choose strings of length $3$ from $S=\{1,2,3,4\}$ for $3$ people if each each digit from $S$ has to appear at least once?
Let $S=\{1,2,3,4\}$. There're three persons: Jack, Mary, Ann which choose $3$ digits from $S$ to compose a string of $3$ digits.
For example, a) Jack chose $112$, Mary... | 2020-09-24T15:55:06 | {
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"openwebmath_perplexity": 127.62016030968104,
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"lm_label": "1. YES\n2. YES"... |
https://math.stackexchange.com/questions/1767559/proving-x-is-a-given-quotient-of-logarithms | # Proving $x$ is a given quotient of logarithms
I'm practicing some questions on logarithms at the moment in order that I'm up to speed with the problem solving aspect before I embark on my PHD in chemical engineering at Boston college next year.
I've been studying the laws of logarithms and what I am to do when it i... | 2019-06-18T12:59:48 | {
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"lm_q1_score": 0.9861513869... |
https://math.stackexchange.com/questions/4254023/largest-positive-integer-n-for-which-n3100-is-divisible-by-n10/4254343#4254343 | # Largest positive integer $n$ for which $n^3+100$ is divisible by $n+10$
Problem: What is that largest positive integer $$n$$ for which $$n^3+100$$ is divisible by $$n+10$$?
The solution from Art of Problem Solving: If $$n+10 \mid n^3+100$$, $$\gcd(n^3+100,n+10)=n+10$$. Using the Euclidean algorithm, we have $$\gcd(... | 2021-12-08T13:18:29 | {
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"openwebmath_perplexity": 257.52636264340657,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2... |
http://www.askamathematician.com/2011/05/q-is-0-9999-repeating-really-equal-to-1/ | # Q: Is 0.9999… repeating really equal to 1?
Mathematician: Usually, in math, there are lots of ways of writing the same thing. For instance:
$\frac{1}{4}$ = $0.25$ = $\frac{1}{\frac{1}{1/4}}$ = $\frac{73}{292}$ = $(\int_{0}^{\infty} \frac{\sin(x)}{\pi x} dx)^2$
As it so happens, 0.9999… repeating is just another wa... | 2017-01-18T18:11:49 | {
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.993611678144426,... |
http://krizak.com/7ep86ie/g58j054.php?cd1127=vector-derivative-rules | Answer: As with the dot product, this will follow from the usual product rule in single variable calculus. 4 cos(4x + 2) And that is the derivative of your original function. ax, axp ax, In finding the derivative of the cross product of two vectors $\frac{d}{dt}[\vec{u(t)}\times \vec{v(t)}]$, is it possible to find the... | 2021-08-02T08:57:37 | {
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http://mathhelpforum.com/calculus/15750-evaluate-line-integral.html | # Thread: Evaluate the line integral
1. ## Evaluate the line integral
Hello,
please try to solve this question.
Thanks
2. $\oint_C x^3 dx - 2xy dy = \iint_D \left( \frac{\partial (-2xy)}{\partial x} - \frac{\partial x^3}{\partial y} \right) \ dA = -2\iint_D y \ dA =$ $- 2\int_0^2 \int_0^{2-x} y \ dy \ dx$
3. Evalua... | 2013-12-19T17:37:46 | {
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https://math.stackexchange.com/questions/1837763/integration-with-limits-and-options | # Integration with limits and options.
I found this exercise in an old exam but I don't know how to attack it because is a limit of an integration and I don't know if the limit affects the process of the integral or it makes it easier. The exercise is this:
The value of the limit $$\lim_{h\to 0}\frac{1}{h}\int^{2+h}_... | 2019-08-25T12:23:37 | {
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http://semesta.lviv.ua/0zsekb/adjacent-angles-which-are-not-in-a-linear-pair-58eba1 | But they are not a linear pair because they are not connected, and they do not share a common side. The line through points A, B and C is a straight line. Since the non-adjacent sides of a linear pair form a line, a linear pair of angles is always supplementary. Linear Pair: Definition, Theorem & Example ... we can say... | 2021-05-06T13:42:27 | {
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https://mathematica.stackexchange.com/questions/230459/exact-division-and-geometric-sequences | # Exact division and geometric sequences
I imagine this problem has a name that I don't know; it's probably some sort of exact division problem. Here goes: imagine you have to divide 4 cookies among 11 people. Divide the cookies equally among the 11 people with the constraint that you are a World Champion at halving c... | 2020-10-23T02:59:21 | {
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http://techiemathteacher.com/2014/10/29/hard-algebraic-expansion/ | # The Powers of Sum: Solving Hard Problem Algebraically
One of the active members of a Facebook group called Elite Math Circle (EMC) posted a question that seems interesting. Same question I enc0unter when I was actively solving problems at Brilliant.
It was posted by Russelle Guadalupe, an elite member of Philippine... | 2017-06-29T03:44:05 | {
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https://cs.stackexchange.com/questions/136636/median-of-medians-confusion-the-approximate-median-part | Median of medians confusion — the “approximate” median part
I'm struggling with the median of medians algorithm, and I think it's perhaps more of a semantics thing rather than a technical thing. I've always thought the median of medians algorithm as finding an approximate median $$p$$ such that $$p$$ is within $$20\%$... | 2021-05-17T12:37:13 | {
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https://math.stackexchange.com/questions/2122264/whats-the-probability-of-the-target-being-destroyed | What's the probability of the target being destroyed?
Target gets hit by three missiles.
The probability of hitting the target with the
- First missile is 0.4;
- Second missile is 0.5;
- Third missile is 0.7;
The target has a probability of 0.2 getting destroyed with one missile, 0.6 by two missiles and for sure (1)... | 2023-03-31T05:45:06 | {
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https://math.stackexchange.com/questions/2713547/how-does-munkres-prove-that-lower-limit-topology-is-finer-than-the-standard-topo | # How does Munkres prove that lower limit topology is finer than the standard topology on $\mathbb{R}$
The proof in question (from the book "Topology" by Munkres):
Let $\mathcal T$ and $\mathcal T_\mathscr{l}$ be the standard and lower limit topology on $\mathbb R$ respectively. Given a basis element $(a,b)$ for $\ma... | 2019-12-07T14:49:09 | {
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https://stats.stackexchange.com/questions/282455/two-questions-involving-bayes-theorem | # Two questions involving Bayes Theorem
You draw two balls from one of three possible large urns, labelled A, B, and C. Urn A has 1/2 blue balls, 1/3 green balls, and 1/6 red balls. Urn B has 1/6 blue balls, 1/2 green balls, and 1/3 red balls. Urn C has 1/3 blue balls, 1/6 green balls, and 1/2 red balls. With no prior... | 2019-11-14T00:58:06 | {
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http://slideplayer.com/slide/229581/ | # Partial Orderings Section 8.6.
## Presentation on theme: "Partial Orderings Section 8.6."— Presentation transcript:
Partial Orderings Section 8.6
Introduction A relation R on a set S is called a partial ordering or partial order if it is: reflexive antisymmetric transitive A set S together with a partial ordering ... | 2019-02-22T06:25:20 | {
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http://math.stackexchange.com/questions/50919/calculate-the-sum-of-the-infinite-series-sum-n-0-infty-fracn4n | # Calculate the sum of the infinite series $\sum_{n=0}^{\infty} \frac{n}{4^n}$
A previous problem had us solving $\sum_{n=0}^{\infty} \frac{1}{4^n}$ which I calculated to be $\frac{4}{3}$ using a bit of mathematical manipulation.
Wonderful. Thank you for all the prompt responses. Could anyone suggest an alternate tec... | 2015-05-27T20:18:12 | {
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https://ece.uwaterloo.ca/~ece050/149u/ | Lesson 149u: Sieve of Eratosthenes
Suppose you wanted to find all prime numbers less than or equal to a given number $N$. The easiest way to do this is to create an array that can hold the integers from $1$ to $N$. We will initialize the array so that array[k] == k. If we ever determine that a number k is not prime, w... | 2022-08-15T14:31:55 | {
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https://puzzling.stackexchange.com/questions/23147/visualise-whirled-peas | # Visualise Whirled Peas
My eldest came home with some interesting maths homework.
We have three bowls containing peas.
Distribute the peas evenly across the bowls, by moving peas from one bowl to another. The only move allowed, is doubling the amount of peas in one bowl by taking them from one other bowl.
For exam... | 2021-01-26T15:22:37 | {
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https://www.jiskha.com/questions/1561900/Suppose-A-is-directly-proportional-to-B-B-is-inversely-proportional-to-C-and-C-is | # Math Ratios
Suppose A is directly proportional to B, B is inversely proportional to C and C is inversely proportional to D. Determine whether A and D are directly proportional, inversely proportional, or neither.
1. C is inversely proportional to D ---> C = p/D
B is inversely proportional to C ---> B = qC
so B = q/... | 2018-08-20T21:13:30 | {
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https://math.stackexchange.com/questions/2559445/let-x-n-be-a-cauchy-sequence-of-rational-numbers-define-a-new-sequence | # Let $\{x_n\}$ be a Cauchy sequence of rational numbers. Define a new sequence $\{y_n\}$ by $y_n = (x_n)(x_{n+1})$. Show that $\{y_n\}$ is a CS.
What I am thinking so far is following:
Construct another sequence $\{b_n\}$ such that $b_1=x_2, b_2=x_3, \ldots, b_n=x_{n+1}.$ Since $\{x_n\}$ is a Cauchy sequence, $\{b_n... | 2019-06-24T22:21:00 | {
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https://math.stackexchange.com/questions/2332842/proof-by-mathematical-induction-difficulties | # Proof by mathematical induction, difficulties
Usually, proofs by mathematical induction are not that difficult (at least the ones I encountered so far in my mathematical journey), but I am stuck with this one... Spent at least 2-3 hours on it. I just can't see it...
$$\sum_{i=0}^n \frac{1}{2^i}\tan\left(\frac{x}{2^... | 2021-09-22T05:34:48 | {
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https://math.stackexchange.com/questions/729315/sum-frac11-times2-frac11-times3-frac12-times5-frac13-times8/729339 | # Sum $\frac{1}{1\times2}+\frac{1}{1\times3}+\frac{1}{2\times5}+\frac{1}{3\times8}+\cdots$
If $f_n$ is the Fibonacci series, with $1,1,2,3,5,8,\ldots$ prove that
$$\sum_{i=2}^\infty\frac{1}{f_{i-1}\cdot f_{i+1}} = 1$$
So my idea was to try to convert this series into a telescoping sum somehow, because otherwise I ca... | 2021-05-13T02:25:28 | {
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https://math.stackexchange.com/questions/2702249/pigeon-hole-principle-proof-writing | # Pigeon hole principle proof writing
I'm currentely discussing pigeon hole principle (simple and generalised) in class. However, when solving problems, I get the idea, but I never know the proper way to write it, I always feel like I'm either writing too much or not enough. Here is an example of a very simple problem... | 2019-10-14T03:40:59 | {
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https://math.stackexchange.com/questions/1926470/intuition-about-infinite-sums | I am particularly concerned about these two sums: $$\sum_{x=\color{red}0}^\infty \frac{1}{2^x} = 1 + \frac{1}{2} + \frac{1}{4} ... = 2$$
and
$$\sum_{x=1}^\infty \frac{1}{x} = 1 + \frac{1}{2} + \frac{1}{3} ... = \infty$$
Now, I know and I understand the proofs that say the first sum converges to two and the second on... | 2019-11-15T17:48:40 | {
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https://heaveyduty.com/docs/7p3l3.php?a930b0=unit-of-acceleration | Select Page
In each case, the acceleration of the object is in the positive direction.
α Since acceleration is a vector quantity, it has a direction associated with it. Likewise, the integral of the jerk function j(t), the derivative of the acceleration function, can be used to find acceleration at a certain time: Ac... | 2022-01-16T10:39:56 | {
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http://mathhelpforum.com/algebra/281216-need-equation-line-intersecting-two-points-involving-y-x-x-1-a.html | # Thread: Need Equation for Line Intersecting Two Points Involving y = x/(|x|+1)
1. ## Need Equation for Line Intersecting Two Points Involving y = x/(|x|+1)
So I'm trying to solve for an equation that produces a line that intersects two specific points and is shaped approximately like this:
This equation is express... | 2018-09-25T03:03:48 | {
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https://math.stackexchange.com/questions/2985431/a-cauchy-sequence-x-n-with-infinitely-many-n-such-that-x-n-c | # A Cauchy sequence $\{x_n\}$ with infinitely many $n$ such that $x_n = c$.
Is the following argument correct?
Proposition. If $$\{x_n\}$$ is Cauchy sequence such that $$x_n = c$$ for infinitely many $$n$$, then $$\lim_{n\to\infty}x_n = c$$.
Proof. Let $$\epsilon>0$$. Since $$\{x_n\}$$ is a Cauchy sequence, there ex... | 2019-09-19T08:38:38 | {
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https://fundacja-pe.nazwa.pl/ml7v30/circumference-of-an-oval-calculator-684c61 | The Ellipse Circumference Calculator is used to calculate the approximate circumference of an ellipse. Oval Tank Volume Calculator Find the volume of oval tanks in cubic inches and gallons. Note the major and minor axes of your ellipse and find the exponent of both. This calculator converts the area of a circle into an... | 2021-07-30T04:35:54 | {
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https://math.stackexchange.com/questions/65569/uses-of-lim-limits-h-to-0-fracfxh-fx-h2h | # Uses of $\lim \limits_{h\to 0} \frac{f(x+h)-f(x-h)}{2h}$
I have been wondering whether the following limit is being used somehow, as a variation of the derivative:
$$\lim_{h\to 0} \frac{f(x+h)-f(x-h)}{2h} .$$
Edit: I know that this limit is defined in some places where the derivative is not defined, but it gives u... | 2020-10-01T13:48:30 | {
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https://stats.stackexchange.com/questions/318625/why-do-the-leading-eigenvectors-of-a-maximize-texttrdtad/318644 | Why do the leading eigenvectors of $A$ maximize $\text{Tr}(D^TAD)$?
Given a matrix $X\in\mathbb{R}^{m\times n}$, I am trying to maximize $\text{Tr}(D^TX^TXD)$ over $D\in\mathbb{R}^{n\times l}$ ($n<l$) subject to $D^TD=I_l$, where $\text{Tr}$ denotes the trace, and $I_l$ denotes the identity matrix of size $l$.
More s... | 2019-10-19T05:40:31 | {
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https://forum.math.toronto.edu/index.php?PHPSESSID=dfjc6ko9j5jd8fkgh5p05s7o04&action=printpage;topic=2264.0 | Toronto Math Forum
MAT244--2019F => MAT244--Lectures & Home Assignments => Chapter 9 => Topic started by: Richard Qiu on November 18, 2019, 02:19:33 PM
Title: differences between proper and improper nodes
Post by: Richard Qiu on November 18, 2019, 02:19:33 PM
Hello guys, could anyone help me to explain the difference... | 2021-11-29T03:48:26 | {
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https://math.stackexchange.com/questions/1188243/8-athletes-run-a-race-problem | # 8 Athletes run a race problem
8 Athletes run a race and no two athletes finish exactly together. What is the number of different possible results for the first, second and third positions?
I said that the answer is simply 8 choose 3, which gives an answer of 56. When I checked the memo, it said the answer was 336. ... | 2021-12-08T23:44:51 | {
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"lm_q1_score": 0.9875683476832692,
"lm_q2_s... |
https://math.stackexchange.com/questions/2399621/if-n-is-the-integer-2433527-find-the-smallest-positive-integer-m-such-t | # If $N$ is the integer $2^43^35^27$ find the smallest positive integer $m$ such that $x^m \equiv 1 \mod N$ for all integers coprime to $N$
If $N$ is the integer $2^43^35^27$ find the smallest positive integer $m$ such that $x^m \equiv 1 \mod N$ for all integers coprime to $N$.
I understand that I can do this for ind... | 2019-11-13T04:57:25 | {
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http://www.cataclysmuo.com/q5656e/how-to-prove-a-rhombus-in-coordinate-geometry-56992b | by misbrooks. Find the coordinates of C and D, such that ABCD is a rhombus. (ii) In any square the length of diagonal will be equal, to prove the given shape is not square but a rhombus, we need to prove that length of diagonal are not equal. Hi, in C1 coordinate geometry questions relating to shapes often come up and ... | 2021-06-13T06:22:52 | {
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https://forum.math.toronto.edu/index.php?PHPSESSID=dftck8b0bjhducb5knhnfofef3&action=printpage;topic=1510.0 | # Toronto Math Forum
## MAT244--2018F => MAT244--Tests => Quiz-6 => Topic started by: Victor Ivrii on November 17, 2018, 04:01:01 PM
Title: Q6 TUT 5102
Post by: Victor Ivrii on November 17, 2018, 04:01:01 PM
The coefficient matrix contains a parameter $\alpha$.
(a) Determine the eigenvalues in terms of $\alpha$.
(b)... | 2022-06-30T00:43:31 | {
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https://math.stackexchange.com/questions/1244191/minimum-volume-of-a-circular-right-cone-with-a-sphere-inscribed-in-it | # Minimum Volume of a circular, right cone, with a sphere inscribed in it.
Question: A sphere of radius $r$ is inscribed in a circular, right cone.
What is the minimum radius and height of the circular cone? (Thus, volume)
Because the answer would specifically be proportional to the radius given $r$,
I have set the... | 2022-08-20T05:07:41 | {
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https://tex.stackexchange.com/questions/395107/difference-between-symbols-for-absolute-value | # Difference between symbols for absolute value?
I know all of the following are used for showing the absolute value:
• $\lvert x \rvert$
• $| x |$
• $\mid x \mid$
I myself think that there is another one \abs; but I can't use this last one.
What is the difference between them?
• Possible Duplicate: Absolute Value... | 2022-05-16T18:28:28 | {
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https://math.stackexchange.com/questions/3254239/minimum-of-a-trigonometric-function-involving-absolute-value | # Minimum of a trigonometric function involving absolute value
Given $$f(x) = | \sin( | x | ) |$$, I am told to found the local and global minimum and maximum of $$f$$ (If they exist).
Simply from sketching the graph of $$f$$ I get that the function maximizes periodically for every $$x = k \frac{\pi}{2}$$ with $$k$$ ... | 2019-07-21T00:17:08 | {
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https://gateoverflow.in/846/gate-cse-2002-question-2-16 | 8,554 views
Four fair coins are tossed simultaneously. The probability that at least one head and one tail turn up is
1. $\frac{1}{16}$
2. $\frac{1}{8}$
3. $\frac{7}{8}$
4. $\frac{15}{16}$
reshown
Total outcomes - 24 (Because 4 coins are tossed simultaneously and each coin has 2 outcomes-either head or tail)
Now o... | 2022-09-28T03:54:13 | {
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http://arcivasto.it/zmhn/exponential-fourier-series-of-sawtooth-wave.html | # Exponential Fourier Series Of Sawtooth Wave
You can also find the Fourier coefficients using the approach you showed, and the integral is c_n = 1/(2pi)∫f(t) exp(-jnt) dt, integrated from -pi to pi. Another term the Fourier series,. We will now derive the complex Fourier series equa-tions, as shown above, from the si... | 2020-08-15T16:32:30 | {
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http://mathhelpforum.com/calculus/88310-question-about-differentiability.html | # Math Help - Question about differentiability
Cusps, which are not differentiable, often exist within absolute value functions and at certain points of piecewise functions.
My question is... can piecewise functions be differentiable throughout? Well, you know, suppose two functions are connected to each other in a s... | 2015-07-01T06:46:32 | {
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https://math.stackexchange.com/questions/283706/classify-the-singularities-of-the-function/283735 | # Classify the singularities of the function
$$f(z)=\frac{z^3+1}{z^2(z+1)}$$
has singularities $z=0, z=-1$ right?
How can I determine the type of singularity of this points?
Classifications:
1.)Removable pole (Then $f(z_0)$ is bounded, $f(z)$ has a limit if $z \to \infty$
2.) Pole of order $m \implies |f(z)|\to \... | 2019-12-07T22:23:25 | {
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"lm_q1_score": 0.9643... |
https://www.physicsforums.com/threads/question-on-jacobian-determinant.657469/ | # Question on Jacobian determinant
1. Dec 7, 2012
### mnb96
Hello,
it is true that linear transformations have constant Jacobian determinant.
Is the converse true? That is, if a transformation has constant Jacobian determinant, then is it necessarily linear?
2. Dec 7, 2012
### Vargo
Hello,
Yes, linear transform... | 2018-02-22T13:14:55 | {
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"l... |
https://mathoverflow.net/questions/9484/number-of-permutations-with-a-specified-number-of-fixed-points | # Number of permutations with a specified number of fixed points
Let $$F(k,n)$$ be the number of permutations of an n-element set that fix exactly $$k$$ elements.
We know:
1. $$F(n,n) = 1$$
2. $$F(n-1,n) = 0$$
3. $$F(n-2,n) = \binom {n} {2}$$
...
4. $$F(0,n) = n! \cdot \sum_{k=0}^n \frac {(-1)^k}{k!}$$ (the subf... | 2021-04-12T13:31:24 | {
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https://brilliant.org/discussions/thread/1-3/ | # #1
How many positive integers less than $$1000$$ have the property that the sum of the digits of each such number is divisible by $$7$$ and the number itself is divisible by $$3$$?
Note by Vilakshan Gupta
8 months ago
MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bu... | 2018-04-20T01:10:39 | {
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https://math.stackexchange.com/questions/3959757/visual-intuition-for-the-definition-of-asymptotically-equivalent | # Visual intuition for the definition of "asymptotically equivalent"
I'm trying to intuitively grasp the following definition:
The real-valued functions $$f$$ and $$g$$ are asymptotically equivalent as $$x \to \infty$$ if $$\lim_{x \to \infty} \dfrac{f(x)}{g(x)}=1.$$ We write this as $$f \sim g$$.
My question is: ho... | 2021-10-28T06:22:09 | {
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https://quant.stackexchange.com/questions/30362/how-to-perform-monte-carlo-simulations-to-price-asian-options/32574 | # How to perform Monte-Carlo simulations to price Asian options?
If I wish to price a fixed-strike Asian Call option via Monte-Carlo (This has no early-exercise), are my following steps correct?:
1) Simulate random asset prices. (Milstein)
$\ d S(t) = \ rS(t)dt + \sigma S(t) d B(t)$
$\ S_{t+dt} = S_t + r S_tdt + \s... | 2021-05-11T06:28:32 | {
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"openwebmath_perplexity": 636.0036123093302,
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"lm_label": "1. YES\n2. YES",
"lm_q... |
https://math.stackexchange.com/questions/1049808/asymptotic-development-of-a-recurrent-sequence | # Asymptotic development of a recurrent sequence
Let $u_0 = 1$ and $u_{n+1} = \frac{u_n}{1+u_n^2}$ for all $n \in \mathbb{N}$.
I can show that $u_n \sim \frac{1}{\sqrt{2n}}$, but I would like one more term in the asymptotic development, something like $u_n = \frac{1}{\sqrt{2n}}+\frac{\alpha}{n\sqrt{n}} + o\bigl(\frac... | 2021-04-17T05:29:21 | {
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"openwebmath_perplexity": 782.0506571149555,
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9752018... |
https://math.stackexchange.com/questions/2239321/is-0-1-closed-covering-of-interval-0-1/2239492 | # Is [0,1] closed covering of interval [0,1]?
I know it's true in case of open interval and open covering.
Also, in this case what will be Lebesgue number ?
$I = [0, 1]$ is closed as a subset of itself, making $\{ I \}$ a closed covering of $I$.
$B_{\delta}(x) \cap I \subset I$ for each $x \in I$ and each $\delta \i... | 2019-05-20T16:25:16 | {
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"openwebmath_perplexity": 184.51593638823664,
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"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.98737... |
https://math.stackexchange.com/questions/703288/prove-sum-n-1-inftye-sum-k-0n-frac1k-1 | # Prove $\sum_{n=1}^\infty(e-\sum_{k=0}^n\frac1{k!})=1$
This comes from the comments section of this question here, credits Lucian.
The statement is
$$\sum_{n=1}^\infty\left(e-\sum_{k=0}^n\frac1{k!}\right)=1$$
This looks really interesting, so I was wondering if anyone has any ideas/suggestions or even better the w... | 2019-11-20T01:23:25 | {
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"lm_q1_score": 0.987375048489419... |
https://math.stackexchange.com/questions/2325458/does-introducing-new-open-sets-in-topology-improves-its-t-axiom-properties | # Does introducing new open sets in topology improves it's “T”-axiom properties?
This question might be silly, however I'd like to be $100\%$ sure.
Suppose we have some topology $\tau$ on a set $X$ which gives us the $T_i$ space for some $i<6$. It's totally possible to improve topological properties (here I'd like to... | 2020-02-22T17:29:01 | {
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"openwebmath_score": 0.9089652895927429,
"openwebmath_perplexity": 186.0619697190165,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES... |
https://math.stackexchange.com/questions/2711621/alternative-for-calculating-the-nth-of-quadratic-sequence/2711632 | # Alternative for calculating the nth of quadratic sequence
Given the quadratic sequence $$f(n)=1, 7, 19, 37, \cdots$$
To calculate the $f(n)$ for $n\ge1$. $$f(n)=an^2+bn+c$$
We start with the general quadratic function, then sub in for $n:=1,2$ and $3$
$$f(1)=a+b+c$$ $$f(2)=4a+2b+c$$ $$f(3)=9a+3b+c$$
Now solve th... | 2021-03-06T23:55:31 | {
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"openwebmath_perplexity": 475.03723669077266,
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"lm... |
https://math.stackexchange.com/questions/2767678/we-have-two-coins-a-and-b-for-each-toss-of-coin-a-the-probability-of-getting | # We have two coins, A and B. For each toss of coin A, the probability of getting head is 1/2…
We have two coins, A and B. For each toss of coin A, the probability of getting head is 1/2 and for each toss of coin B, the probability of getting Heads is 1/3. All tosses of the same coin are independent. We select a coin ... | 2019-11-15T21:01:51 | {
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"openwebmath_perplexity": 231.28077818769313,
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https://math.stackexchange.com/questions/1696366/let-a-be-the-n-times-n-matrix-with-a-1-in-every-entry-what-are-the-eigenv | # Let $A$ be the $n\times n$ matrix with a $1$ in every entry. What are the eigenvalues of $A$? Is $A$ diagonalizable?
Let $A$ be the $n\times n$ matrix with a $1$ in every entry. What are the eigenvalues of $A$ and a basis for each eigenspace? Is $A$ diagonalizable?
Having some trouble with this one. I tried using t... | 2019-07-24T08:30:50 | {
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https://brilliant.org/discussions/thread/a-tv-show-paradox/ | ×
Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to ... | 2018-01-23T17:46:05 | {
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"lm_q2_score": 0.9032... |
https://www.physicsforums.com/threads/moment-of-inertia-of-a-bar-with-two-spheres.702749/ | # Moment of inertia of a bar with two spheres
1. Jul 24, 2013
### duplaimp
1. The problem statement, all variables and given/known data
A dumbbell has two spheres of radius 0.10m and mass 10kg (each). The two spheres are connected using a bar with length 1.0m and mass 12kg.
What is the moment of inertia of the dumbb... | 2017-10-17T23:20:39 | {
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https://math.stackexchange.com/questions/2723526/how-many-lines-tangent-to-the-graph-of-f-are-parallel-to-the-line | # How many lines tangent to the graph of $f$ are parallel to the line
I'm getting stuck with this problem:
How many lines tangent to the graph of $f(x)=x^3+3x$ are parallel to the line $y=6x+1$?
What I've done is this:
Since we're looking for lines parallel to $y=6x+1$ then obviously we're looking for lines of the ... | 2019-07-23T04:42:43 | {
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"openwebmath_perplexity": 232.2767825204329,
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http://math.stackexchange.com/questions/43226/reason-why-these-two-probabilities-are-equal-picking-balls-in-exact-order-witho | # Reason why these two probabilities are equal (Picking Balls in exact order without Replacement)
I realize the probability of the following two events are equal. I am curious: is there a reason, besides coincidence, that the probabilities are equal?
Suppose there are five balls in a bucket. 3 of the balls are labell... | 2015-04-25T11:18:51 | {
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https://math.stackexchange.com/questions/2411618/partial-fraction-decomposition-with-complex-number-frac1z2-2i | # Partial Fraction Decomposition with Complex Number $\frac{1}{z^2 - 2i}$.
How do I decompose the fraction
$$\dfrac{1}{z^2 - 2i}$$
into partial fractions? I understand how to do partial fraction decomposition with real numbers, but I am unsure of how to do it with complex numbers. I attempted to find examples online... | 2019-08-20T20:57:41 | {
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"openwebmath_perplexity": 248.2326175669736,
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"lm_label": "1. YES\n2. YES",
"lm_q1_s... |
https://math.stackexchange.com/questions/1292836/line-integral-of-a-conservative-field-over-a-squre | # Line integral of a conservative field over a squre
I am trying to evaluate $$\oint _C \frac{-ydx+xdy}{x^2+y^2}$$
clockwise around the square with vertices (−1,−1), (−1,1), (1,1), and (1,−1).
So from the question, $$\vec{F}=<\frac{-y}{x^2+y^2},\frac{x}{x^2+y^2}>$$
I first conducted the gradient test $\frac{\partia... | 2019-12-10T11:11:41 | {
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"lm_q1_score": 0.98... |
http://gmatclub.com/forum/factorial-94770.html?fl=similar | Find all School-related info fast with the new School-Specific MBA Forum
It is currently 27 Jul 2016, 08:43
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... | 2016-07-27T15:43:07 | {
"domain": "gmatclub.com",
"url": "http://gmatclub.com/forum/factorial-94770.html?fl=similar",
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9504109798251322,
"lm_q2_score": 0.91490096427... |
http://mathhelpforum.com/calculus/169622-integration-zero-where-d-2z-dt-2-0-a.html | # Math Help - Integration of Zero where d^2z/dt^2 = 0
1. ## Integration of Zero where d^2z/dt^2 = 0
Suppose a particle of mass 1 kg is initially at (1, 0, 0) and with initial
velocity ˆ−j +2ˆk and moves under a constant force F = −i +2ˆj. Find
the position and velocity for all time.
The Equation of motion ma = F imp... | 2015-03-27T02:34:24 | {
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https://math.stackexchange.com/questions/2582575/intuition-behind-logarithm-change-of-base/2582589 | # Intuition behind logarithm change of base
I try to understand the actual intuition behind the logarithm properties and came across a post on this site that explains the multiplication and thereby also the division properties very nicely:
Suppose you have a table of powers of 2, which looks like this: (after revisio... | 2019-10-15T06:00:40 | {
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.987... |
https://math.stackexchange.com/questions/4458641/what-is-the-probability-that-camilla-and-cameron-are-paired-with-each-other | # What is the probability that Camilla and Cameron are paired with each other?
Textbook problem: A teacher with a math class of 20 students randomly pairs the students to take a test. What is the probability that Camilla and Cameron, two students in the class, are paired with each other?
My answer: 1/190. There is on... | 2022-06-27T15:41:17 | {
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"url": "https://math.stackexchange.com/questions/4458641/what-is-the-probability-that-camilla-and-cameron-are-paired-with-each-other",
"openwebmath_score": 0.763693630695343,
"openwebmath_perplexity": 764.1570150897315,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES... |
https://math.stackexchange.com/questions/2390183/the-number-of-ways-to-divide-5-people-into-three-groups | # The number of ways to divide 5 people into three groups
How many ways can 5 people be divided into three teams where each team must have at least one member?
Assumably they can either be put in one group of 3 people then two groups with 1 person, or two groups with 2 people then one group of 1 person. Hence my answ... | 2020-02-21T07:29:17 | {
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"url": "https://math.stackexchange.com/questions/2390183/the-number-of-ways-to-divide-5-people-into-three-groups",
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"openwebmath_perplexity": 339.0953552120505,
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"lm_label": "1. YES\n2. YES",
"lm_q1_score":... |
https://math.stackexchange.com/questions/3345624/need-help-figure-out-a-fibonacci-related-math-trick/3345755 | # Need help figure out a Fibonacci related math trick
My math teacher used to do a trick where he would have a student write $$2$$ numbers on the board then add the first to the second to create the third then add the second to the third and so on until there were $$10$$ numbers. He would then turn around and add them... | 2020-09-22T10:29:31 | {
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"url": "https://math.stackexchange.com/questions/3345624/need-help-figure-out-a-fibonacci-related-math-trick/3345755",
"openwebmath_score": 0.8956186175346375,
"openwebmath_perplexity": 288.0881938066654,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_sco... |
http://techiemathteacher.com/2014/06/05/facts-about-cyclic-quadrilateral/ | Cyclic quadrilateral is a special kind of quadrilateral inscribed in a circle. Inscribe means that the vertices of quadrilateral are on the circumference of the circle. A square, rectangle, isosceles trapezoid are some of cyclic quadrilaterals. Below are the some facts about this special figure.
1. The opposite angle ... | 2017-05-26T11:04:45 | {
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"openwebmath_perplexity": 1924.2584384620136,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.9908743631497862,
... |
https://www.themathdoctors.org/open-or-closed-intervals-it-depends/ | # Open or Closed Intervals? It Depends
#### (Archive Question of the Week)
Students commonly expect that textbooks all say the same thing (in fact, some think they can ask us about “Theorem 6.2” and we’ll know what they’re talking about!). The reality is that they can even give conflicting definitions, depending on t... | 2021-05-08T16:18:19 | {
"domain": "themathdoctors.org",
"url": "https://www.themathdoctors.org/open-or-closed-intervals-it-depends/",
"openwebmath_score": 0.7156360149383545,
"openwebmath_perplexity": 436.6461464098039,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9908743620718528,
"lm_q2_score"... |
https://math.stackexchange.com/questions/1992464/how-is-irrational-exponent-defined | How is irrational exponent defined?
I am trying to understand the most significant jewel in mathematics - the Euler's formula. But first I try to re-catch my understanding of exponent function.
At the very beginning, exponent is used as a shorthand notion of multiplying several identical number together. For example,... | 2020-11-26T18:27:56 | {
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"url": "https://math.stackexchange.com/questions/1992464/how-is-irrational-exponent-defined",
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"openwebmath_perplexity": 287.95063053383217,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9817357173731319,... |
https://www.jiskha.com/questions/1304448/the-sixth-term-of-gp-is-16-and-the-third-term-is-2-find-the-first-term-and-common-ratio | # Maths
The sixth term of GP is 16 and the third term is 2.Find the first term and common ratio. 6th term =16 3rd term=2 So ar^5=16 and ar^2=2, then divide. So r^3=8, and r^3 =2^3. Therefore r =2 and a=1/2
1. 👍
2. 👎
3. 👁
1. Looks good to me.
1. 👍
2. 👎
2. The formula of the GP
1. 👍
2. 👎
3. Thanks 😊
1. 👍
2.... | 2021-07-29T22:56:30 | {
"domain": "jiskha.com",
"url": "https://www.jiskha.com/questions/1304448/the-sixth-term-of-gp-is-16-and-the-third-term-is-2-find-the-first-term-and-common-ratio",
"openwebmath_score": 0.8588218092918396,
"openwebmath_perplexity": 875.9343107499399,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",... |
https://math.stackexchange.com/questions/2945793/how-to-determine-the-eigen-values-of-ata-where-xta-atx-alpha-xtx-f | How to determine the eigen values of $A^tA$ where $x^tA A^tx=\alpha x^tx ~~~~ \forall x \in \Bbb{R}^m$ holds for some $\alpha$
Problem. A be an $$m\times n$$ matrix of rank $$m$$ with $$n>m$$. If for some nonzero real $$\alpha$$ we have $$x^tA A^tx=\alpha x^tx ~~~~ \forall x \in \Bbb{R}^m$$ then $$A^tA$$ has
1. exact... | 2019-10-19T19:28:29 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/2945793/how-to-determine-the-eigen-values-of-ata-where-xta-atx-alpha-xtx-f",
"openwebmath_score": 0.9322331547737122,
"openwebmath_perplexity": 114.95464641516347,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"l... |
http://math.stackexchange.com/questions/266788/want-to-show-sum-n-2-infty-frac12nn-converges | # Want to show $\sum_{n=2}^{\infty} \frac{1}{2^{n}*n}$ converges
Want to show $\sum_{n=2}^{\infty} \frac{1}{2^{n}*n}$ converges. I am trying to show this by showing that the partial sums are bounded. I have tried doing this by induction but am not seeing how to pass the inductive assumption part. Do I need to instead ... | 2015-08-30T02:17:49 | {
"domain": "stackexchange.com",
"url": "http://math.stackexchange.com/questions/266788/want-to-show-sum-n-2-infty-frac12nn-converges",
"openwebmath_score": 0.956654965877533,
"openwebmath_perplexity": 423.42401219483224,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.981735720... |
http://mathhelpforum.com/number-theory/150362-fibonacci-series-slight-variant.html | # Math Help - fibonacci series - a slight variant
1. ## fibonacci series - a slight variant
Let me define a recurence like this
S(1) = 1
S(2) = 1
S(n) = S(n-1) + S(n-2) + a; where a is some number
Q1: What is the relation beween S(n) and F(n) [nth Fibonacci number]
I found out this is S(n) = F(n) + K(n)*a
Where ... | 2015-05-26T00:47:04 | {
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"url": "http://mathhelpforum.com/number-theory/150362-fibonacci-series-slight-variant.html",
"openwebmath_score": 0.8737853765487671,
"openwebmath_perplexity": 1267.174961653112,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.981735722716895... |
https://datascience.stackexchange.com/questions/107152/association-mining-is-buying-independent/107277 | Association Mining - is buying Independent?
I have a problem. I can't not solve this exerciese. What is the best way to solve this exerciese? What are the approaches for this kind of exerciese?
The following table summarizes transactions in a supermarket where customers bought tomatoes and/or mozzarella cheese or nei... | 2022-05-19T17:45:52 | {
"domain": "stackexchange.com",
"url": "https://datascience.stackexchange.com/questions/107152/association-mining-is-buying-independent/107277",
"openwebmath_score": 0.6739176511764526,
"openwebmath_perplexity": 549.3927228044944,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0... |
https://math.stackexchange.com/questions/325082/is-the-inverse-of-a-symmetric-matrix-also-symmetric | # Is the inverse of a symmetric matrix also symmetric?
Let $A$ be a symmetric invertible matrix, $A^T=A$, $A^{-1}A = A A^{-1} = I$ Can it be shown that $A^{-1}$ is also symmetric?
I seem to remember a proof similar to this from my linear algebra class, but it has been a long time, and I can't find it in my text book.... | 2022-05-25T13:10:23 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/325082/is-the-inverse-of-a-symmetric-matrix-also-symmetric",
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"openwebmath_perplexity": 285.7312607947454,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes\n\n",
"lm_q1_score": ... |
https://gmatclub.com/forum/a-manufacturer-makes-and-sells-2-products-p-and-q-the-revenue-from-t-242847.html | GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 19 Jan 2019, 20:52
### 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 Prep Questions via email.
Customize... | 2019-01-20T04:52:25 | {
"domain": "gmatclub.com",
"url": "https://gmatclub.com/forum/a-manufacturer-makes-and-sells-2-products-p-and-q-the-revenue-from-t-242847.html",
"openwebmath_score": 0.4579028785228729,
"openwebmath_perplexity": 6127.9643102423615,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes\n\n",
"lm_q1_scor... |
http://math.stackexchange.com/questions/88008/which-is-the-greatest-possible-natural-number-that-divides-p3p-7-where | Which is the greatest possible natural number that divides $(p+3)(p-7)$, where $p$ is a prime number greater than $3$?
Which is the greatest possible natural number that definitely divides $(p+3)(p-7)$, where $p$ is a prime number greater than $3$?
This one is from my module, comes as a fill in the blanks with no ans... | 2015-03-03T11:09:49 | {
"domain": "stackexchange.com",
"url": "http://math.stackexchange.com/questions/88008/which-is-the-greatest-possible-natural-number-that-divides-p3p-7-where",
"openwebmath_score": 0.8795627951622009,
"openwebmath_perplexity": 242.12830396334473,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"... |
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