Homework questions are welcome as long as they are asked honestly, explain the problem, and show sufficient effort. Please do not use this as the only tag for a question. For the answers on homework questions, helpful hints or instructions are preferred to a complete solution. Please do not add ...

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0answers
38 views

How Can I figure out when cosine = $\frac{2}{\pi}$?

So I'm doing Mean Value theorem homework which states $$f'(c)=\frac{f(b)-f(a)}{b-a}$$ So I am trying to find $c$ for $f(x)=\sin x$ over the interval $[0,\frac{\pi}{2}]$. So using the Mean Value ...
-2
votes
2answers
52 views

What is the value of $(72^2 - 64^2) : (44^2 - 24^2)$ [on hold]

What is the value of $(72^2 - 64^2) : (44^2 - 24^2)$ How to calculate this without calculator?
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votes
3answers
50 views

Determing if $f(x,y)$ is continuous at $(0,0)$

I would really appreciate if someone could help me figure out where to start on this problem. The question is to determine if $f$ is continuous at the origin. $$\begin{equation} ...
0
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1answer
8 views

InformationGain on Two Continuos classes instead on inary

I've a problem regarding an excersise with information gain. I can't seem to get the right answer, because the excersises differs from what we learned. Usually, a target class is a binary variable ...
0
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0answers
22 views

Find the center of mass of a region with uniform density [on hold]

A region on the graph is bound by the lines y=x/2, y=0, x=2 How can I calculate the ...
0
votes
1answer
11 views

Converge of an inversion to a mirrorring

I want to ask something about a mirroring and a inversion in $\mathbb{R}^n$. The following map is called in inversion, and the unit circle is mapped to itself right? $$ v \ \longmapsto \ ...
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votes
2answers
22 views

How to find the halfway point of a volume of a solid [on hold]

How can I calculate the x coordinate which marks exactly half of the volume of a solid generated by the following region? y=(x)^1/2, ...
0
votes
0answers
22 views

Surface Integrals, orientation and parametrizations.

I'm trying to solve the following problem: Integrate $f(x,y,z)=(x,y,z)$ over the surface $z=12$ $x^2 + y^2 \leq 25$ I parametrized the surface with $\sigma (r, \theta) = r \sin(\theta), r ...
1
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1answer
16 views

probability and random sample

suppose that a body mass index for a population of 30-60 year old men follows a normal distribution with mean 26 and standard deviation 4. If we take a random sample of 7 men age 30-60 years old. whe ...
2
votes
2answers
35 views

Proof About Division of Integers

Here is a problem I just finished working on: Prove that if $n$ is composite then there are integers $a$ and $b$ such that $n$ divides $ab$ but not $n$ does not divide either $a$ or $b$. One ...
0
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1answer
34 views

A few questions regarding the cosine difference identity

I've a few questions that stem from the proof given in my textbook regarding the cosine difference identity. The proof goes like this: Let $\alpha$ and $\beta$ be angles plotted in standard ...
0
votes
2answers
30 views

Can a set of 4 vectors with 3 entries each only span R2 if the third row reduces to all zeros?

I'm a bit confused as to how dimension, dimension of span, and dimension of column space all relate with regards to a basis. The question is worded as follows: Find the dimension of the span of the ...
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0answers
10 views

Trying to prove that two angles are congruent in a isosceles trapezoid

I was given this assignment to do the following. Write a paragraph proof for the following scenario. Given: KLMN is an isosceles trapezoid. Prove: ∠LKM is congruent to ∠MNL The thing is that I ...
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votes
0answers
21 views

Another version of the Poincaré Recurrence Theorem (Proof)

The task is to prove the following version of Poincaré's Recurrence Theorem: Let $(X,\Sigma,\mu)$ be a finite measure space, $f\colon X\to X$ a measurable transformation that preserves the ...
0
votes
1answer
21 views

How to find the volume of revolution around a vertical line x

How can I evaluate the volume of a solid generated by the following lines using the washer method: $y=x$, $y=0$, $y=4$. Rotated about $x=5$. I have tried to find the outer radius of $5-x$ and the ...
1
vote
1answer
27 views

How to find the volume of revolution around a line y

Using the washer method how can I calculate the Volume of a solid generated by the lines y=x,x=0 ...
0
votes
0answers
17 views

How to evaluate the graph? [duplicate]

$ \frac{|x-2|} {(x^2-4)}+\frac{(x-2)} {|x-2|} = b $ determine for which values of $b$ the equation has one and only solution. I tried sketching the graph, but was unable to do so accuratly...also, ...
0
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1answer
10 views

Hypergeometric Distribution Function?

I'm looking for a function that I can use in excel to calculate the probabilities of having certain cards in an opening hand. For example a function that will calculate the probability to get AT ...
0
votes
0answers
23 views

derivation of fundamental solution of heat equation by reduction to ODE

In the derivation of fundamental solution for heat equation ( as in PDE by L.Evans ), we come across the reduction to following ODE : $\alpha w + {1\over2}r w'+ w'' +{n-1\over{r}}w' = 0$ Set ...
-1
votes
1answer
42 views

Inverse Trigonometry proof

Please help me prove this equation as ive been trying for days and not able to solve the $\tan^{-1}( \cot^3 x)$ part. $$\tan^{-1}(\cot x)+\tan^{-1}(\cot^3 x)+\tan^{-1}(\frac{1}{2} \tan 2x)=0$$
0
votes
0answers
12 views

$H_I^n(R)=0$ and $H_I^n(M)\neq 0$

question: find R and M as an R-module such that $H_I^n(M)\neq 0$ and $H_I^n(R)=0$, where I an ideal of R and $n\in N$. plz give some hints to find this example.
1
vote
1answer
56 views

How to solve this graphing question?

$ \frac{|x-2|} {(x^2-4)}+\frac{(x-2)} {|x-2|} = b $ determine for which values of $b$ the equation has one and only solution. I tried sketching the graph, but was unable to do so accuratly...also, ...
1
vote
1answer
17 views

Question about convergence in $H^1_0$

Please how to prove that if $u_n\rightarrow u$ on $H^1_0$ we have that $||u_n||\rightarrow ||u||$ ? Please i need your help Thank you
0
votes
1answer
33 views

How to find the equation of two lines at a given point?

Here's the problem: Give the equations of two lines that meet at the point (-1, 5, 2) and which meet at right angles, but do not use that point in either of the equations. Any ideas?
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0answers
7 views

why not applicable categorical variables using ANOVA F or Levene test?

For independent test data is a categorical variable using the Pearson chi-squared test. But, why not applicable categorical variables using ANOVA F or Levene test? Are there any theories on this ...
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3answers
33 views

getting the slopes of the sides of an equilateral triangle given 2 points

I want to get the slopes of an equilateral triangle given the 2 vertices. Let's say they are (0, 0) and (5, 5). Graphing this would give 2 triangles forming a diamond. I tried to use distance formula ...
0
votes
1answer
31 views

Density and convergence

i have a small question: is it true that if the basis of a space $A$ is dense in a space $B$ ($B\subset A$) then if $u_n\rightarrow u$ in $A$ we have that $u_n\rightarrow u$ in $B$ ?
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votes
1answer
25 views

How do I find the critical values to find the maximum of this function?

The total daily profit in dollars realized by the TKK Corporation in the manufacture and sale of x dozen recordable DVDs is given by the total profit function below. $$P(x) = −0.000001x^3 + 0.001x^2 + ...
1
vote
1answer
31 views

Small question about convergence

I have a small question: if i have that $$\int_0^{+\infty}p(t)|u'_n(t)-u'(t)|^2dt\rightarrow 0$$ is it true that $$\int_0^{+\infty} p(t)|u'_n(t)|^2 dt\rightarrow \int_0^{+\infty} p(t)|u'(t)|^2 dt $$ ...
0
votes
1answer
111 views

Why elements of the set can be Goldbach pairs for a given even number? [on hold]

Let's take even number $100$ as an example (an example in the paper): Fom $2$ to $\sqrt{100}$ there's four primes:$\ 2,\ 3,\ 5,\ 7.\ $Let $$ \begin{align*} &A=\{n: n \in \mathbb{Z^+}, ...
0
votes
1answer
27 views

What is the effect of taking the sine of inverse cosine?

How can I evaluate the sine of an inverse cosine? for example: sin(arccos((x)^1/2))
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4answers
40 views

Finding the $\cot\left(\sin^{-1}\left(-\frac12\right)\right)$

How can I calculate this value? $$\cot\left(\sin^{-1}\left(-\frac12\right)\right)$$
3
votes
3answers
131 views

I need help finding the critical values of this function.

So $h(t)=t^{\frac{3}{4}}-7t^{\frac{1}{4}}$. So I need to set $h'(t)=0$. So for $h'(t)$ the fattest I've gotten to simplifying os $h'(t)=\frac{3}{4 \sqrt[4]{t}}-\frac{7}{4\sqrt[4]{t^3}}$ and that is as ...
0
votes
0answers
56 views

Showing that two sums are equivalent

given \begin{gather} U_d(x,y,q\mid i_1,\ldots,i_k)=\sum\limits_{n,m\geq0}x^ny^m\sum\limits_{\sigma = i_1\ldots i_k\sigma_{k+1}\ldots\sigma_m\in C_{[d]}(n,m)}q^{v(\sigma)}. \end{gather} show ...
1
vote
0answers
29 views

Easiest way to find the highest count of sequential numbers in an array? [on hold]

I'm having a programming problem that I'd like to know if there's an easy way to mathematically solve it. Say I have an array of integers, how can I easily find the highest number of sequential ...
0
votes
0answers
26 views

How to show this is the minimal polynomial

I'm trying to the following problem. But I can't show some irreducibility of the polynomials. Put $L=\mathbb{C}(X,Y,Z)$, $\omega=\frac{-1+\sqrt{-3}}{2}$. Define two automorphism $\sigma, \tau$ of ...
1
vote
2answers
48 views

How to express a trigonometic equation in $\sin 2\theta $ and $\cos 2\theta $?

How do I express the given equation in $\sin 2\theta $ and $\cos 2\theta $ in terms of x? $x + 3 = 7\sin \theta $ with $\frac{\pi }{2}{\text{ < }}\theta {\text{ < }}\pi $ for $\sin 2\theta ...
3
votes
2answers
105 views

Combination of quadratic and arithmetic series

Problem: Calculate $\dfrac{1^2+2^2+3^2+4^2+\cdots+23333330^2}{1+2+3+4+\cdots+23333330}$. Attempt: I know the denominator is arithmetic series and equals ...
0
votes
0answers
23 views

Deducing an optimal gambling strategy (using martingales).

Apologies in advance for the length, I tried being precise. Suppose a game where in each turn you can gamble a certain amount of money on the result of a fair coin toss. If the coin comes out tails ...
2
votes
4answers
432 views

Proving 7n+5 is never a cubic number?

This is from a question that starts with: An arithmetic progression of integers an is one in which $a_n=a_0+nd$, where $a_0$ and $d$ are integers and n takes successive values $0, 1, 2, \cdots$ Prove ...
0
votes
2answers
33 views

How to find the third vertex of an isosceles triangle given 2 points.

This is the full problem: The points $A(5,1)$ and $B(-3,6)$ represent one of the equal sides of an isosceles triangle. Determine one of the possible points that would represent the third vertex of the ...
0
votes
2answers
37 views

Solving equations with powers without logarithms

Im taking an introduction to logarithms. Of course a short review of exponentiation is inherent for a clear understanding of logarithms. I was asked to find, for example, $27^x = 3$. (without the use ...
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votes
0answers
22 views

Question about convergence

If i have that $$\int_0^{+\infty} a(t)|u_n(t)-u(t)|^2 dt \rightarrow 0 $$ how we can deduce that $$\int_0^{+\infty} a(t)|~|u_n(t)|-|u(t)|~|^2 dt \rightarrow 0 $$ where $a>0, a\in ...
4
votes
4answers
81 views

Polynomials that satisfy $(x-1)(p(x+1))=(x+2)(p(x))$ where $p(2)=12$?

I am taking a graduate class on Equation Theory and one of my homework questions asks me to "Determine all polynomials $p(x)$ such that $(x-1)(p(x+1))=(x+2)(p(x))$ and $p(2)=12$. A provided hint is to ...
1
vote
1answer
33 views

Find the radius of four congruent circles inside a right triangle

Below is a homework assignment I'm working on, along with a correct method for solving it and what appears to be an incorrect method. I'm hoping someone could explain what is wrong with the second ...
0
votes
1answer
32 views

Formula alteration

is there any way to transform the formula$ \frac {1-x}{x-3}$ into something that can be easily sketched, or which will help eliminate $x$ from the denominator?
0
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0answers
22 views

checking the solution of PDE

Let $u(x)$ be an entire solution of $\Delta u = 1$ on $R^{n}$, $n>1$. If $u(x)$ is also convex, that is $(D^{2}u(x))$ is non-negative definite for all $x$. Then $u(x)$ is given be a quadratic ...
1
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1answer
38 views

Completing the following equation by the suitable method

i got this linear equation two variable problems for my school. I understand the basics of the normal linear equation but this seems different instead having a pure number after the "=" they got a ...
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votes
1answer
31 views

to prove partial derivative of a function f is bounded [duplicate]

Let$$ f(x,y) = \begin{cases} 0 & (x,y)=(0,0) \\ \dfrac{x^3}{x^2+y^2} & (x,y) \neq (0,0) \end{cases}$$ Prove that $D_1 f$ and $D_2 f$ are bounded ...
-5
votes
2answers
42 views

Five apples, three pears and two bananas cost £3.18. Four apples, eight pears and three bananas cost £4.49. [on hold]

Five apples, three pears and two bananas cost £3.18. Four apples, eight pears and three bananas cost £4.49. How much more expensive is an apple than a pear? A. 5p B. 6p C. 7p D. 8p E. More ...