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2
votes
1answer
72 views

Positive and négative Parts

we denote by $u^+=\max(u,0)$ and $u^-=\max(-u,0)$ the positive and the negative parts of $u$ we have that $u=u^+-u^-$ my question is : what is $u'$ using $u^+$ and $u^-$ ? and what is ...
0
votes
3answers
278 views

What is the probability that A will win…

Two players are rolling two dices, if they get 6 Player A wins, if they get 7, player B wins, else they rolling the two dices again... What is the probability that A will win? I'd like to get any ...
0
votes
2answers
30 views

Least squares approximation: Legendre polynomial

Find the best quadratic least squares approximation to $f(x)=e^x$ on $[-1,1]$ with respect to the inner product $\langle f(x),g(x) \rangle = \displaystyle\int_{-1}^1 f(x)g(x)dx$. I cannot figure out ...
0
votes
1answer
46 views

Calculate length of radial intersecting a rectangle

In a rectangle like below, I need to calculate the length of any radial, from the center of the rectangle to where it intersects with the edge of the rectangle. Further, the angle of the radial is ...
0
votes
2answers
50 views

Linear algebra proof

Let $W$ be a subspace of $\mathbb{R}^n$. Let $\vec{v}_1 ,\vec{v}_2 \in \mathbb{R}^n$. Suppose that $\vec{p}_1$ is the projection of $\vec{v}_1$ onto $W$ and $\vec{p}_2$ is the projection of ...
0
votes
1answer
36 views

Orthogonality question

Been stuck on this one: If $\vec{x}$ is orthogonal to $\vec{u}$ and $\vec{v}$ then $\vec{x}$ is orthogonal to $\vec{u}-\vec{v}$. Any hints?
4
votes
2answers
308 views

True/ False differential equation

Are the statements in Problems 46-54 true or false? If $F(x)$ is an antiderivative of $f(x)$, then $y=F(x)$ is a solution to the differential equation $\frac{dy}{dx}=f(x)$. If $y=F(x)$ is a solution ...
1
vote
1answer
52 views

How to find the value of $c$ using the mean value theorem?

So I'm doing Mean Value theorem homework which states $$f'(c)=\frac{f(b)-f(a)}{b-a}$$ I have $f(x)=e^{\frac{-x}{2}}$ over the interal [0,12]. Using the mean value theorem I ...
1
vote
1answer
92 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
85 views

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

What is the value of $(72^2 - 64^2) : (44^2 - 24^2)$ How to calculate this without calculator?
0
votes
3answers
80 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
votes
1answer
15 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 ...
1
vote
1answer
39 views

Converge of an inversion to a mirrorring

I want to ask something about a mirroring and a inversion in $\mathbb{R}^n$. An inversion in a sphere with center $m$ and radius $\rho$ can be written as $$ v \ \longmapsto \ ...
0
votes
0answers
31 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
vote
1answer
17 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
39 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
votes
1answer
66 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
37 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 ...
1
vote
0answers
57 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 ...
-1
votes
1answer
27 views

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

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 ...
0
votes
1answer
35 views

How to find the volume of revolution around a line y [closed]

Using the washer method how can I calculate the Volume of a solid generated by the lines y=x,x=0 ...
0
votes
0answers
20 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
votes
1answer
11 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
43 views

Derivation of fundamental solution of heat equation by reduction to ODE - Question on integration factor

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
48 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. $$\tan^{-1}(\cot x)+\tan^{-1}(\cot^3 x)+\tan^{-1}(\frac{1}{2} \tan 2x)=0$$
1
vote
0answers
57 views

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

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 $n\in N$. I found it in Cohen Macaulay rings. there`s nothing to find.
1
vote
1answer
72 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
21 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
53 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?
0
votes
0answers
9 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 ...
0
votes
3answers
67 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
56 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 $B$ ?
0
votes
1answer
28 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
34 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
186 views

Why elements of the set can be Goldbach pairs for a given even number?

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
28 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))
1
vote
4answers
41 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
141 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
57 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
1answer
51 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
49 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 ...
4
votes
2answers
153 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 ...
2
votes
1answer
108 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
457 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
40 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
40 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 ...
0
votes
0answers
24 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
87 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
2answers
42 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 ...
2
votes
1answer
87 views

Uniform convex space

Please I want to know if this space $$H^1_{0,p}([0,+\infty))=\lbrace u, u\in AC([0,+\infty)), u(0)=u(+\infty)=0,\sqrt{p}u'\in L^2\rbrace$$ where $p>0$, $p\in L^1((0,+\infty))$ ...