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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0
votes
3answers
43 views

Solving the complex polynomial

For the complex polynomial $z^3 -5z^2 +(7-2i)z +6i-3 = 0 $ $1)$ show that $2+i $ is a root. $2)$ solve the given equation. Attemp to solve: I'm not really sure how to solve this, but I ...
4
votes
2answers
59 views

what is the sum of this series: $\frac{2}{\pi}\Sigma_{k=1}^{\infty}\frac{(-1)^{k-1}}{2k-1}$

Can anyone help me with this? What is the sum of this series: $\frac{2}{\pi}\Sigma_{k=1}^{\infty}\frac{(-1)^{k-1}}{2k-1}$ I got it after plugging $x=-1$ in a fourier series Thank you!
1
vote
3answers
36 views

Computation of surfaces areas of some objects

I want to calculate the surface area of the following objects: 1) A cylinder with height $h$ and radius $r$ 2) A cone $C=\{(x,y,z) \in \mathbb R^3 : x^2+y^2=z^2, 0<z<4\}$ 3) A torus At first ...
0
votes
0answers
18 views

Question regarding permutations and combinations? [duplicate]

Hi, I was just wondering on how you are supposed to approach this question. I keep getting 114 as an answer, but the answers say it is 174. How would anyone do this question, because I feel like I'm ...
2
votes
1answer
28 views

Dirac Delta Function, Initial Value Problem

Hi I finished this IVP but I cant seem to get the right answer can someone give me some advice as to where I went wrong and point me in the right direction as to how to fix it. Here is the problem and ...
1
vote
3answers
52 views

Question regarding permutations and combinations?

Hi, I was just wondering on how you are supposed to approach this question. I keep getting 114 as an answer, but the answers say it is 174. How would anyone do this question, because I feel like I'm ...
0
votes
2answers
283 views

Two groups A and B are playing a game…

Two groups A and B are playing a game. The first group that wins 3 times is the winner. The probability that group A will win at on game is $\frac12$ and the same thing for group B. $X$ = The number ...
0
votes
3answers
37 views

distance from a point to line segment not it 's perpendicular line's distance

how to find distance between line and point in the picture ? what is the shortest distancing point in the line ? Note: distance between line and point means line segment,(the intersecting point ...
3
votes
0answers
56 views

Show that a certain operator is symmetric

I am trying to prove that the operator $L^2 = -\partial_\theta^2 - \cot\theta\,\partial_\theta - \frac{1}{\sin^2\theta}\partial_\phi^2$ fulfills the following property: For $y_{l,m} = ...
1
vote
2answers
62 views

Sketch $y=2x^3/(x^2-2)$ [closed]

Sketch the curve $$y=\frac{2x^3}{x^2-2}.$$ Can someone answer this for me as basic as possible. Year 11 extension if possible. Thanks
0
votes
3answers
41 views

Differential equation True/ False

Every continuous function has an antiderivative I thought this statement was false, but it seems that it is true. I thought that it suppose to be every antiderivative is a continuous but the ...
3
votes
7answers
57 views

Suppose that $m \ge 0$ show that $49 \mid 5\cdot3^{4m + 2} + 53\cdot2^{5m}$

I've re-written the equation in a few different ways hoping for a few different approaches: $$49y = 5 \cdot 3^{4m + 2} + 53 \cdot 2^{5m} $$ I think the first equation has more potential, since it ...
1
vote
0answers
35 views

having trouble with a 3-dimensional basis-change problem/

Let $V$ be a 3d vector space with a chosen basis $\alpha=\{e_1,e_2,e_3\}, \beta=\{f_1,f_2,f_3\}$ for $V$ satisfying: $$\begin{align}e_1 & =f_1+f_2+f_3 \\ e_2 &=f_2+2f_3 \\ e_3 & =f_3 ...
0
votes
1answer
16 views

Find the equation of a line tangent at a specific point

I have to find an equation for the line tangent to the graph of $\large\frac {\sqrt{x}}{6x+5}$ at the point $(4,f(4))$, and write it out in the form of $y=mx+b$ Using the quotient rule I get.. ...
0
votes
2answers
37 views

i am having trouble with one of the homework question regarding to linear algebra(vector and span)

$V$ is a vector space of some dimension, with $\vec u,\vec v,\vec w$ independent set of vectors in $V$. define the subspace of $V$ given by $W = \operatorname{span}(\vec u-\vec v+\vec w, 2\vec u+\vec ...
1
vote
3answers
63 views

Steps to solve $\int \sqrt{\frac{11}{x}}\,\mathrm{d}x$?

What are the steps required to solve the following? $\int \sqrt{\frac{11}{x}}\,\mathrm{d}x$ I'm not looking for anyone to do my homework. I usually have no problem figuring these things out -- ...
0
votes
0answers
35 views

After removing the parameter from $x=\sec \theta$ and $y=\cos\theta$, why does the domain become $|x|\geq1, |y| \leq1$?

For the parametric equations $x=\sec \theta$ and $y=\cos\theta$ with initial domain $0\leq\theta\lt\frac{\pi}{2}$, $\frac{\pi}{2}\lt\theta\leq\pi$, I understand that you arrive at $y = \frac{1}{x}$ ...
0
votes
1answer
62 views

The Pigeonhole principle and sum of integers in subset of Z

S⊂{1,2,3,...} and the cardinality of S is 7. m is the maximum element in S.Find the possible values of m so that there exists distinct subsets B,C with s(B)=s(C) [s(B) means the sum of the objects in ...
0
votes
1answer
16 views

How to write a polynomial basis with conditions

I don't understand how to do problem where you have to write a basis for a polynomial. For a example a typical problem would be something like: Let U = {p $\in$ $P_n(F)$: p(2) = p(5) or p''(1) = ...
1
vote
4answers
110 views

$7^n-1$ is divisible by $6$ for all natural number $n$ [closed]

How to prove $7^n-1$ is divisible by $6$ for all natural number $n$. Thanks for your help.
1
vote
1answer
47 views

Is this sufficient for linear independence proofs??

I've been doing all of these proofs the same basically, I just want to make sure I'm doing them right, I didn't include all the details but I have the outlines of my proofs here. 1) U and W are ...
2
votes
1answer
19 views

If $A$ is a primitive / irreducible C*-algebra, then $M(A)$ has trivial center.

Recall some definitions: a sub-C*-algebra $A$ of $B(H)$, the algebra of bounded operators on a Hilbert space $H$, is called irreducible if the only closed $A$-invariant subspaces of $H$ are $0$ and ...
0
votes
0answers
25 views

harmonic oscillator exercise

An object with a mass of 8 kg stretches a spring over 0.06 m This object is drawn further down to 0.30 m and set in motion by an upwardly directed velocity of 0.30m/s in a substance that has a ...
2
votes
1answer
45 views

Are These Two Definitions of a Disconnected Set Equivalent?

I found two definitions of a disconnected set $E \subset \mathbb R$. $E$ is disconnected if: (1) there are disjoint open sets $A, B$ such that $A \cap E$, $B \cap E \ne \emptyset$, and $(A \cap E) ...
0
votes
0answers
35 views

Min. Spanning Tree - Same weight

Prove that every minimum spanning tree of a connected graph, $G$, has the same maximum edge. Intuitively, this makes sense to me. You need to have that heavy edge because that is the cheapest ...
0
votes
1answer
36 views

Extreme points in compact convex domain [closed]

Let $f(x)$ be a continuous quasi-convex function in $R^n$ and let be a compact convex domain. If one denotes $ \Gamma:=[x\in \Omega: \operatorname{arg max}_x f(x) ]$ then $ \Gamma$ contains an ...
-1
votes
2answers
29 views

We are making a Bernoulli experiment…

We are making series of independent Bernoulli experiment with $\frac13$ chance to success. What is the probability that we got success at the first experiment, if we know that we get two successes at ...
0
votes
2answers
27 views

Applying the cosine even identity to the cosine difference identity

I'm slightly confused over what happens when you're applying cosine's "even identities" to the difference identity. Here's how I go about, please tell correct me as I feel i'm going wrong somewhere. ...
1
vote
0answers
39 views

The volume is to be found

Find the volume of $A=\{(x,y,z) \in \mathbb{R}^3: 2x^2+3y^2 \leq z \leq 4+2x+3y\}$ I know we are to solve it by using triple integral...
3
votes
1answer
34 views

Proving Cauchy inequality involving four expression

Show that $$(a^2 + b^2 + c^2) (a^2b^2 +b^2c^2 +c^2a^2) \geq (a^2b + b^2c + c^2a)(ab^2 + bc^2 + ca^2)$$ i should prove this inequality by making it a Cauchy form inequality(as teacher stated). my ...
2
votes
1answer
70 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
29 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
41 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
307 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
votes
0answers
30 views

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

A region on the graph is bound by the lines $y=x/2$, $y=0$, $x=2$ How can I calculate the center of the mass assuming a uniform density of "p" throughout the region?
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 \ ...
-1
votes
2answers
27 views

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

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
30 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
38 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
63 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
36 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 ...