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 ...

learn more… | top users | synonyms

1
vote
0answers
8 views

Is the complement of the inversion relation (in the context of permutations) transitive?

I'm studying from An Invitation to Discrete Mathematics where I came upon an exercise which confuses me. Let $\pi$ be a permutation of the set $\{1,2,\dots,n\}$ and let $I(\pi)$ denote the set of ...
0
votes
0answers
3 views

find E($\bar{Y^4})$ by using moment generating function for a normal distribution with mean μ and variance 1.

Let $Y_1, Y_2, . . . , Y_n$be a random sample from a normal distribution with mean μ and variance 1. I would like to find E($\bar{Y^4})$ by using moment generating function. The setup I have right ...
2
votes
0answers
25 views

How to find the inverse of this particular symmetric matrix

Basically, I have a $n \times n$ symmetric matrix, which looks like this: $$ \begin{bmatrix} 1 & \alpha & \cdots & \alpha \\ \alpha & 1 & \cdots &\alpha \\ \vdots &\vdots ...
2
votes
0answers
16 views

Fundamental Solution of a Nonlinear ODE (using Riccati Transformation & Wronskian)

I am given the differential equation: \begin{equation*} y^{\prime}(t) = y(t)^{2} + 2\sin(t)\cos(t) - \sin^{4}(t) \end{equation*} and one solution $y_{1}(t) = \sin^{2}(t)$. I wish to find a second ...
1
vote
0answers
15 views

Euler Equation and Marginal Rate of Substitution

I was wondering if someone could help me clarify a result from my lecture notes. I have put them as a picture. It concerns the result on the last slide (the other three slides are included as well ...
0
votes
3answers
33 views

Prove this identity? $\cos t ⋅ \cos u ⋅ \cos v = \frac14(\cos(t + u + v)+ \cos(t + u - v)+cos(t-u-v))$

The problem reads as follows. Prove the identity $$\cos t⋅\cos u⋅\cos v =\frac14\big(\!\cos(t + u + v)+\cos(t + u - v)+\cos(t-u-v)\big)$$ Hint: begin with the right side and use cosine sum identity ...
1
vote
3answers
53 views

Range of f(x) = $\frac{\sqrt3\,\sin x}{2 + \cos x}$ [duplicate]

Can you give any idea about the range of the following function? $$f(x) = \frac{\sqrt{3}\,\sin x}{2 + \cos x}$$
0
votes
2answers
27 views

How to show that the $\phi $ and $\varphi$ satisfy the Cauchy Riemann equation

when u=(u,v)=($\frac{\partial\varphi}{\partial y},-\frac{\partial\varphi}{\partial x}$) and u(x)=grad$\phi$(x)=$\nabla\phi$(x) how can you use the equations above to prove that the $\phi$ and the ...
-3
votes
1answer
61 views

Reflexive. What does it mean? [on hold]

I would like to know the definition for reflexive. I have not found anything on the internet or in my book.
0
votes
0answers
16 views

set functions and relation multiplication

$\ M$ is the set of all relations on $\ A = \{1,2,3\}$ $\ K$ is the the following relation on A $\ K=\{(1,1),(2,1),(3,1)\}$ let there be $\ f :M\rightarrow M$ $\ f(R) = RK$ is f injective? ...
1
vote
1answer
34 views

a question about convergence of sequecce!I have tried cauchy method, but it doesn't work

suppose $a_n>0$,and$\sum_{i=0}^\infty a_i$ is convergent,so we need to prove $\sum_{n=1}^\infty{ {1\over n}(a_n+a_{n+1}+\cdots+a_{2n})}$ is also convergent! I have tried cauchy method, but maybe ...
0
votes
0answers
19 views

How to show uniqueness of $\nabla\phi$ using Green's theorem when the value of Neumann problem exists.

It says getting function $\phi(x,y,z)$ that satisfies the following conditions $\frac{\partial\phi(x)}{\partial n}$=h(x), x$\in$S is called the Neumann problem. The problem is to show the uniqueness ...
0
votes
1answer
12 views

Moment Generating Function of the Chi-Squared Distribution

The questions wants us to show that the MGF for the chi-squared distribution is equal to I know that to show that I need to evaluate this integral. I'm not sure where to begin to evaluate it. ...
1
vote
1answer
20 views

2 dimensional Laplace's equation in polar coordinates

The problem asks you to get Laplace's equation in 2 dimensions in polar coordinates using the fact that $\operatorname{div}(\cdot)$ in two dimensional vector field could be written as $$\nabla \cdot u ...
2
votes
0answers
29 views

($\cos^4x$)($\sin^2x$) in terms of first power of cosine

I believe that I have his correct but if someone could check it and see that'd be great. Here's a pic! [IMG]http://i58.tinypic.com/2dgm5ic.jpg[/IMG]
0
votes
0answers
10 views

Find the intersection of three bisection lines

Let $p_1 = (a_1, b_1), p_2 = (a_2, b_2), p_3 = (a_3, b_3)$ be three, non-colinear points in the plane. For each pair of these points, let $L_{ij}$ denote the line segment from $p_i$ to $p_j$. (a) For ...
2
votes
0answers
13 views

Characteristic curves of 2nd-order PDEs under invertible coordinate transformations

First off, I'm not very experienced with the subject and English is also not my first language, so if there are any inaccuracies in the following text, let me know. Given a linear, scalar, ...
1
vote
0answers
8 views

probability and applied statics 4 [on hold]

In cairo 30% of residents listen to the local fm radio . ten residents are chosen at random? a) state the distribution of the random variable b) find the smallest value of s so that P (x >or equal ...
1
vote
2answers
26 views
1
vote
0answers
17 views

Circle Tangent question

I would like to ask for assiatance on the following: Find the eqation of a circle, with a radius of$\sqrt 2$ , which also has as tangetns the lines: $ y=x+2 $ , $ y=-7x $. It is known that the ...
0
votes
1answer
21 views

Bilinear forms and scalar product

Forgive me for these may not be the correct English mathematical terms. Let $(V, \langle, \rangle)$ be a euclidean vector space of finite dimension $n$ and $f:V \times V \rightarrow \mathbb{R}$ a ...
2
votes
1answer
26 views

Suppose that $G$ is a group of order 5 and let $\varphi: \mathbb{Z_{30}} \rightarrow G$ Determine the kernal of $\varphi$

Suppose that $G$ is a group of order 5 and let $\varphi: \mathbb{Z_{30}} \rightarrow G$ be and epimorphism. Determine the kernel of $\varphi$ Since $\ker\varphi \unlhd \mathbb{Z_{30}}$ (theorem) then ...
0
votes
1answer
21 views

Uniform-norm of $f_n(x)=ne^{-nx^2}$

Consider a sequence of functions, $(f_n(x))=ne^{-nx^2}$. I think the uniform norm is $ne^{-n}$, but according to my solution, it is $n$. Why is this the case? Don't we just take out the $x$ for the ...
0
votes
1answer
26 views

Finding Distinct Elements and Permutation in Partitioned Set

I am having a hard time figuring out where to start on a homework problem. The question is: A set of $nk$ elements is partitioned into $k$ subsets in two ways, each subset having size $n$: one ...
0
votes
0answers
11 views

Got stuck with this $L^2(-1, 1)$ optimization problem. Any ideas where it comes from?

Statement Let $u(x) \in L^2(-1, 1)$. Solve the following optimization problem: $$ \begin{cases} J(u) = 4 \int_{-1}^{1} \sqrt{|x| (1 - |x|)} u(x) dx + \left(\int_{-1}^1 \sin(3\pi x) u(x) dx\right)^2 ...
1
vote
1answer
29 views

Prove there exists an element in the function…Beginning function proof

Having trouble with the last part of my proof: Let f: $\mathbb{Z}\rightarrow \mathbb{Z}$ be a function with $f(x+y)=f(x)+f(y)$ for all $x,y \in \mathbb{Z}$. Prove there exists an element $a\in ...
1
vote
1answer
16 views

Pointwise convergence of arctan(nx)

Question 6 section 8.1 of Introduction to real analysis by Bartle and Sherbert. Show that lim(Arctan nx) = (pi/2)sgn x for x in R, x>=0. I have a final coming up and I've started doing some of the ...
0
votes
1answer
18 views

Proving If $\int^{\frac{\pi}{2}}_{0} f(x) \cos x dx \lt f \left(\frac\pi2\right),$ then $ \int^{\frac{\pi}{2}}_{0} f'(x) \sin x dx \gt 0. $

how do i tackle such problems? Let f(x) be a function differentiable on the interval$ $$\Bigl[$$ 0, \frac\pi2 $$\Bigr]$$ $ such that f'(x) is integrable on this interval. Prove the following ...
6
votes
4answers
85 views

If a polynomial $g$ divides $f$ and $f'$, then $g^2$ divides $f$?

Here's a homework problem from Artin's Algebra that I'm having a lot of trouble with Let $f(x) \in F[x]$ (where $F$ is a field of characteristic $0$). If $g$ is an irreducible polynomial that is ...
0
votes
1answer
29 views

Hint finding exact value of half-angle when $\tan (\theta) = {3}$

Unlike others I've tried, I'm having a hard time with this half-angle exercise: If $tan(\theta)={3}$ and $\theta$ is in QIII, find $\tan\left(\frac{\theta}{2}\right)$ Here's what I know (or think I ...
0
votes
1answer
16 views

Beginning Proof on functions and Sum of functions

I've been having a hard time with this proof because I do not know where to go from where I am. The proof we were assigned to in class is as follows: Let $f : \mathbb Z \rightarrow \mathbb Z$ be a ...
0
votes
0answers
30 views

What does my teacher mean by 'choosing' from a vector?

I'm revising some lecture notes from a class I missed, I'm just struggling to figure out what she means at this point. What is choosing x1=0, x2=1... etc mean? Could someone explain?
1
vote
3answers
26 views

Find the real parameter so as the equation has no real solutions…

My question is: For which values of parameter $a\in \mathbb{R}$ the following equation $$25^x+(a-4) \,5^x-2a^2+a+3=0$$ has no real solutions? My idea is: First of all we should transform the ...
1
vote
2answers
20 views

Find the angle between two tangent lines…

I have such an exercise: Find the measure of angle formed by the tangent lines drawn through $A(2,-1)$ to the following function: $$f:R\to R, f(x)=x^2$$ My solving was going well till I got stuck at ...
0
votes
1answer
26 views

Mean value theorem does not hold for the complex function $f(z)=z^3$

Consider $f(z)=z^{3}$, two point $z_{1}=1$ and $z_{2}=i$. show that Do Not exist a point $c$ on the $y=1-x$ between $1$ and $i$ such that Do Not satisfying ${f(z_{2})-f(z_{1})\over ...
1
vote
0answers
11 views

Proof continuity equation of incompressible fluid using the Gauss theorem and the fact that the sum of the fluid that went through the surface is 0

It says the answer is -$\frac{q}{\Delta_V}$=($\frac{\partial_u}{\partial_x}$+$\frac{\partial_v}{\partial_y}$+$\frac{\partial_w}{\partial_z}$)=_div_u=$\nabla$·u=0 and I don't even know where to start ...
0
votes
1answer
31 views

A problem on mathematical induction

This question I am feeling very difficult to solve. It is said to be a problem on mathematical induction: On a circular path, there are are $n$ cars and among them they have enough fuel to cover ...
0
votes
0answers
20 views

is it all right my pf?

PB: Give a proof that the image of a circle under a linear transformation is a circle. (Let $z$ be a $z=z_{0}+Re^{it}$, $t$ is a angle.) I tried it. Can you check my pf? (is it all right?) My Pf) ...
0
votes
0answers
10 views

Euler characteristic and free action

If $K$ is a finite simplicial complex, and $G$ acts simplicialy on $K$ with no fixed points, show $\chi(K) = |G|\cdot\chi(K^2/G)$. Could I have a hint for how to start this question? I was told to ...
0
votes
0answers
10 views

Representing trees in Set builder notation?

Is there a way to represent graphs and minimum spanning trees using set builder notation? e.g. I have a weighted graph of n nodes, all connected to each other in a mesh network manner. I am to ...
0
votes
1answer
11 views

Lorenz curve and Gini index using PDFs

I've been given that $f(w) = \frac{1}{4\sqrt{w}} $ for $0<w \le4$, and $F(w)$ is the associated CDF and represents the fraction of the population with income less than w. I know that the lorenz ...
0
votes
1answer
14 views

permutations and combination

How many different strings of lights can be created by placing 40 coloured lights on a horizontal string if 12 of them are red, 6 are blue, 14 are green and 8 are yellow? Assume that lights of the same ...
0
votes
2answers
16 views

A question about series ratio test

Could you please give me some hint how to deal with this question: Suppose $\left|\frac {a_{n+1}}{a_n}\right|\le c_n$ for each n and $c_n<1$. May we conclude that $\left|\frac ...
1
vote
1answer
18 views

Two combinatorics questions

I would like help on these questions please: 1). How many numbers between 1 and 99999 have a digit sum of 7? 2). How many numbers between 1 and 100 are prime? In 1 I thought of representing all ...
1
vote
0answers
23 views

To construct a right triangle given the hypotenuse and sum of two legs [duplicate]

NOTE: I want a hint only. A compass and a straightedge construction:Given a hypotenuse and the sum of lengths of the legs,we need to construct a right triangle. MY TRY: From any ray $BE$, ,let ...
-1
votes
0answers
10 views

Hybrid encryption RSA with AES?

A common variant of textbook RSA is the following: During key generation, the modulus N is chosen as usual. We chose e as e := 3 (instead of random). Then d is chosen with ed ≡ 1 mod φ ( N ) (as ...
3
votes
0answers
55 views

L'Hopital quicky

suppose L'Hopital applies and $$\lim_{x\to\infty}\frac{f(x)}{g(x)} = \lim\frac{f'(x)}{g'(x)}$$ under what conditions is it true then that $$\lim_{x\to\infty}\frac{\frac{f(x)}{g(x)} }{ ...
0
votes
1answer
17 views

Constructing nontrivial $\mathbb{Z}$-bilinear map from $\mathbb{R} \times (\mathbb{R} / \mathbb{Z})$

I'm trying to show $\mathbb{R} \otimes_\mathbb{Z} (\mathbb{R} / \mathbb{Z})$ is nontrivial, where my tensor product is defined using the universal property. This problem can be easily reduced ...
6
votes
4answers
73 views

A question about inequality ${(n+1)\over e^n}^n<n!$

How to prove the inequality $${(n+1)\over e^n}^n<n!$$ I have tried mathematical induction, but it doesn't work! Are there other methods to solve it?
1
vote
1answer
27 views

Recurrence relation with generating function problem

I've got a recurrence problem that I'm close to solving, but having trouble with finishing up. Solve the following recurrence relation using generating functions: $$g_n = g_{n-1} + g_{n-2} + ...