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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2answers
53 views

Cardinality, Finite Sets Proof

Let $S$ and $T$ be finite sets. Prove that if $|T-S| = |S-T|$, then $|S| = |T|$.
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3answers
96 views

Topologist's Comb

I've already posted another question because I've got an assignment to finish (still got half a day left :/) and had to realise that I'm a bit lost. Anyway, the question has to do with the following ...
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0answers
20 views

Confidence Interval [on hold]

The data for this problem is in the image below. I attempted this problem in the work shown above. I understand the formula to find the confidence interval for this data, but I am stuck at a certain ...
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2answers
35 views

Proving That a $1 \times 1$ Matrix has a Rank of $1$

I have an assignment that asks me to prove something but I've hit a roadblock. Let $u$ be a $3 \times 1$ matrix with $u_{1}$, $u_{2}$, and $u_{3}$. Let $v$ be a $3 \times 1$ matrix with $v_{1}, ...
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0answers
44 views

Proof on Prime Numbers

Please can someone explain to me the meaning of the this question and what does it asked for. For real I do not know where to start. Can someone just give me a hint so I can do it myself and will post ...
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0answers
33 views

Irrational numbers prove or find a counter example

Please give me feedback on my answer to this question: Question:Prove of find a counterexample: For all real numbers x and y it holds that x+y is irrational if, only if, both x and y are irrational. ...
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1answer
34 views

Distance of a point to a plane

Let $T$ be the plane $x+2y+3z=11$. Find the shortest distance $d$ from the point $P=(2, 4, 5)$ to $T$, and the point $Q$ in $T$ that is closest to $P$. This is just one of the questions on my ...
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2answers
30 views

Find the parameter M

m(x+1)=e^|x| , m is a real number .Find the interval to which the parameter 'm' belongs , so that the previous equation has exactly two different solutions . Any idea how to approach this kind of ...
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0answers
35 views

Consecutive natural numbers [duplicate]

Please I want to know what is the most appropriate expression that if it is asked to find the counterexample of "The product of any three consecutive natural numbers is divisible by 9" My expression ...
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1answer
34 views

probability of playing music player on shuffle and listening to every song.

I have a few problems I am trying to work out but I am not totally confident in my answers: The problem is such: Suppose you have a playlist consisting of four songs. You play your playlist in ...
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0answers
16 views

Finding the volume of water on the cylinder

A cylindrical geyser of radius 21cm and length 50cm is placed with its curved surface on a horizontal ground.It is filled partially with water and the segment formed by 120 degrees and 10.5cm below ...
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1answer
29 views

$E[\hat{\theta}_{MME}] = E[\frac{1- 2\overline{y}}{\overline{y}-1}] = \int_0^1 \frac{1- 2\overline{y}}{\overline{y}-1}(\theta+1)y^\theta dy$..?

Let $Y_1, Y_2,\dots , Y_n$ denote a random sample from the probability density function $$f (y | θ)=\begin{cases} (θ + 1)y^θ, & 0 < y < 1; θ > −1,\\ 0 ,& ...
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0answers
9 views

How we can show that Dirichlet function is measurable with respect to borelian algebra? [on hold]

Satisfying the definition of measurability? But, how we can show it?
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1answer
31 views

Gaussian vectors and covariance matrix.

The following is a part of a question I was given in stochastic processes course. It goes like this - I am given a series of gaussian iid random variables $\{V_i\}_{i=1}^N$ , the variable $X_0 \sim ...
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0answers
35 views

Geometry of Curves and Surfaces

The following is a question regarding Elementary Geometry of Differentiable Curves. Venture a guess of the number of irregular values of $t$ for the trochoid with $h = 1, \lambda = \frac{m}{n}$, ...
2
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2answers
43 views

Prove that integral of continuous function is continuously differentiable

Lots of things going on here. I immediately know that $F(x)$ does exist since $f$ is riemann integrable due to the fact that it is continuous. First I need to show that $F$ is continuous, then find ...
2
votes
2answers
43 views

Is it possible to triangularize a matrix only by adding scalar multiples of rows to each other?

I am working on showing if $B$ is a $s \times s$ matrix, $D$ is a $t \times t$ matrix, $C$ is a $s \times t$ matrix, and $0$ is a $t \times s$ zero matrix, then $\det(A)=\det(B)\det(D)$, where $$A = ...
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1answer
19 views

Logic and consistency

This is a past exam questions, and I was wondering if my thinking was correct If it is satisfiable, it is consistent We can construct a truth table and verify if there exist a truth value it is ...
1
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1answer
18 views

Computing fractions Weierstrass curves and DLP problem

I am preparing for a crypto exam by making an old practise exam. I got stuck on the following assignment. I got this weierstrass curve The curve $y^2 = x^3$ is not an elliptic curve over $F_{71}$ but ...
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1answer
27 views

So-called Artin-Schreier Extension

Let $F$ be a field of characteristic $p$. Let $K$ be a cyclic extension of $F$ of degree $p$. Prove that $K=F(\alpha)$ where $\alpha$ is a root of the polynomial $p(x) = x^{p} - x - a$ for $a \in ...
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2answers
38 views

Find the generator of Markov Process

Homework question: Consider the Markov process $X_t=B_t-t^2+t$ where $B_t$ is the Brownian motion. Find the generator $Q$ of this process. I am completely confused how to find the generator for ...
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3answers
38 views

Functions definition + question

Am I correct in saying that for Functions, the below is the correct definition: For each value of x in the domain there is only one value of y in the range. Hence, the picture below means that it is ...
2
votes
4answers
66 views

Second partial derivative test is inconclusive

I am trying to find the critical points of the function: $f(x,y)=2x^4-3x^2y+y^2$ and find the Max, Min and saddle points. What I've done so far is: $f_x=8x^3-6xy=0 , f_y=-3x^2+2y=0 , ...
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1answer
24 views

vector projection on to subspaces

If given a subspace of R4 that is spanned by the set of orthogonal vectors W =span { (0,1,1,1),(1,1,0,-1) }. How to find the projection of a vector u onto the subspace? if u = (2,1,2,0)? What I have ...
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6answers
205 views

Prove that $\sum_{k=0}^n k^2{n \choose k} = {(n+n^2)2^{n-2}}$

Prove that: $$\sum_{k=0}^n k^2{n \choose k} = {(n+n^2)2^{n-2}}$$ i know that: $$\sum_{k=0}^n {n \choose k} = {2^n}$$ how to get the (n + n^2)?
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1answer
22 views

What's wrong with this recursion of counting codes of length $n$ formed by $a$, $b$, and $c$ such that no three consecutive letters are distinct

I found the following problem in a combinatorics book and gave it a try. Let $B_n$ denote the set of codes of length $n$ formed by using the letters $a$, $b$, and $c$, none of which contains three ...
1
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1answer
26 views

Die Question with Random Variables

I have a homework question: Roll a fair die, and let d be contained in $\{1,2,3,4,5,6\}$ . Then sample $d$ independent uniform random variables on $[0,1]$ and let $Y$ be the maximal of these random ...
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0answers
19 views

Distribution and Laplace transform

I'm having trouble understanding this problem from Resnick's Adventures in Stochastic Processes: The problem says: Suppose $F$ is a distribution of a positive random variable and $p_k \geq 0, ...
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3answers
60 views

Are curves closed in $\mathbb{R}\times \mathbb{R}$ with the standard topology?

Given the graph of the curve $y=\frac{1}{x}$, can we determine if the curve is closed or open in $\mathbb{R}^{2}$ with the standard topology?
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2answers
42 views

Vectors Question

I have a question regarding Vectors; Find the equation of the plane perpendicular to the vector $\vec{n}\space=(2,3,6)$ and which goes through the point $ A(1,5,3)$. (A cartesian and parametric ...
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2answers
63 views

Fundamental Group of Punctured Plane

What is the fundamental group of $(\mathbb{C} \setminus {\{0\}})~/~\{e,a\}$, where $e$ is the identity homeomorphism and $az = -\bar{z}$? Clearly this is homeomorphic to the half cylinder , which is ...
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0answers
22 views

Edges and Vertices in relation to Free subgroups

Let $\Gamma$ be a finite connected graph (1-dimensional simplicial complex), with $V ( \Gamma)$ vertices and $E(\Gamma )$ edges (1-simplices). Show that $\pi_1(\Gamma, v)$ is a free group with ...
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1answer
17 views

How do I calculate the area under a curve using the midpoints of rectangles?

I figured out how to calculate the area under the curve from the Right endpoint and Left endpoints, but I can't figure out how to calculate it using the midpoints. Especially when it says $M_3$. Ill ...
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7answers
287 views

Factoring a fourth degree polynomial

How would I go about factoring $$x^4-x^2-12=0$$ I'm supposed to find the roots of this without the use of calculators (well we do have TI's but some don't so I suppose they're assuming we can solve ...
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1answer
33 views

Analysis of stability of a linearized ODE with a periodic solution

I am asked to find the stability of the following ODE: \begin{equation*} \dot{y} = y^{2} + 2\cos(t)\sin(t) - \sin^{4}(t) \end{equation*} by linearizing around a particular solution $\eta = ...
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1answer
22 views

Help with if x = y at z the what does x equal if q [on hold]

If it takes 30 minutes to get to your destination at 60 mph then how longs does it take at 70 mph?
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2answers
41 views

Area under the curve $f(x) = \sin x$

Find the area under the curve $f(x) = \sin x$ on the interval $[0, \pi]$ if $\sin x \ge 0$ My handbook give this as $$\int_0^\pi \sin x \space dx = (\cos \pi) - (\cos 0) = (-1) - (-1) = 2$$ what ...
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0answers
18 views

Discontinuity of principal argument in nonpositive real axis

Let $Arg(z)$ be principal argument function defined in branch $(-\pi, \pi]$. Prove that $Arg(z)$ is discontinuous in every point in nonpositive real axis. "Solution": Let $z_0$ be a point on the ...
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0answers
17 views

Stochastic Process Calculus [on hold]

I have a question about the stochastic process calculus. Is there anyone could help me solve it? Thanks!
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3answers
31 views

How to find the $n$ zeros of $\displaystyle1+z^n$?

How to find the $n$ zeros of $1+z^n$?
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2answers
37 views

Range for the function $f(x) = 3x + 2$ with domain $x > 0$

The function below is defined for continuous domains Sketch the graph and state the range of the function Question: $f(x) = 3x + 2$ for the domain $\{x \in \mathbb{R} : x > 0 \}$ The straight ...
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4answers
43 views

How to calculate this area in $\mathbb{R}^2$?

Write the area $D$ as the union of regions. Then, calculate $$\int\int_Rxy\textrm{d}A.$$ First of all I do not get a lot of parameters because they are not defined explicitly (like what is $A$? what ...
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1answer
32 views

Applied Max/Min [on hold]

Please show work, thank you. A) Find the dimensions of the rectangle with the greatest area that can be built so the base of the rectangle is on the $x$-axis between $0$ and $1$ ( $0\leq x \leq 1$ ) ...
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1answer
11 views

Derived Distribution - Joint Probability

I am trying to find the 1. P(Z < z) :: 0 < z < 1 2. P(Z < z) :: z > 1 When ...
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2answers
46 views

what is the maximum number of non loop edges that can exist in an undirected graph

please tell me a equation to find maximum number of non loop edges that can exist in an undirected graph. for example if vertices are 10 then how many non loop edges can exist?
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3answers
50 views

Finding the limit of a sequence by diagonalising a matrix

Consider the sequence described by: $\frac11 , \frac32 , \frac75 , ... ,\frac {a_{n}}{b_{n}}$ where $ a_{n+1} = a_n +2b_n $ and $b_{n+1} = a_n+b_n$ Find a matrix $A$ such that ...
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0answers
13 views

Poisson distribution confidence intervals and hypothesis

I think I have A and B correct but I have troubles with parts C and D. A) What is the p value if we suppose the following : finding golden apples in a tree follows a Poisson P(2) with $\lambda = 2$ ? ...
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0answers
23 views

Linear Programming Newspaper and Tv Commercial

Tim is the head of marketing division. Tim has the annual marketing budget of $200,000. Some of the budget will be spent on TV commercial and some of the budget will be spent on newspaper ads. The ...
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0answers
21 views

Maths Information about demo [on hold]

Good evening friend . Am an MCA guy. I have to give a demo in maths for 10th class students. Which topic I have to choose?
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0answers
11 views

Linear Programming Question Phone Survey Project

You are the leader of a market research team to complete a phone survey project. The project requires responses from at least 120 married women, 150 married men, 110 single women and 100 single ...