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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12 views

Using Polar Integrals to find Volume of surface

Here's the Question and the work that I've done so far to solve it: Use polar coordinates to find the volume of the given solid. Enclosed by the hyperboloid $ −x^2 − y^2 + z^2 = 61$ and the plane $z ...
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3answers
18 views

X :compact and continuous function $f(x)\neq x$

Let (X,d) be a compact metric space and $f:X\to X$ be a continuous function such that $f(x)\neq x,\: \forall x\in X$. Prove that there exists $\epsilon > 0$ such that $d(x, f(x))>\epsilon$, for ...
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1answer
21 views

Convergence parameter: Find the value of $p>0$ for which the series converge

For the sum for $k=2$ to infinity: $$\frac{\ln k}{k^p}\ $$ The textbook says the answer is $p>1$.
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0answers
10 views

Curvature, torsion.

Question A space curve is given parametrically by x = t + (t^3)/3 y = t - (t^3)/3 z = t^2 Starting from the Frenet-Serret formulas d(t-hat)/ds = k(n-hat) d(b-hat)/ds = -(tau)(n-hat) Find the ...
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1answer
12 views

Show a set is in the null space of the transpose of A

I'm trying to show that for $A \in F^{MxN}$ (a matrix with the nth column $a_n$) the following set is in the null space of $A^T$, that is: $N(A^T) = \{x \in \Re^M : A^Tx = 0\} = \{x \in F^M : ...
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1answer
21 views

Question on sequence space (as a linear space)

Let $X$ be the space $\ell_\infty$ of all bounded sequences of real scalars. If $Y$ is the set of all $x\in X$ that have bounded partial sums (1) Can I say $Y$ is a linear space (as a subspace of ...
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0answers
9 views

Show $W_{\infty}$ is not tail measurable but {$W_{\infty}=0$} is

The random walk: ({$\omega_{n}$},$\mathbb{P}$) simple random walk on d-dimensional integer lattice $\mathbb{Z}^{d}$ and the random environment: $\eta$={$\eta(n,x):n\in\mathbb{N}, x\in \mathbb{Z}^{d}$} ...
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2answers
20 views

finding a boolean function with specific property

The problem I am trying to solve is: Prove that not every boolean function is equal to a boolean function constructed by only using $\wedge$ and $\vee$. My solution is $$\left(p\wedge\thicksim ...
2
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1answer
40 views

Twin Prime conjecture current status

Can someone help me with a link to read about the status of the Twin Prime conjecture. I have browse on the internet and have read some articles but still I have no clue of the updated status of Twin ...
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2answers
19 views

Is sequence convergent in subspace of compact metric space?

Problem is as follow. Let X be a compact metric space and A be a closed subset of X. Prove that every sequence in A has a convergent (note: convergent in A) subsequence. It is from my note. My ...
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1answer
43 views

What is the statement |x+y|≤|x|+|y| saying

|x+y|≤|x|+|y| I know that |x| means the cardinality of x for example. But it looks to me like its saying the cardinality of x plus y is less then or equal to the ...
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1answer
35 views

Proving that $\frac 1 2 t^3+\frac 1 2 t, (t\in \mathbb N)$ will always be a whole number

Is there any way to show that $\dfrac 1 2 t^3+\dfrac 1 2 t$ will always be a whole number? Assuming that t is always a whole number greater than or equal to one? If i think about it logically it seems ...
0
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1answer
8 views

Proving Boolean Function

Can anyone help me if I am right....!! The Question Reads: Prove that not every boolean function is equal to a boolean function constructed by only using ^ and v. This is my answer by the double ...
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0answers
10 views

How to do This Torque problem? [on hold]

The answer for the Question is 0.15kg. Is there any problem with the question because I cant seem to solve it. You can try working backwards.
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0answers
7 views

For heat and mass transfer of infinite slab, how to verify the slab is infinite for one-dimension?

For one dimensional heat and mass transfer of infinite slab, how to verify the slab is infinite as there is no such infinite thing in reality? It there a specific value like aspect ratio L/D or ...
0
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0answers
11 views

Probability of $t$-test rejecting null when $X$ and $Y$ are Cauchy

I have a homework problem that states: The Wilcoxon test is valid for a broad class of distributions, meaning that the actual type I error is as specified. Note that the $t$-test does not have this ...
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1answer
19 views

calculate an approximate value of integral

Calculate an approximate value of integral : $$\int_1^{3.4}\frac {2}{\sqrt{x}+x}$$ Take 8-subintervals $n=8$ by using trapezoidal rule How can I calculate this?
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0answers
9 views

Franck and Hertz graph function

I need a function whom graph is the following (the Franck and Hertz experiment graph): Currently I wrote the following function: ...
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1answer
39 views

Counterexamples in set theory [duplicate]

I have a question which states that: Prove or find a counterexample of sets $A, B, C$ such that $A\cap B = B\cap C = A\cap C =\emptyset$ but $A\cap B\cap C \neq\emptyset$ I know ...
3
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0answers
40 views

Solving integral $\int\frac{\sin x}{1+x\cos x}dx$

How I can find the anti-derivative? $$\int\frac{\sin x}{1+x\cos x}dx$$
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2answers
24 views

A question about limsup and limif

Could you please help me understand this question: Suppose $a_n$ is bounded sequence and $A<\liminf a_n$, $B>\limsup a_n$. Prove : $A<a_n<B$ for all n>N. It seems to me to simple to be ...
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2answers
23 views

Calculate the following sequence $\sum_{n=0}^{+\infty }\left ( -\dfrac{1}{4\alpha } \right )^{n}\dfrac{ (2n)!}{n!},\; \alpha >0$

Calculate the following sequence $$\sum_{n=0}^{+\infty }\left ( -\dfrac{1}{4\alpha } \right )^{n}\dfrac{ (2n)!}{n!},\; \alpha >0$$
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0answers
14 views

Real analysis question involving inhomogenous linear ODE

So I had another problem like this but the ODE was homogenous, now there is a non zero right side. I completed part (i), $\large c(x) = \int \frac{b(x)}{g(x)} dx$. I am stuck on (ii) and the rest. ...
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0answers
20 views

probability of covariance proof [duplicate]

I started with covariance formula and then I got stuck. I don't know how to do further steps Let $X$ denote a random variable and $Y = g(X)$ where $g$ is increasing (on $\operatorname{Ran}(X)$). Show ...
2
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1answer
36 views

Determine whether the series converge (adding fractions)

$$\frac{1}{1 \cdot 3} + \frac{1}{3 \cdot 5} + \frac{1}{5 \cdot 7} + ... $$ Help convert to summation. Not sure what test to use.
2
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1answer
25 views

How does negating a matrix affect its eigenvalues?

I'm working on the following problem: "If $Ax = \lambda x$, find an eigenvalue and an eigenvector of $e^{At}$ and also of $-e^{-At}$." So far, I have figured that $e^{\lambda t}$ will be an ...
0
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1answer
24 views

Use comparison or limit comparison test to determine whether the series converge [on hold]

Summation symbol $$\frac{(k^2+1)^{1/3}}{(k^3+2)^{1/2}} \ .$$
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0answers
11 views

Finding characteristic roots and characteristic vectors

V is a two-dimensional vector space over the field of real numbers, with a basis $v_1, v_2$. Find the characteristic roots and corresponding characteristic vectors for T defined by $v_1(T) = v_1 + ...
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0answers
7 views

Calculate the auto correlations and mean of the following time series [on hold]

$$Y)t=0.7+0.4Y_t−1+0.12Y_t-2+Z_t$$ calculate $E(Y_t)$ Also calculate the auto correlations $p_1-p_4$.
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2answers
12 views

Time series analysis. Understanding the arma model [on hold]

Determine wether $Y_t= 0.7 + 0.4Y_{t-1} + 0.12Y_{t-2} +Z_t$ is a stationary process.
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2answers
20 views

radius of 6 Circles inside a bigger Cricle

6 identical circles are placed inside a bigger circle of radius R. What is the formula to find the radius r of the 6 identical circles? This is what I found but I can't find the formula, look at ...
1
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2answers
25 views

Help solving this proportion

$$3n(n-5) = n-6(3n+1)$$ I can distribute the $3n(1n-5)$, but I don't know how to distribute the $1n-6(3n + 1)$
2
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1answer
17 views

Find the first two iteration of the Jacobi method for the following linear system, using $x^{(0)} = 0$

$$3x_{1} - x_{2} + x_{3} = 1,$$ $$3x_{1} + 6x_{2} + 2x_{3} = 0,$$ $$3x_{1}+3x_{2}+7x_{3} = 4$$ So, from this I got T = \begin{bmatrix} 0 & \frac{-1}{3} & \frac{1}{3} ...
1
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2answers
26 views

fourier series analysis, show that for every integer n, using euler's formulas relating trigonometric and exponential functions

Show that for every integer $n$, $$\int_0^{\pi} \cos nt~\sin t~\mathrm{d}t = \begin{cases} \dfrac{2}{1-n^2} & \text{if } n \text{ is even} \\[10pt] 0 &\text{if } n \text{ is odd} ...
0
votes
1answer
30 views

Find values so matrix not invertible?

$$ \begin{pmatrix} 2 & 4 & k \\ 1 & 3 & 2 \\ 3 & k & 9 \\ \end{pmatrix} $$ For what values of $k$ is the above matrix not invertible. Need help. Don't know where to ...
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5answers
49 views

Find the solution to the recurrence relation: $a_n=3a_{n-1}+1; a_0=1$

$$a_n=3a_{n-1}+1; a_0=1$$ The book has the answer as: $$\frac{3^{n+1}-1}{2}$$ However, I have the answer as: $$\frac{3^{n}-1}{2}$$ Based on: Which one is correct? Using backwards substitution ...
0
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0answers
9 views

finding distribution based on 1st and 2nd moment

I am to determine the unbiased probability densities $p_1 (x)$ and $p_2 (x)$ given the only constraints that the magnitude of the first moment of p1 is fixed (i.e. $<x> = a$ for some real a) and ...
0
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0answers
12 views

Show that the D'Alembert operator is a formally self-adjoint operator.

A problem asking me to prove that the D'Alembert operator, defined as: $$\hat\Box^2=\frac{\partial^2}{\partial t^2}-\bigtriangledown^2$$ is a formally self-adjoint operator. To demonstrate the ...
2
votes
3answers
62 views

Lagrange multipliers from hell

I was asked to solve this question, decided to try and solve it with lagrange multipliers as I see no other way: "Find the closest and furthest points on the circle made from the intersection of the ...
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votes
0answers
24 views

Finding the solutions of an equation

I've got a huge problem that I haven't been able to understand , no matter how hard I tried . Let $f(x)$ be a random real function , and $f(x)=m$ an equation. The question is : To which interval does ...
1
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1answer
22 views

Continuous-time Markov Question

I have a question about a continuous-time Markov process on the discrete space. I am given the generator and asked for find the expected time the Markov process needs to get back to state 3, given ...
1
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0answers
21 views

Parametrizing a “surface” that is actually a curve, then integrating to find the area?

Find a parametrization of the surface $x^2-y^2=1$, where $x>0$, $-1 \leq y \leq1$ and $0 \leq z \leq 1$. Use your answer to express the area of the surface as an integral. I'm confused because ...
1
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1answer
36 views

Induction: Sum of the squares of 6 consecutive natural numbers

Define for every natural n: $$ a_{n}=\sum\limits_{i=0}^{5}(n+i)^2$$ in other words, $\ a_n$ is the sum of the squares of 6 consecutive natural numbers, the first number is $n^2$ and the last is ...
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2answers
17 views

Linear Algebra: show $\sum_{m=1}^{M} a_m x_m = 0$ is a subspace

I have a problem that I can't get my head around. It says that a is any vector in $\mathbb{F}^M$ and to verify (by the three properties of subspaces) that $\sum_{m=1}^{M} a_{m}x_{m} =0$ is a subspace ...
0
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1answer
51 views

Field of algebraic numbers over $\mathbb{Q}$

Let $F$ be the field of algebraic numbers over $\mathbb{Q}$. I do remember that this means $F$ is a field extension of rationals over $\mathbb{Q}$. How do I show that the field extension of $F$ is ...
0
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2answers
41 views

Integrating $g: ℝ^2\to ℝ$ - Order of Integration

The problem: My work: I found the two integrals to be equal to each other, which is clearly not the desired result. Any suggestions/pointers? Thanks!
1
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1answer
25 views

Which means adjoint problem of a differential equation?

I wanted to know if anyone can help me with the following problem: Get the adjoint problem (differential equation and boundary conditions) for the problem given by: $$\frac{d^2 u}{dx^2}=f(x)$$ ...
0
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1answer
35 views

complex inner product from the real

Let $V$ be a real inner product space. If $W=V\times V$ with the operations $(u_1,v_1)+(u_2,v_2)=(u_1+u_2,v_1+v_2)$ and $(\alpha +i\beta)(u,v)=(\alpha u-\beta v,\alpha v+\beta u)$, where $u, ...
0
votes
1answer
39 views

Implication or Bidirectional in “x is a Prime”

I have a question regarding First Order Logic. I have to express the property "x is a Prime" in First Order logic. So far I have the following solution: $\forall x\;Prime(x) \leftrightarrow \neg ...
0
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3answers
26 views

How to get from $3\int_{-1}^0 (x^3-x) dx \,\,\,- \,\,\, 3\int_0^1 (x^3-x) dx$ to $6\int_{-1}^0(x^3-x)dx$?

Homework problem: Set up the definite integral that gives the area of the region. Two functions are given: $y_1 = 3(x^3-x)$ $y2 = 0$ The graph of $y1$ runs from x=-1 to x=1. I've gotten this ...