# Tagged Questions

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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### $\ell^1(\mathbb{Z})$ with discrete convolution and the Gelfand transform

I want to show the following: $\ell^1(\mathbb{Z})$ with the discrete convolution $*$ is isomorphic to a subalgebra of $C(T)$ where $T = \{z \in \mathbb{C} : |z| = 1\}$. The following theorem ...
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### Homoclinic orbit Hamiltonian system

The question is for which $a \in \mathbb{R}$ the system: $x'' + x - x^3 + a = 0$, has a homoclinic orbit. I let $y = x'$ so the system becomes: $x' = y$ $y' = x^3 - x - a$ and determined the ...
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### Poisson Processes and Equally Likely

A typing agency employs 2 typists. The average number of errors per article is 3 when typed by the first typist and 4.2 when typed by the second. If your article is equally likely to be typed by ...
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### Noninital ordinal of a set

If $\mathbb R$ is well ordered by an order $\ll$ such that the ordinal of R and that order $\alpha$ is not initial. How can I show that there is a closed interval $[a,b]$ ($a<b$) such that the ...
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### In a standard deck of 52 cards, how many different 7 card hands are there in which 3 cards are hearts and the other 4 are of different suits?

I know there are 13 cards in each suit, so that would mean I needed 3 of the 13 hearts or 13 P 3, then the other 4 would need to be out of 39 so it would be 39 P 4 but I don't know where to go from ...
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### Proving AB,AC perpendicular to each other when vectors are median

I want to prove this claim: Triangle ABC with $A(2,4,6),B(6,2,2),C(0,0,0)$ median, AC and BC perpendicular to each other. what I did is to the $AB,BC$ make a dot product and thought it will be ...
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### Find $x$ such that $x-15\%x=950$.

I have the following problem: Find $x$ such that: $$x - 15\%x = 950$$ When I do this, $950 + 15% = 1092.5$ but when $1092.5 - 15% = 928.625$ which is not correct. So, what is the correct way to ...
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### Trying to prove a limit of a simple multi case function

Full disclosure: This is my attempt at solving a homework assignment Another full disclosure: This is my first time using LaTeX, so pardon any errors We were asked to prove / disprove the existance ...
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### counting double

lets say there are 42 balls in an urn, 3 green balls, 6 orange balls, 33 red ones. a) What is the probability of getting all 3 colours? given that you are taking 4 balls my first intuition ...
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### Pitch Graph Plane or Planar? [on hold]

Is a graph of pitch and frequency plane or planar? Does connectivity between two 12-tone classes decompose to K3, 3 subsets?
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This is homework. I have $\displaystyle \qquad S\frac{dh(t)}{dt} + \frac{1}{R}\sqrt{h(t)} = q(t)$ and need to linearize it. Setting all derivatives to zero, I get the steady-staty value of $h - ... 2answers 275 views ### How many prime ideals does$\mathbb Q[x]/(x^m -1)$have? (multiple choice) Let$m$be a positive integer, and$a_m$denote number of distinct prime ideals of$\mathbb Q[x]/(x^m -1)$. Then which of the following are true?$a_4=2a_4=3a_5=2a_5=3$0answers 20 views ### How to apply Successive Overrelaxation (SOR) method to equation with boundary conditions? I have got equation:$U_{xx} + U_{yy} = sin\pi x * sin \pi y (x + y); 0\le x \le 1; 0 \le y \le 1$with conditions$U(x, 0) = U(x, 1) = U(0, y) = U(1, y) = 0$Main part SOR formula:$u^*_{j, l} = ...
chebyshev polynomials are defined as such: $T_n(x)=cos(n*arccos(x))$ I'm asked to show that $deg(T_j(x))=j$ and that $T_0,T_1,T_2,...,T_n$ are an orthogonal basis of $\mathbb R_n[x]$. I think I can ...
There is an isomorphism between $P_n(x) = \{p(x) : p(x) = a_0 + a_1x + a_2x^2 +\ldots+ a_nx^n,\ \forall a_i \in \Bbb R\}$ and $\Bbb R^{n+1}$, in the sense that $a_0 + a_1x + a_2x^2 + ... ... 1answer 52 views ### Grade 11 functions I need help with three questions for my homework. Any answers would be appreciated. Please try to explain steps or just show them, as I would like to know how to do them. Thanks. Determine if the ... 1answer 80 views ### A curious problem about Lebesgue measure. The Problem: Let$(B(x_{m},0.5))_{m}$be a sequence of disjoint open discs in$\mathbb{R}^{2}$centered in$x_{m}$and with radius 0.5. Let$\psi(n)$be the number of these discs contained in the ... 4answers 43 views ### Evaluate:$\int \frac{1}{(x+a)(x+b)}\$
Evaluate: $$\int \frac{1}{(x+a)(x+b)}$$ My attempt: $$\int \frac{1}{(x+a)(x+b)} = \frac{A}{x+a} + \frac{B}{x+b}$$ $$1 = A(x+b) + B(x+a)$$ $$x = -b$$ $$1 = A(-b + b) + B(-b + a)$$ $$1 = B(-b + a)$$ ...