# 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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### Topology and Arithmetic Progressions

I'm self-studying from "Elementary Topology Problem Textbook" by O.Ya.Viro et al. This is Exercise 2.Lx : Consider the following property of a subset $F$ of the set $\mathbb{N}$ of positive ...
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### solving system of equations involving basic trigonometry

I am trying to solve the following system of equations: $$\frac{kq^2}{d}=mg(L-L\cos(α))+\frac{kq^2}{r}$$ $$\sin(α)=\frac{x}{L}$$ $$r^2=(L-L\cos(α))^2+(x+d)^2$$ $$\frac{kq^2}{r^2} cos (β) = Tsin(a)$$ ...
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### Problems with Simplifying Using Factoring of Binomial Expressions

I am running into problems simplifying using factoring of binomial expressions. The problem at hand is this: $(x-1)^3*(2x-3)-(2x+12)*(x-1)^2$ I first expanded the left side of the minus sign, like ...
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### How to get numbers with distinct digits within some range?

I have a little program I'm working on for my project (a simple practice in school), part of the program is that it should receive input composed of an array of 7 digit (or less) numbers which should ...
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### solving system of equations(nonlinear)

I am trying to solve the following system of equations: $$\frac{kq^2}{d}=mg(L-L\cos(t))+\frac{kq^2}{r}$$ $$\sin(t)=\frac{x}{L}$$ $$r^2=(L-L\cos(t))^2+(x+d)^2$$ The parameters are: $k,L,d,q,m,g$ The ...
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### Fourier Transform of Poisson Equation

While trying to solve the Poisson Equation by using Green's Function I have to Fourier transform the equation i.e $$-\nabla^{2}\phi(r)=\rho(r).$$ In the book after Fourier transform, the solution ...
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### solving the equation

let there be a function $f(x)= \ln x-kx^2, k>0$ determine for whihc values of $k$ ,the equation $f(x)=0.5$ has a single solution; attemp to solve: $$0.5 = \ln x-kx^2$$ $$kx^2 +0.5 = \ln x$$ ...
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### Show that $rank(A)+rank(B) \leq n$, when $A,B$ are $2$ matrices of size $n \times n$, and $AB=0$

Question from homework in Linear Algebra: Let $A,B$ be two matrices of size $n \times n$ such that $AB=0$. Show that: $rank(A) + rank(B) \le n$ . It probably has something to do with the dim of ...
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### Time and work aptitude problem for CAT preparation [on hold]

$A$ can do a job in $10$ days, $B$ in $12$ days and $C$ in $15$ days. They all start working together but $A$ leaves after $2$ days and $B$ leaves $3$ days before the job is completed (i.e. $C$ works ...
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### Matrix Rank calculation

I have a matrix A . A can be written as A=B+D. I know rank of B. It is 3. Is it possible for A to have ranks $<3$ . If so please prove.
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### Need help with statistics homework

The financial department at a large hospital would like to estimate the average outstanding balance owed by patients who have not paid their bills in full. In order for the interval to be useful in ...
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(a) Determine the radius of convergence to the power series $f(x)= \displaystyle\sum\limits_{n=0}^\infty \frac{(2n)!}{(n!)^2}x^n$. Should I use the ratio test? (b) Assume the validity of the ...
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### Can we deduce that $X$ is $\sigma-$compact? [on hold]

Assume that a quotient space of the space $X$ is compact. Can we deduce that $X$ is $\sigma-$compact?
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### Using Chain Rule and Product Rule to find derivative

I have to find the derivative of the following function: $$f(x) = (x^3+ 4)(4x^5 + 2x − 5)^{1/2}$$ To start solving this, I've dissected the equation and realize that I must use the product and chain ...
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### Doubts on locus and its equation

Find the equation to the locus of a point which is col-linear with points M(a,0) and N(0,b) Answer is:- x/a + y/b How i tried to find the solution:- P is a point whose assigned coordinates are (x,y) ...
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### Is S a group under matrix addition

Another matrix question! Let $$S=\{A \in M_2(\mathbb{R}):f(A)=0\}\text{ and }f\left(\begin{bmatrix}a&b\\c&d \end{bmatrix}\right)=b$$ Is S a group under matrix addition. Either prove that ...
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