# Tagged Questions

This tag is in the process of being removed; please do not add this tag to new questions. Rather, use tags that describe the subject of your question, like [calculus], [algebra-precalculus], etc. For more information, see meta: http://meta.math.stackexchange.com/questions/16425.

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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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### 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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### 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 [closed]

$A$ 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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### 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? [closed]

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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### How do I find the sum of the series?

$$\sum_{k=1}^{7}40 \left( \frac{1}{2}\right)^{k-1} = \frac{635}{8}$$ The image of the orginial eqn is on the link above and so is the answer, but I need help in how to solve it. when I did solve it I ...
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### A circle wheel 28 inches in diameter rotates (moves) the same number of inches per second

A circle wheel 28 inches in diameter rotates (moves) the same number of inches per second as a circular wheel 35 inches in diameter. If the smaller wheel makes x revolutions per second, how many ...
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### How does $\frac{t^2}{t+1}$ equal $t-1+\frac{1}{t+1}$?

I do the long division: 1: t+1 goes into $t^2$ t times 2: Subtract $t^2$ + 1 from $t^2$ and get -1 3: Answer: t - $\frac{1}{t+1}$ Am I missing something here?
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### How would I solve these types of equations

Going back to college and been a few years since I've had to do any algebra/trig. How would I go about solving these types of equations and do they have a name? a(y-b)=by+c then, except when the ...
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### If $a^2$ divides $b^2$, then $a$ divides $b$

Let $a$ and $b$ be positive integers. Prove that: If $a^2$ divides $b^2$, then $a$ divides $b$. Context: the lecturer wrote this up in my notes without proving it, but I can't seem to figure out ...
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### Word Problem, Calculus estimation homework

Roger runs a marathon. His friend Jeff rides behind him on a bicycle and clocks his speed every 15 minutes. Roger starts out strong, but after an hour and a half he is so exhausted that he has to ...
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### How do I find the sum of the infinite geometric series?

$$2/3-2/9+2/27-2/81+\cdots$$ The formula is $$\mathrm{sum}= \frac{A_g}{1-r}\,.$$ To find the ratio, I did the following: $$r=\frac29\Big/\frac23$$ Then got: $$\frac29 \cdot \frac32= \frac13=r$$ and ...
I don't know if the anwser to my question is obvious because I cannot find any explanation anywhere on google. Question The blue region $R$ is bounded by the curve C with equation \$r^{2} = ...