# All Questions

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### Calculate and Forecast Churn Rate of Members

I need to estimate the total number of times users logged in to an app, cumulatively at the end of a year. If I have a mobile app, and 100,000 people download it. And they only use it once, then the ...
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### Some questions concerning continuity and relations

A lot of equivalent conditions for functions between topological spaces $$X\overset f\longrightarrow Y$$ is proved on this site. Here some of them formulated from the perspective of 'relations': ...
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### The effect of exchanging two rows on the determinant of a matrix

Answer: is -6 because of the following:
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### Naive proof that $\sum_{n=1}^{N-1}\cos(2\pi\frac{n}{N})=-1$ [duplicate]

As part of a larger proof, I must show that: $$\sum_{n=1}^{N-1}\cos(2\pi\frac{n}{N})=-1$$ I have thought about this but can't figure out how to get my hands on the value since I don't know any ...
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### use logical way to calculate the least percentage [on hold]

If 70 per cent. have lost an eye, 75 per cent. an ear, 80 per cent. an arm, 85 per cent. a leg q1: what is the least percentage lost all four q2: what is the least percentage lost one of them q3 what ...
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### Impuls after collision [on hold]

I am trying to understand collision and collision response for two spheres. This is my current knowledge background Collision Response The linear momentum is no problem. But I am stuck with the ...
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### Proportionals and squares

Let $a,b,c,d \in \mathbb{Z^+}$ and $a:b::c:d$ and $ac$ is a square. Can we prove that $bd$ is a square too?
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### A identity relating a infinite series and a definite integral

Prove that, $$\sum_{n=1}^{\infty} \frac{1}{n^n} = \int_{0}^{1} x^{-x}dx$$ I made no significant progress, I'm looking for hint/ideas to approach this problem. Thanks!