# All Questions

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### Convergent series, is this telescoping?

Let $\left(x_{n}\right)_{n}\subset\mathbb{R}$ and $v_{n}:=\sum_{k=1}^{n}|x_{k+1}-x_{k}|$. If $\left(v_{n}\right)_{n}$ is bounded, prove that both $\left(v_{n}\right)_{n}$ and $\left(x_{n}\right)_{n}$ ...
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### Why do level curves of a function and its harmonic conjugate intersect each other orthogonally?

So I've had this assignment in which I had to proof that two level curves of a function and one of its harmonic conjugates intersect each other orthogonally. The proof itself wasn't that difficult, ...
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If I'm adding the sum of £100 +£320+£220+£20+£6+50p+20p+10p+5p+2p, how would I write that using column math. Thanks
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### Poisson distribution for rare event

I was taught in school that Poisson distribution is usually used to model rare events. And I understand the Poisson process is such that the probability of an event in one interval is independent of ...
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### What is present value of the carbon expense for five years?

Suppose I have computed the cost of carbon per mile for my car at 0.009 per mile. Assume that the interest rate is 5% and that I drive the car 20,000 miles per year. What is present value of the ...
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### Basis and their orientation

let V be a vectorspace with $v_1 = (3,2,1), v_2 = (2,2,1), v_3 = (1,1,1)$. Do the two basis $A = (v_1, v_2, v_3)$ and $B = (v_2, v_3, v_1)$ have the same orientation? Since this is a new thematic for ...
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### Are there hidden events?

Consider the sample space S = {a, b, c, d} and a probability function Pr : S ->R on S. De fine the events A = {a}, B = {a, b}, C = {a, b, c}, and D = {b, d}. You are given that Pr(A) = 1/10, Pr(B) = ...
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### Largest Singular value of a Matrix

Prove that if $A\in \mathbb{R}^{m\times n}$, then $$\sigma_{\text{max}} (A) = \underset{y\in\mathbb{R}^m\\x\in \mathbb{R}^n}{\text{max}}\frac{y^TAx}{\Vert{x}\Vert_2\Vert y\Vert_2}.$$
Two vehicles are heading for a crossroad (point C) and intend to pass straight through. Vehicle A is $100$ km due North travelling at $80$ km/hr towards C Vehicle B is $150$ km due East travelling at ...