Velvet Star Monitor

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Modelling the "Moving Sofa"

I believe that many of you know about the moving sofa problem; if not you can find the description of the problem here. In this question I am going to rot...

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Given f(3) = 4 and f ′(3) = 5 , find g′(3) where g(x) = 5x/f(x)

I'm not sure how to go about this problem.

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Notation of complement of set

Given, $U=\{1,2,3,4,5,6\},A=\{1,2,3\}$. We have to find the complement of the set A. We start by, Since set $A=\{1,2,3\}$, so $A'=\{1,2,3\}'=\{4...

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Help with Maclaurin series of $\cos(\ln(x+1))$?

Hi I've almost completed a maths question I am stuck on I just can't seem to get to the final result. The question is: Find the Maclaurin series...

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Determining Period From A Graph

I'm having trouble understanding what exactly the period is in a graph. My understanding is that the period is horizontal distance between 2 curves i...

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How far can you go with the Martingale Roulette strategy

I am currently arguing with my friends that just learned the Martingale roulette technique for the casino that consist of doubling your initial bet as muc...

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Proof for the relationship between Cardinality of Natural numbers and Cardinality of Real Numbers [duplicate]

(I am a 13 year old so when you answer please don't use things that are TOO hard even though I actually can understand quite complex stuff) I was stu...

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What is $ {n\choose k}$?

This is the Binomial theorem: $$(a+b)^n=\sum_{k=0}^n{n\choose k}a^{n-k}b^k.$$ I do not understand the symbol $ {n\choose k}.$ How do I actually compute th...

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Proving that DEF is also an equilateral triangle

The question gives that ABC is an equilateral triangle, AD = BE = CF and ∠DAB = ∠EBC. I tried using only cases of triangle congruences to prove it, but I&...

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how to find value of $x$ in following equation?

How to find the value of $x$ in $(x^{2}+1)^{35}=0$? we can find value of $x$ in $(x^{2}+1)^{2}=0$ by using algebraic identity i.e. $$x^{2}+2x+1=0$$ ...

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