Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 172

How to use stars and bars to count how many terms there are in a polynomial expansion?

So here's what I understand from this. The number of terms in the expansion (before combining like terms) of any polynomial is given by ${k^{n}}$ where ${k}$ is...

Asked on 12/19/2020 by grompchompz

2 answer

Cross Product in Euclidean Space with infinite Dimensions

How can the cross product of two vectors with infinite tuples be found? ieIf $ A = (a_1, a_2, a_3,.....) $ and $ B = (b_1, b_2,...

Asked on 12/19/2020 by Enock Kabibi

1 answer

How to prove that $lim_{xtoinfty}frac{(log_2 x)^3}{x^n}=0$

I need help with proving the following $$lim_{xtoinfty}frac{left({log}_2xright)^3}{x^n}=0 , quad forall n>0.$$I used wolframalpha and got it and I...

Asked on 12/19/2020 by Shiran Shaharabani

4 answer

Probability theory (heads and tails)

A coin was tossed $N$ times. The number of heads is 10% more than the number of tails. At what $N$ can we say that the coin is...

Asked on 12/19/2020 by dshunevich

1 answer

Infinite set as a countably infinite union of infinite disjoint subsets

I am struggliglng with an exercise as the title. I have been able to get to a proof, if the set is infinitely countable, but I am having problems on...

Asked on 12/19/2020 by XuUserAC

1 answer

Can $Tleft( nright) = 4Tleft({nover 2}right) + 2^{nover2}$ be solved using Akra-Bazzi method?

$$Tleft( nright) = 4Tleft({nover 2}right) + 2^{nover2}$$Using Akra-Bazzi method$a = 4, b = {1over2}, g(n) = 2^{nover2}, h(n) = 0$ $$g'(n) = {dover dx}(2^{nover2})=2^{{nover2}-1}ln 2$$ Since ...

Asked on 12/19/2020 by Akash Karnatak

2 answer

Integral involving distance to the boundary

Let $Omega$ be a bounded open subset of $mathbb{R}^{n}$ and $alpha<1$. My question is when the integral$$int_{Omega}frac{dx}{text{dist}(x,partialOmega)^{alpha}}$$is finite?...

Asked on 12/19/2020 by Isak

0 answer

In a compact metric space, a sequence with a certain property is convergent

The question: Let $(K,d)$ be a compact metric space, if ${x_n}$ is a sequence such that ${d(x_n,x)}$ converges for all $x in K$, then ${x_n}$...

Asked on 12/19/2020 by StAKmod

1 answer

can you help with this exponential decay question?

Suppose that $100$kg of a radioactive substance decays to $80$kg in $20$ years. a) Find the half-life of the substance (round to the nearest year). b)Write down...

Asked on 12/19/2020 by Perfectoid

2 answer

Linear combinations of four-dimensional vectors

Let $v_1 = begin{pmatrix} 1 \ 1 \ 0 \ 0 end{pmatrix}$ $v_2 = begin{pmatrix} 0 \ 1 \ 1 \ 0 end{pmatrix}$ $v_3 ...

Asked on 12/18/2020 by Sammy

2 answer

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