Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 67

Prove that if $a, b, c$ are positive odd integers, then $b^2 - 4ac$ cannot be a perfect square.

Prove that if $a, b, c$ are positive odd integers, then $b^2 - 4ac$ cannot be a perfect square. What I have done: This has to either be done with...

Asked on 11/26/2021 by Topher

6 answer

Multiplying and adding fractions

Why multiplying fractions is equal to multiply the tops, multiply the bottoms?$$frac{a}{b}times frac{c}{d}=frac{atimes c}{b times d},$$And why$$frac{a}{b}times frac{c}{c}=frac{a}{b},$$Also why$$frac{a}{b}+frac{c}{b}=frac{a+c}{b}.$$I understand it, but I want...

Asked on 11/26/2021

4 answer

Bijection between tensors and permutations (in linear $O(n)$ time)

The number of permutations of the set $S={1, dots, n}$is $n!$, or in other words the permutation group $S_n$ has $n!$ elements The number of tensor components of a...

Asked on 11/26/2021 by Nikos M.

1 answer

How to Solve a Stars and Bars Discrete Math Problem

After a (not very successful) trick or treating round, Candice has 15 Tootsie rolls and 10 Twizzlers in her pillow case. Her mother asks her to share the loot with...

Asked on 11/26/2021 by Kristen M. Day

2 answer

Closed form of $int_0^infty arctan^2 left (frac{2x}{1 + x^2} right ) , dx$

Can a closed form solution for the following integral be found:$$int_0^infty arctan^2 left (frac{2x}{1 + x^2} right ) , dx,?$$I have tried all the standard tricks such as...

Asked on 11/26/2021

3 answer

Finding the limit of $mathbb{E}[theta^n]/mathbb{E}[theta^{n-1}]$

Let $theta$ denote a smoothly distributed random variable with support $[0, 1]$. I am trying to evaluate $$ lim_{n rightarrow infty} frac{mathbb{E}[theta^n]}{mathbb{E}[theta^{n-1}]}$$ I suspect, but cannot show,...

Asked on 11/26/2021

1 answer

Degree of a determinant

Let $p$ be a prime number and $ninmathbb N$. Consider the determinant $$M_n = begin{vmatrix}frac1{x^{p^{n+1}}-x}&frac1{x^{p^{n+1}}-x^p}\ frac1{x^{p^{n+2}}-x}&frac1{x^{p^{n+2}}-x^p}end{vmatrix} in mathbb F_p(x)$$ Numerical computations suggest that $$deg(M_n)=p-(p+2)p^{n+1}$$ Is it...

Asked on 11/26/2021

1 answer

Are basic feasible solutions, vertices, and extreme points equivalent for semidefinite programs (SDPs)?

First some definitions. Given a polyhedron (intersection of finitely many halfspaces) $P subseteq mathbb{R}^n$, we say a point $x in P$ isa vertex if there exists $c...

Asked on 11/26/2021

1 answer

Find all functions $f:mathbb{R}^+to mathbb{R}$ such that $xf(xf(x)-4)-1=4x$

Find all functions $f:mathbb{R}^+to mathbb{R}$ such that for all $xinmathbb{R}^+$ the following is valid:$$xfbig(xf(x)-4big)-1=4x$$All I could do is:$f(x)> {4over x}$ for all $x$...

Asked on 11/26/2021

2 answer

Fourier transform of $1/ sqrt{m^2+p_1^2+p_2^2+p_3^2}$

Let $m>0$ and consider the function $f:mathbb R^3tomathbb C$defined through$$ f(p_1,p_2,p_3) = frac{1}{sqrt{m^2+p_1^2+p_2^2+p_3^2}}.$$ I would like to compute the Fourier transform of $f$. This...

Asked on 11/26/2021 by Sebastien B

1 answer

Ask a Question

Get help from others!

Mathematics : Recent Questions and Answers (Page 67)

Ask a Question