Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 127

Factorize the polynomial $f(x)=4x^2-4x+8$ over $mathbb{Z}[x]$, $mathbb{Q}[x]$ and $mathbb{Z}_{11}[x]$

Factorize the polynomial $f(x)=4x^2-4x+8$ in $mathbb{Z}[x]$, $mathbb{Q}[x]$ and $mathbb{Z}_{11}[x]$My approach First we consider in $mathbb{Z}[x]$.Let $$f(x)=4x^2-4x+8=2*2*(x^2-x+2)$$ I claim that $2$ and ...

Asked on 02/07/2021

1 answer

For each of the following sets A, B prove or disprove whether A ⊆ B and B ⊆ A

Would this proof be sufficient for just proving B ⊆ A alone? $A = {x ∈ Bbb Z : ∃y∈Bbb Z,x = 5y + 1}, $$B = {x ∈...

Asked on 02/07/2021

1 answer

Finding $AC$ given that $ABCD$ is inscribed in a circle

Suppose quadrilateral $ABCD$ is inscribed in a circle such that $AB=4, BC=5, CD=6,$ and $DA=7.$ Find the length of $AC.$I do realize that this is...

Asked on 02/07/2021 by questionasker

1 answer

Proofing Metropolis Hastings

I need to prove the correctness of the Metropolis Hastings algorithm in a presentation.Sadly, I am having trouble on where to start and what to actually proof. So if...

Asked on 02/07/2021 by Nestroy

0 answer

How to solve this limit $lim_{nto infty}(frac{2^n}{n^k})$?

It's not allowed to apply L'Hopital's rule . I tried using binomial distribution $2^n=(1+1)^n$ in order to manipulate with numerator but don't know what to do with denominator. P.s...

Asked on 02/07/2021

4 answer

Is a ring homomorphism surjective if the restriction to the group of units is surjective?

Let $R_1,R_2$ be two rings and suppose that $f:R_1to R_2$ is a ring homomorphism. Denote $R_1'$ and $R_2'$ for the groups of units of $R_1$...

Asked on 02/07/2021 by Barry Allen

1 answer

$Var(X_1 X_2)=Var(X_1) Var(X_2)$

Let : $X_1$ and $X_2$ two independent variables, square-integrable et non constant. At which necessary and sufficient condition, do we have $ Var(X_1 X_2)= Var(X_1) Var(X_2)$ ?...

Asked on 02/07/2021

2 answer

Principal component analysis for 'signal extraction'

This question might sound very odd to people with better understanding and the question is very fundamental, but lets try:I have for example 1000 individual signals that are not...

Asked on 02/07/2021 by Mat P

0 answer

Show that ${a log n }$ is not equidistributed for any $a$

I need to prove that the sequence ${a log n }$ is NOT equidistributed for any $a in mathbb{R}$. Now, I think that Weyl's criterion will be a good...

Asked on 02/07/2021 by Dark_Knight

1 answer

Monotone Convergence Property $iff$ Order Completeness in an arbitrary ordered field.

I have found an answer here but having some doubts about the first answer(highest rep.) posted by Jonas Meyer. There in Claim 1. He states for all $epsilon>0$,...

Asked on 02/06/2021

1 answer

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