Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 23

What is the equation of the quadratic function whose vertex of the graph is on the $x$-axis and passes through the two points $(1,4)$ and $(2,8)$?

What is the equation of the quadratic function whose vertex of the graph is on the $x$-axis and passes through the two points $(1,4)$ and $(2,8)$? Here...

Asked on 12/23/2021

3 answer

Lebesgue measure of boundary of an open set.

Let $g$ be a continuous function on $mathbb{R}^n$ and $$O={xin mathbb{R}^n:g(x)neq 0}.$$Is it true that Lebesgue measure of Boundary of $O$ always zero?...

Asked on 12/23/2021 by Santanu Debnath

1 answer

Chinese Remainder Theorem for moduli that are not necessarily pairwise coprime

Assume that ${n_1},cdots ,{n_k}$ is a finite set of $k$ positive integers. We are not assuming that these integers are pairwise coprime. Consider the homomorphism of additive groups...

Asked on 12/23/2021

1 answer

Prove that $x^m$ is a generator of the cyclic group $G$ of order $n$ if and only if $(m,n) = 1$

I want to check my proof of the statement. First, i'll state the following theorem: Theorem 1.Let $o(x)$ be the order of $x in G$. If ...

Asked on 12/23/2021 by Morganuz

1 answer

Must a local homomorphism from a Noetherian local ring to an artinian local ring factor through a power of its maximal ideal

Let $f : Brightarrow A$ be a local homomorphism of Noetherian local rings where $A$ is moreover Artinian. Must $f$ factor through $B/m_B^n$ for some ...

Asked on 12/23/2021

1 answer

If Mu is a projection matrix, how can I show that Mu^2=Mu by direct computation?

The definition of Mu, or the projection matrix, I am working with is Mu(a)=Pu(a). Let's say that a set of vectors (v1, v2.....vm) is an orthonormal basis of U. Then,...

Asked on 12/23/2021 by johnathan

1 answer

Expressing one gradient in terms of the other

Suppose I have the following relation:$mathbf{v}=t|mathbf{k}|^{t-2}mathbf{k}$ where $mathbf{v}$ and $mathbf{k}$ are $d-$dimensional vectors and $tinmathbb{R}$. I want to express $nabla_{mathbf{v}}$ in terms of...

Asked on 12/23/2021

0 answer

Show that $m({xin[0,1]:text{$x$ lies in infinitely many $E_j$}})geqfrac{1}{2}$ when $m(E_j)geqfrac{1}{2}$

Question: Suppose $E_1, E_2,ldots$ is a sequence of measurable subsets of $[0,1]$ with $m(E_j)geqdfrac{1}{2}$. Show that $m({xin[0,1]:text{$x$ lies in infinitely many $E_j$}})geqdfrac{1}{2}$, where $m$...

Asked on 12/23/2021

1 answer

Stars and bars but with distinct objects

The total number of ways which 5 balls of different colors can be distributed among 3 persons so that each person gets at least one ball is..?My attempt: So, first...

Asked on 12/23/2021

4 answer

Laurent Series and residue of $frac{z}{(z-1)(z-3)}$ around z = 3

As mentionned in the title, I'd like to get the function's Laurent series and after its residue, I have tried to separate the two denominators to get a partial fraction...

Asked on 12/23/2021 by Dimitri

3 answer

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