Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 195

Area of a triangle using determinants of side lengths (not coordinates of vertices)

Given the side lengths of a triangle (and not the coordinates of vertices) is there a way to find the area of a triangle using determinants?For example, if the three...

Asked on 11/12/2020 by rohitt

0 answer

Prove that iterated $x_{i + 1} = x_i - log x_i$ is sublinear.

Define a recurrence as: $$x_0 = n, x_{i + 1} = x_i - log x_i, forall i geq 0.$$ Let $N_n$ be such that $x_{N_n} < 1$....

Asked on 11/12/2020 by thienle

3 answer

Find value of $ frac{C_0}{2}-frac{C_1}{3}+frac{C_2}{4}+...+(-1)^nfrac{C_n}{n+2}, $ where $C_i = binom{n}{i} $

I saw some posts in the net with solution to this, with lots of calculations on formula for combinations, wondering if it can be obtained with less calculations. My try:...

Asked on 11/11/2020 by Monalisha Bhowmik

2 answer

Find the number of solutions for the equation $(F(x))^2=frac{9x^4}{G(x)}$

Let $f_1(x)$ and $f_2(x)$ be twice differentiable functions, where $F(x)=f_1(x)+f_2(x)$ and $G(x)=f_1(x)-f_2(x)$, for all $x in mathbb{R}$, $f_1(0)=2$ and $f_2(0)=1$. If $f_1'(x)=f_2(x)$...

Asked on 11/11/2020 by Identicon

1 answer

Which is the best English term for "the result of a mathematical integration"?

I am writing an academic paper. And I wonder which is the best English term for "the result of a mathematical integration". For example, I have a mathematical integration as...

Asked on 11/10/2020 by Jundan Luo

2 answer

Equivariant Diffeomorphism $S^2 times S^3$ to itself with respect to the following $mathbb{Z}_4$ action

Let $mathbb{Z}_4$ be the cyclic group generated by $(R,j)$ where $R in$ SO$(3)$ is the rotation matrix $R =begin{pmatrix}-1 & 0 & 0...

Asked on 11/09/2020 by TuoTuo

1 answer

Hartshorne's Exercise I.4.9: What is the desired projection explicity?

Again I'm here to ask for clarification on some already existed posts on the Hartshorne Exercise I.4.9, which goes like this:Exercise: Let $X$ be a projective variety of dimension...

Asked on 11/09/2020 by Hetong Xu

1 answer

Characteristic function vs Moment generating function

Normal distribution $N(mu, sigma^2$) has the moment generating function $$m_X(t) = exp (mu t+frac{sigma^2t^2}{2})$$ and the characteristic function $$phi_X(t) = exp (i mu t-frac{sigma^2t^2}{2})$$ which looks almost...

Asked on 11/09/2020 by nessy

0 answer

I don't understand the meaning of commute and i can't find any info about it

Might be duplicate I don't know but Properties of a binary operator; trouble understanding question. begin{equation*} begin{array}{c} ...

Asked on 11/07/2020 by needHelp

2 answer

Natural map to the adic spectrum

I'm struggling to understand the following proposition regarding the adic spectrum corresponding to a normal curve over a field $k$:Proposition: Let $C$ be a normal curve over a...

Asked on 11/07/2020 by test123

1 answer

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