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Let $X$ and $Y$ be compact and closed subset of a metric spaces $M$ respectively, then prove that $inf {d(x,y)|xin X, yin Y}=d(x,y)$ for some ...
1Mathematics Asked on 2 years ago
How to show that the distance of the points of tangency along a tangent line on two tangent circles with radius $a$ and $b$ is equal to ...
2Mathematics Asked on 2 years ago
Solve in $mathbb{R}$ $begin{cases}&x+y+frac{x^2}{y^2}=7 ~cdots (text{I})\&frac{(x-y)x^2}{y^2}=12~~~~~ cdots (text{II})\end{cases}$ A friend's attempt:$ I.(x-1)= x^2 - 7x + 12= y^2 - 7y rightarrow x...
3Mathematics Asked by peta arantes on 2 years ago
I have a double integral: $$iint (x+y),dx, dy$$ with circle constraint:$$x^{2}+y^{2}=x+y$$ I tried to calculate it with transition to polar coordinates: $$x^{2}+y^{2}=x+y$$$$left(x-frac{1}{2}right)^{2}+left(y-frac{1}{2}right)^{2}=frac{1}{2}$$ In polar...
3Mathematics Asked on 2 years ago
Let $I=Atimes B,$ where $A,Bsubset mathbb{R}$ are closed sets of positive Lebesgue measure, and $Esubset mathbb{R}^2,$ be a set of zero Lebesgue measure. Is it true that...
1Mathematics Asked by Prof.Hijibiji on 2 years ago
I am currently looking into Halley's Method. However, I wanted to see if there were better methods to solve the problem I am looking to solve. Fast means a low...
0Mathematics Asked on 2 years ago
Let G be a group and A an abelian subgroup of G. I want to prove that for each irreducible representation $p$ we have that $dim(p)leq [G:A]$.I...
1Mathematics Asked by Myanklana on 2 years ago
The Leibniz integral rule states $${displaystyle {frac {d}{dx}}left(int _{a}^{b}f(x,t),dtright)=int _{a}^{b}{frac {partial }{partial x}}f(x,t),dt}$$ when the integral bounds are not a function of $x$, i.e. the variable...
3Mathematics Asked on 2 years ago
Let $X$ and $Y$ be two random variables with values in $[0,1]$, such that $$E[X] = E[Y]$$ and $$ E[X+(1-X) ln(1-X)] = E[Y+(1-Y) ln(1-Y)] .$$...
1Mathematics Asked by Adrien Deliège on 2 years ago
We have tha matrix begin{equation*}A:=begin{pmatrix}1 & 5 & 8 & 2 \ 2 & 4 & 6 & 0 \ 3 & 3 & 8 & 2 \...
1Mathematics Asked on 2 years ago
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