Imagine that we have a set of points with defined x coordinate and mass for each of them: {($x_i$, $m_i$)}. Canonical center of mass is a point $x_0$ that...

While trying some problems along with my friends we had difficulty in this question. True or False: The value of the infinite product $$\prod\limits_{n=2}...

So I know normally that dy/dx is equal to the velocity of a particle at a specific point if the original equation indicates the position of that particle....

"For every" $x\in S$ would be $\forall x\in S$ which it's same as "for all" $x\in S$. But, is "for some" is same as "there exist"? It seems Yes, but ...

Write $x^k - y^k$ as the product of two factors. $x^3 - y^3 = (x-y)(x^2+xy+y^2)$ $x^4 - y^4 = (x-y)(x^3+x^2y+xy^2+y^3)$ $x^5 - y^5 = (x-y)(x^4+x^3y+x^2y^2...

The sum of squares of $k$ independent standard normal random variables $\sim\chi^2_k$ I read here that if I have $k$ i.i.d normal random variables where $...

I am currently taking Discrete Mathematics and while I understand most of the topics covered, the one topic which I still don't quite understand is M...

The actual question is : $$d^2x/dy^2$$ equals : $$1. (d^2y/dx^2)^{-1}$$ $$2. -(d^2y/dx^2)^{-1}(dy/dx)^{-3}$$ $$3.(d^2y/dx^2)(dy/dx)^{-2}$$ $$4.-(d^2y/dx^2...

How many ways are there to place 7 people into three groups of any size? I know for this question I would have to find all the possible combinations. I�...

For this question I have managed to sketch the region however I don't understand how to solve this sort of a problem where we have two regions? Also ...