I have a cone with $r=1$ with the tip pointing upward. The volume of liquid in the cone is given by $$V(h)=\pi\left(h-\frac{h^2}{3}+\frac{h^3}{27}\right)$...

In the thread at the end of the post the asker asks for pseudonyms for famous mathematicians or (secretive) groups of famous mathematicians. The famous &q...

Solve for $x$: $$ \displaystyle \frac{60x - 20}{16} = 4x - 2$$ Then what must $x$ equal?

$X \sim \mathcal{P}( \lambda) $ and $Y \sim \mathcal{P}( \mu)$ meaning that $X$ and $Y$ are Poisson distributions. What is the probability distribution la...

Given a complete graph with n vertices such that all edge weights are distinct. Prove that we can find a monotonically increasing path of length n-1. I tr...

I've a confession to make. I've been using PDF's and PMF's without actually knowing what they are. My understanding is that density eq...

I was doing a problem today, and arrived at the (correct) answer of $x^3 = 16000\sqrt2$ Obviously I want to simplify this further. My text book jumps stra...

I'm not sure how to check bibo stability. On a test there were two state space representations: A1 = $\begin{bmatrix} 1 & 0 \\ 0 & -2 \\ \end...

I'm trying to implement the integral test for sum convergence on the following series: $$ \sum_{n=1}^{\infty}\dfrac{1}{\sqrt{n}\cdot e^{\sqrt{n}}} $$...

Find $$\int_{0}^{T}W(t)dW(t)$$ using Ito's Lemma. Now, I know that the answer to that question is: $\int_{0}^{T}W(t)dW(t)= \frac{W^2(T)}{2}-\frac{T}{...