The radius, $r$, of the base of a circular cylinder increases by 2 feet per second while the height, $h$, decreases by 1 foot per second. How fast is the ...

X is compact set iff X closed and pre-compact. X is called pre-compact if $\overline{X}$ is compact. But in some texts, I found that X pre-compact is tota...

Sorry for the simple problem, but I wanted to make sure that my idea is right (this is is the problem 1.8.50 from Rice's book) Two dices are rolled a...

For example, "Solve the congruence (if possible), listing all the incongruent solutions:" $$561x\equiv 3575\mod{1562}$$ I found $x\equiv 37+142t,\ 0\leq t...

Hartshorne defines a closed immersion as a morphism $f:Y\longrightarrow X$ of schemes such that a) $f$ induces a homeomorphism of $sp(Y)$ onto a closed su...

I was given this assignment to do the following. Write a paragraph proof for the following scenario. Given: $ KLMN $ is an isosceles trapezoid. Prove: $ \...

I am doing some homework exercises and stumbled upon this question. I don't know where to start. Prove that the union of countably many countable set...

I've seen it written two different ways: $$\frac{\partial f}{\partial x} = \lim\limits_{h \rightarrow 0} \frac{f(x + h, y) - f(x,y)}{h}$$ and $$\frac...

A)Sylvester's criterion states that a Hermitian matrix M is positive-definite if and only if all leading principal minors are positive. AA) a Hermiti...

Theorem statement: Let $u(x)$ and $v(x)$ be differentiable functions on some interval $I$ and let $u'(x)v(x)$ have a primitive function on interval $...