I want to prove that the set of all algebraic numbers is countable. I know the proof where we show that the set of all polynomials with integer coefficien...
I have encountered several times of a special way of calculating a vector from the divergence of the vector. It has at least appeared in the theories of e...
Is there any type of objects or ideas for which asking about their equality makes sense, but asking about non-equality doesn't? (or vice versa) Intui...
If I have a rectangle of any dimensions $a \times b$, how can I resize those dimensions so that, depending on their proportions one (or both) will meet th...
Can anyone explain me as to why Tensor Products are important, and what makes Mathematician's to define them in such a manner. We already have Direct...
Consider the random variable X with probability density function $$f(x) = \begin{cases} 3x^2; & \text{ if, } 0 < x < 1 \\ 0; & \text{ otherw...
Menger's Theorem is defined in Introduction to Graph Theory as follows: Menger's Theorem. Let $u$ and $v$ be nonadjacent vertices in a graph $G$...
A tank has the shape of an inverted circular cone with height 10 m and base radius 4 m. It is filled with water to a height of 8 m. Find the work required...
A cylinder is $(x-a)^2+(y-a)^2=r^2$ with axis at $z$. I don't see where the '$z$' is in the equation. The book (calc 3) I'm using ment...
If an $n \times n$ symmetric A is positive definite, then all of its eigenvalues are positive, so $0$ is not an eigenvalue of $A$. Therefore, the system o...
I have an equation of the form: $$ n \log n = x $$ Upon searching I came across the term "Lambert- W -Function" but couldn't find a proper method for...
This was from a question that was closed recently. It says to find the measure of angle '$a$'. (answer: $60^\circ$) The below is my attempt to s...