Please forgive my lack of knowledge, which i think it's one of those basic formula related to Trigonometry. Let's look at visual example: https:...

I cannot understand why $\mathbb{R}^2$ is not a subspace of $\mathbb{R}^3$. My reasoning is as follows: Choose any elements $v_1$ and $v_2$ from $\mathbb{...

There are theories that prove the existence and non-existence of Souslin trees [exist if $V=L$, don't exist if $\mathsf{MA}(\aleph_1)$] and Kurepa tr...

Theorem: Let $Y=X\beta+\varepsilon$ where $$Y\in\mathcal M_{n\times 1}(\mathbb R),$$ $$X\in \mathcal M_{n\times p}(\mathbb R),$$ $$\beta\in\mathcal M_{n\t...

The picture above has all the information about the cone that is given. L is the length between R and 2R (not the side of the cone). I don't have the...

I have a cylinder of radius 4 and height 10 that is at a 30 degree angle. I need to find the volume. I have no clue how to do this, I have spent quite a w...

Is the inverse of a continuous bijective function also continuous? How to prove it?

I have a triangle circumscribed within a circle. One vertex is the exact center of the circle. To solve the question, I need to figure out the exact coord...

On page 94, the Corollary states: If $H$ and $K$ are subgroups of $G$ and $H \leq N_G(K)$, then $HK$ is a subgroup of $G$. In particular, if $K \trianglel...

19. A circle $C$, of radius $r$, passes through the points $A (a, 0)$, $A_{1} (-a, 0)$ and $B (0, b)$, where $a$ and $b$ are positive and are not equal; a...