I'm currently wondering about the side splitter theorem. Lets say I have this triangle. Now the side splitter theorem says, that if a line is paralle...

In Minkowski spacetime, is it true to say that a null vector is orthogonal to itself? Why or why not? Can a timelike vector be orthogonal to a null vector...

I am currently taking an introductory module on Markov chains, which does not cover any linear algebra aspects. However, I have taken an introductory modu...

I have the following paragraph in my notes: If $G=(V,E)$ is a general graph . Let $U\subseteq V$ and let $F$ be a subset of $E$ such that the vertices of ...

I haven't found a proper solution for this problem, found in Hartshorne's "Geometry: Euclid and Beyond": (4.3) Given a circle, but not given its...

The longer side of a parallelogram is 10 cm and shorter is 6 cm. If the longer diagonal makes an angle 30 degrees with the longer side, find the length of...

In the context of cryptography, I need to find the private key of a message and I need to use modular arithmetic. I understand how modular arithmetic usin...

Find the equations of the normal plane and osculating plane of the helix $r(t) = cost\mathbf{i} + sint\mathbf{i} + t\boldsymbol{k}$ at the point $P(0,1,2)$

I tried to calculate this integral: $$\int \sin(\ln(x))\,dx$$ but it seems my result is wrong. My calculation is: $$\int \sin(\ln(x)) \,dx = \left| \begin...

This is a trivial question; but I just want to make sure: A closed cylindrical container has a capacity of $128\pi \,{\rm m}^3$. Determine the minimum sur...