The zero vector is defined as simply the vector consisting of pure zeros as elements. It is labeled as the number zero with an arrow above $\vec 0$ or as ...

What's the importance of the trig angle formulas, like the sum and difference formulas, the double angle formula, and the half angle formula? I under...

How can we efficiently find square root of 5 in a mod prime field. By quadratic reciprocity we can argue that 5 is a square in modulo p(prime) is p is squ...

If $\int_a^b e^{cosx}(380-x-x^2)dx$ attains its maximum value for some $(a,b)$ such that $a\leq b$, then the value of $b-a$ is? My attempt Factorized the ...

I am asked to show that the pseudosphere has Gaussian Curvature $-1$ at all points. So I parametrized the tractrix as: \begin{equation} \alpha(t) = (\sin{...

We say that a graph $G=(V,E)$ has a $k$-coloring if each vertex can be assigned a color in $\{1,...,k\}$ so that no edge has two vertices of the same colo...

$x^2 = y^2 + xy + 5$, where $x$ and $y$ are natural numbers. Here is what I have so far: $x \neq y$ (from the equation). $x$ is always odd (using the equa...

I'm new to probability and I'm stucking with this problem. Let $X$ be a continuous random variable following a pdf $$p(x|\theta)=\frac{\theta}{2...

In my course material I have the following notation: $$f\in C^{\infty}_0(\Omega, \mathbb{R}),$$ where $\Omega \subset\mathbb{R}^n$ is a bounded open set. ...

I have a power curve relating to a turbo trainer I use on my bike. I save my sessions on a website called strava using speed, cadence, heart rate and time...