Question: Find the number of quadrilaterals formed by joining the vertices of a decagon,that share no common side with the decagon. Approach: Select one v...

The equations $$Ax+By+C=0$$ and $$x\cos \alpha + y\sin \alpha - p=0$$ will represent one and the same straight line if their corresponding coefficients ar...

What exactly is meant by "closed under fill in the blank"? Thanks.

have recently encountered this question in my quiz. A computer randomly dials telephone numbers. When a person answers a note is made whether the person i...

This is a bit of a philosophical question. Wikipedia gives a very intuitive (in my view) description of the four main fields of mathematics, according to ...

$n$th roots of a complex number: For a positive integer $n$, the complex number $z=r(\cos(\theta) + i\sin(\theta))$ has exactly $n$ distinct $n$th roots g...

At small values close to $x=1$, you can use taylor expansion for $\ln x$: $$ \ln x = (x-1) - \frac{1}{2}(x-1)^2 + ....$$ Is there any valid expansion or a...

Studying for an exam and I came across an unfamiliar concept. Can anyone help me out with this practice question? I would really like if someone could go ...

I've been trying to prove this for a while. I can think about it intuitively, but I can't come up with a formal proof. I would appreciate some h...

According to WolframAlpha, $i^i=e^{-\pi/2}$ but I don't know how I can prove it.