I wish to improve on my combinatorial reasoning skills and my step-father gave me this problem that has left me quite confused. It seems to me that becaus...

The problem is completing the square of X^2 +6x +12=0.As I’m looking at each step they put add 9 on both sides. I’m puzzled on how did they get 9?

Prove that if $ f\mathrm{(}z\mathrm{)} $ is analytic at the infinity ,then : $ {\lim}_{{z}\mathrm{\rightarrow}\mathrm{\infty}}{f}\prime{\mathrm{(}}{z}{\ma...

How do we prove $\cos(\pi/5) - \cos(2\pi/5) = 0.5$ without using a calculator. Related question: how do we prove that $\cos(\pi/5)\cos(2\pi/5) = 0.25$, al...

According to Wikipedia: A common convention is to list the singular values in descending order. In this case, the diagonal matrix $\Sigma$ is uniquely det...

For $d\geq1$ let $I^d=[0,1)^d$ denote the $d$-dimensional half-open unit cube and consider a finite sequence $x_1,\ldots,x_N\in{I}^d$. For a subset $J\sub...

Expand $\frac{1}{z-i}$ to power series around $z_0=1$ and find the radius of convergence $$\frac{1}{z-i}=\frac{1}{(z-1)+1-i}=\frac{1}{1-i}\cdot\frac{1}{1+...

To preface this post, I have to admit that I have extremely little measure theory knowledge and I get lost when trying to read about Fubini's theorem...

The joint density function of $X$ and $Y$ is given by $f(x,y) = xe^{-x(y+1)}$, $x > 0, y > 0$. (a) Find the conditional density of $X$, given $Y = y...

It is well known that the Cartesian equation for a general parabola in 2D space is $$(Ax+Cy)^2+Dx+Ey+F=0$$ or in parametric form, $$(at^2+bt+c, pt^2+qt+r)...