How to prove $$ T = S1 $$ $$ i.e \qquad yy_1 - 2a(x+x_1) = y_1^2 - 4ax_1=0$$ as the equation of chord for a parabola y$^2$ = 4ax whose midpoint (x$_1,y_1$...

Suppose $X, Y$ are two independent variables that uniformly distributed on the interval $[-1,1]$. If $s = x^2 + y^2 < 1$, show the result of $\frac{x}{...

Usually people (including, for instance, Calculus teachers) draw the $xyz$ coordinate system in such a way that the $y$ and $z$ axes are perpendicular to ...

So how to prove that $\dfrac{d}{dx}e^{kx}=ke^{kx}$? What I did is to think about $e^{kx}$ not as a single function but as a composition of functions, that...

I'm benchmarking a websocket server and I am very poor at math so please forgive me. I am recording the amount of messages sent, and the elapsed time...

Let's say we have a random variable $X$ of which the distribution is unknown. Now there are these general rules like $E[X + Y] = E[X] + E[Y]$ etc. Bu...

Fifth degree polynomials cannot generally be solved analytically, but at least one solution always exists. Given the normal form $$ax^5+bx^4+cx^3+dx^2+ex+...

I was working on some limit homework and everything was going fine until I reached this problem: $$\lim_{\Delta x \to 0} \frac{2(x + \Delta x) - 2x}{\Delt...

I'm really confused and I can't get the concept. How is 14 in base 8 = 16? And how does 8 in base 8 = 10? In case of 14 isn't 1 * 8 + 4 * 1...

I am slightly confused as to what the difference between Subgame Perfect Equilibrium and Subgame Perfect Nash Equilibrium is. I was told there is a differ...