What is the best way to cacluate the inverse of a percentage? For example: 100 * .85 = 85 85 * x = 100 x = 100 / 85 x = 1.17647 Also, 279 * .85 = 237.15 2...

How can I solve this problem: ${e^x}^y +{x}^2+y-1.2=0 \\ {x}^2 +{y}^2+x-0.55=0$ for various loaded inputs with start points $(x_0 , y_0) = 0.6, 0.5$ Could...

In Stephen Boyd & Lieven Vandenberghe's Convex Optimization book we have following set $$\{x\in \mathbb R^2_+ \mid x_1x_2\geq1\}$$ Now the analyt...

Let $S$ be a smooth oriented surface in $\mathbb R^3$ with boundary $C$, and let $f: \mathbb R^3 \to \mathbb R^3$ be a continuously differentiable vector ...

I'm aware that with L'Hopital's rule, we're dealing with indeterminate forms of $ \lim_{x\to a} \frac{f(x)}{g(x)} $, and that includes...

I'm aware that you have to use the definition of a limit of a sequence, which is: $\lim\limits_{n \to \infty} a_n = L $ if for every $E > 0$, ther...

So the standard Cantor set has an outer measure equal to $0$, but how can you construct a "fat" Cantor set with a positive outer measure? I was told that ...

Let $D$ be a tensor derivation on a mnaifold $M$. I have to show that if $D(\partial_i)=\sum F_i^j \partial_j$, then $D(dx^j)=-\sum F_i^j dx^i$. Any help ...

I am really sure that if two sets have the same power set, then they are the same set. I just am wondering how does one exactly go about proving/showing t...

How do you calculate the missing angle? I couldn't figure it out. This is not homework, just a math practice question that I made up to test myself.