Suppose I have two inequalities: $$k_1 \leq a$$ $$k_2 \leq b$$ where $k_1,k_2,a,b$ are all positive numbers I know that that summation of them can be writ...

Let $E$ be an extension field of a finite field $F$ , where $F$ has $q$ elements. Let $a \in E$ be algebraic over $F$ of degree $n$. Prove that $F(a)$ has...

I was asked to find the derivative of $\arccos$ $x$ with the definition of derivative. I know I have to form this limit. $f^{'}(c)= $ $\displaystyle{...

I am having a hard time coming up with WORDS to explain why is the derivative of a sine function a cosine function? Why? How do I write a few sentences sa...

$f(x,y)=x^2 +xy + y^2 +y$ I find the critical point $p=\left(\frac{1}{3},-\frac{2}{3}\right)$ by solving the system of partial equations. I plug this orde...

I'm reading a book, and this book says "if no two asserted statements of this theory contradict each other" this got me super confused for some reaso...

Given a non-degenerate triangle ABC and an arbitrary point P in 3D space, I can project P onto the plane defined by ABC and check whether the triangle con...

The question is Find the solutions to the equation $$2\tan(2x)=3\cot(x) , \space 0<x<180$$ I started by applying the tan double angle formula and re...

Let $X=\mathbb R$, with the usual metric on $\mathbb R$ and $A=((0,1)\cap \mathbb Q)\cup$ {$2,3$}. Find the limit points of $A$, exterior points of $A$, $...

The Clockblock Problem - problem and solutions I'm preparing myself for AMC 10 (which I'm sure a lot of other students would be doing too), but ...