I have this trig problem where it asks to find $ \sin(10^{\circ})$, given $\cos(40^{\circ})=a$. I tried the write the $\sin(10^{\circ})$ as $\sin(40^{\cir...

Why is the Absorption Law of Propositional Logic so ? p $\lor (p \land q) \equiv$ p Would appreciate an intuitive explanation and not one using a Truth Table

In Euclidean geometry, we have that the distance between two points $p$ and $q$ in $\Re^n$ is $\sqrt{(p_1^2-q_1^2) + (p_2^2-q_2^2) + \ldots + (p_n^2-q_n^2...

I've been reading some papers and found this term "Sharp constant" being used in inequalities frequently. Can anyone provide me a detailed meaning of...

On a measure space $(\Omega,\mathcal{A},\mu)$ a completion of a measure is defined as: $\{A: A_1\subset A\subset A_2$ with $A_1,A_2\in\mathcal{A}$ and $\m...

I think that if we were to say that, for instance, $y$ increases along the curve, (with no specific rate) then this means for the derivative to simply be ...

Given Point A and Point B in 2D space, how can I find the angle Point B is from Point A? 0° can be any direction; it doesn't matter. For example, Poi...

I'm studying derivatives 101 and I can't get my head around the phrasing "with respect to" something. Eg in chain rule we calculate the derivati...

a 2-sphere is a normal sphere. A 3-sphere is $$ x^2 + y^2 + z^2 + w^2 = 1 $$ My first question is, why isn't the w coordinate just time? I can plot a...

I am a bit confused about the range of values for signed binary system. If I have $3$ bit to represent a number system, then number range will be given by...