In How to Prove it by Velleman, for defining disjunctions, he gives the difference between exclusive "OR", and inclusive "OR." Given two events $P$ and $Q...

The equation is $x^2-4x=y^2-4y$ in the case where $x\ne y$. The answer is $x+y=4$. I can start from $x+y=4$ and create the equation very easily, and I can...

This seems like a relatively simple equation, but I have not really found an explanation that works for me. In my probability class, we were simply given ...

Q&A for people studying math at any level and professionals in related fields

Disclaimer: I am an adult learning Calculus. This is not a student posting his homework assignment. I think this is a great forum! $$\lim_{x\to8}{\frac{\s...

I have a question I'm working on. I don't really understand it. Find the value of $k$ for which the graphs of $2y + x + 3 = 0$ and $2y + kx + 2 ...

Suppose you want to generate a password using ASCII characters ($128$ characters.)How many ways can you create a password of 10 characters long that has a...

What is the meaning of the double left-right arrow in the following context? This is from a signal processing paper, Alias-Free Digital Synthesis of Class...

Three non-overlaping regular plane polygons, at least two of which are congruent, all have sides of length $1$. The polygons meet at a point $A$ in such a...

I need to use a calculator to find trigonometric ratios like $\sin(41),\cos(32)$. How do calculators work for trigonometry? Also, as calculators are inven...