$\text{What is the ratio of legs in a right triangle with angles of 15, 75, and 90?}$ I know the ratio of legs in a $30, 60, 90$ triangle, which is the le...

Cauchy matrix $C$ is defined by $$C_{i,j}=\frac{1}{a_i + b_j}$$ where $a_i$ and $b_j$ are any numbers so long $a_i + b_j \neq 0$. Why did Cauchy introduce...

Given a set of data with 11 observations of two variables (response and predictor), I've been asked to "calculate the fitted values $\hat y_i = \hatα...

I am trying to describe how irrational numbers, which are all modeled as a series of fractions, can themselves not be fractions, and are instead part of a...

The problem that I want to solve is: "find all the continuous functions $f\colon \mathbb R\to \mathbb R$ such that for every $x$, $f(f(f(x))) = x $ , I kn...

Reference: https://www.youtube.com/watch?v=ECHpJueKN7c Timestamp:- 1:28 Original Question My doubt:- Why does the perpendicular bisector to the side of sq...

mutual information of tow variables is $\displaystyle\sum\sum p(x,y)\ln\frac{p(x,y)}{p(x)p(y)}$ what is the mutual information of three variables? is it $...

What is the meaning of bounded function in general term? What happens when we put a boundary condition on a function.

How can I prove the product rule of derivatives using the first principle? $$\frac{d (f(x) g(x))}{d x} = \left( \frac{d f(x)}{d x} g(x) + \frac{d g(x)}{d ...

Ok another probably very basic algebra question. With real numbers and integers and complex numbers, one is used to $(-1) \cdot (-1) = 1$, i.e. the additi...