Finding the diagonal of a rectangle.
What fraction of the rectangle is shaded? (You may assume that each line, other than the diagonal of the rectangle, is parallel to some side of the rectan...
Apr 15, 2026 1 VIEWS
Topic: General
5104 Articles 
3-connected graphs simple question
I have a relatively simple question. I was given this exercise A graph $G$ is called $2$–connected if for every pair of vertices $x$ and $y$ there are at ...
Apr 15, 2026 1 VIEWS
Probability of hitting the “bullseye” [closed]
I'm trying to solve this task but I'm obviously stuck. Will anyone help me solve it? John is throwing darts at a target. He is very good at the ...
Apr 15, 2026 1 VIEWS
Understanding the definition of dense sets
I am recently confused about the definition of dense sets. What I learned is as the following In topology and related areas of mathematics, a subset $A$ o...
Apr 15, 2026 1 VIEWS
Motivation behind the definition of flat module
Can someone explain what is the motivation behind the definition of a flat module? I saw the definition but I don't really know why it is important t...
Apr 15, 2026 1 VIEWS
Multiplication of Expected Values
I am trying to understand the proof I tried that $E[X*Y] = E[X]*E[Y]$ for independant variables $X,Y$ In this I assign the the multiplicative expected val...
Apr 15, 2026 1 VIEWS
Equation of Directrix of a Parabola
Find the equation of the directrix of the parabola $y^2+4y+4x+2=0$ I tried it as follows: $$(y+2)^2+4x-2=0$$ $$(y+2)^2=-4(x-\frac{1}{2})$$ On comparing wi...
Apr 15, 2026 2 VIEWS
Unsure how to prove that this function is homeomorphism:
Consider the sets: $S^{1} = \{(x,y) \in \mathbb{R^2}:x^2+y^2=1\}$ and $Q = \{(x,y)\in\mathbb{R}^2:|x|+|y|=1\}$ and the function: $f:Q\to S^1$ given by: $f...
Apr 15, 2026 1 VIEWS
reflexive relation on a set
We know relation $R$ from set $A$ to set $B$ is subset of $A\times B$, then why we define reflexive relation on single set $A$(say) e.g, we have a set $A=...
Apr 15, 2026 1 VIEWS
Use logarithmic differentiation to find the derivative of y = (cos(x))^ln(x)
Okay so this question is on my exam study guide for Calculus 1, and I'm having trouble getting to an answer. Here are the steps I have tried currentl...
Apr 15, 2026 1 VIEWS
Precise mathematical translation of the 68–95–99.7 rule?(Not a proof!)
The rule: In statistics, the 68–95–99.7 rule, also known as the three-sigma rule or empirical rule, states that nearly all values lie within 3 standard de...
Apr 15, 2026 2 VIEWS
Derivatives of functions involving absolute value
I noticed that if the absolute value definition $\lvert{x}\rvert=\sqrt{x^2}$ is used, we can get derivatives of functions with absolute value, without hav...
Apr 15, 2026 2 VIEWS