general
Prove that : A circle consist of infinite points
How to prove a circle consist of infinite points ?Proof using calculas or computational theory is appreciated?
Apr 16, 2026
Archive: General
general
Integration of $(5x^2+2x-5)/(x^3-x)$
The problem is to evaluate $\int \frac{5x^2+2x-5}{x^3-x}\,dx$. This is the solution that I tried: I really have no idea of this problem. After check my so...
Apr 16, 2026
general
Proof of equation $\ln y=-kt+c$ is same as $y=c*e^{-kt}$
I'm trying to prove that one is the same as the other : $$\ln y = -kt+c$$ $$y=ce^{-kt}$$ Where c is undefined and k is defined constant. I got as far...
Apr 16, 2026
general
Find the price that will maximize the profit
Given the functions for price (p) and cost (C): $p=75-.1\sqrt{x}$ $C=30x+400$ Find the price that will maximize the profit. Solution: I will denote profit...
Apr 16, 2026
general
Absolute convergence of an infinite complex series
Let $(z_n)$ be a sequence of complex numbers. If $\sum_{n=1}^\infty \vert z_n\vert$ converges then $\sum_{n=1}^\infty z_n$ does too. Show that this statem...
Apr 16, 2026
general
Trying to grasp the concept of homogeneous inequalities
Given $a,b\in \mathbb{R}^+$, prove the following lower bound for the AM-GM difference: $$\frac{a+b}{2} - \sqrt{ab} \geq \frac{(a-b)^2(a+3b)(b+3a)}{8(a+b)(...
Apr 16, 2026
general
2015 AMC 10A 2015 problem 25
I came across this problem when reviewing previous AMC tens. Let S be a square of side length 1. Two points are chosen independently at random on the side...
Apr 16, 2026
general
How many servings of cereal in 450-gram box?
I am helping my brother with his math again - I need a way to explain this to him!I am ages past this and don't have the time to find an explanation ...
Apr 16, 2026
general
What is the relationship between onto/ one to one and rank?
Let A ∈ R^m×n. What is the rank if A is onto? What about not onto? What is the rank if A is one to one? what about not one to one? I understand what rank ...
Apr 16, 2026
general
Sum of rational cubes
In Hardy & Wright "An Introduction to the Theory of Numbers" there are two theorems: Theorem 233: There are positive rationals which are not sums of t...
Apr 16, 2026
