general
Maximize profit with dynamic programming
I have 3 tables… $$\begin{array}{rrr} \text{quantity} & \text{expense} & \text{profit}\\ \hline 0 & 0 & 0 \\ 1 & 100 & 200 \\ 2 &a...
Apr 21, 2026
Archive: General
general
Find the critical points for $F(x,y,z)=-x^{3}-y^{2}+2xy+x+2z$
I started by taking the first order partial derivatives: $F_{x}=-3x^{2}+2y + 1$ $F_{y}=-2y+2x $ $F_{z}=2 $ Now I would try to solve it for $F_{x}=F_{y}=F_...
Apr 21, 2026
general
Are mathematical articles on Wikipedia reliable?
I know that Wikipedia gets a bad rap, and it seems like some teachers of mine have nothing better to do in class than harp on about the Great Academic Pas...
Apr 21, 2026
general
Looking for an intuitive explanation why the row rank is equal to the column rank for a matrix
I am looking for an intuitive explanation as to why/how row rank of a matrix = column rank. I've read the proof on Wikipedia and I understand the pro...
Apr 21, 2026
general
Understanding the Euler sequence on $\mathbb{P}^n$
I want to get an intuition for the Euler sequence, by understanding the explicit construction of maps between terms. I prefer to use this version: $$ 0 \l...
Apr 21, 2026
general
Why do decimal places "move" when multiplying or dividing decimals?
Suppose we have the two decimal values, 0.2 and 0.3. Of course, multiplying these values yields the result: 0.06. Of course, this is simply the calculatio...
Apr 21, 2026
general
Moment Generating Function of a Truncated Gaussian
The Moment Generating Function of a standard Gaussian distribution is $\exp(t^2/2)$. Let $X$ be a Gaussian r.v., $a>0$ and define the (outer-)truncated...
Apr 21, 2026
general
Closure of a subset of a metric space is closed
From definition, if $X$ is a metric space, if $E \subset X$, and if $E'$ denotes the set of all limit points of $E$ in $X$, then the closure of $E$ i...
Apr 21, 2026
general
How do I reverse engineer this "power of"/exponent?
Take the following: (2)^3 = 8 I understand that this is 2 * 2 * 2 = 8 My question is how do I reverse engineer this if I do not know the power like this: ...
Apr 21, 2026
general
Via **inductive proof** show that $3^{2n}-1$ is divisible by 8 for all natural numbers n
Via inductive proof show that $3^{2n}-1$ is divisible by 8 for all natural numbers n The reason why that I was confused in this problem was because my ste...
Apr 21, 2026
