updates
Calculating the area of an irregular semi-circle
I am very inexperienced when it comes to math and I'd like to calculate the area of an irregular semi circle. This shape is 200 ft wide and an averag...
Apr 17, 2026
Archive: Updates
updates
M/M infinity queueing model.
Customer arrivals at a 7-Eleven is Poisson at the rate of 20 per hour. They can be assumed to spend an average of 12 minutes picking up merchandise, with ...
Apr 17, 2026
updates
Related rates of a cube
Suppose the sides of a cube are expanding at a rate of $2$ inches per minute. How fast is the volume of the cube changing at the moment that the area of t...
Apr 17, 2026
updates
Good reference for local fields?
I learned and studied basic algebraic number theory (like number fields and extensions, prime decompositions, local fields, some of class field theory, .....
Apr 17, 2026
updates
Find the value of constant K in line.
Three points have coordinates $A (0, 7)$ $B (8, 3)$ and $C (3k, k)$. Find the value of the constant $k$ for which: i) $C$ lies on the line that passes thr...
Apr 17, 2026
updates
Notation for Expressing Sets of Functions
In my book ( a generic introduction to higher math textbook ), we are given the following: $B^{\{1,2,...,n\}}$ is the set of all n-sequences. I'm tak...
Apr 17, 2026
updates
$e^{1/z}$ and Laurent expansion
$e^\frac1z$ is not holomorphic at $z=0$, but it is known that it can be expanded as $$e^\frac1z=1+\frac1z+\frac1{2!z^2}+\frac1{3!z^3}+\cdots$$ The coeffic...
Apr 17, 2026
updates
How many 10-letter words are there in which each of the letters e,n,r,s occur at most once?
Solve with a generating function. My solution was $$g(x)=\left(\frac{x^0}{0!} + \frac{x^1}{1!}\right)^4 \left(\frac{x^0}{0!} + \frac{x^1}{1!} + \frac{x^2}...
Apr 17, 2026
updates
Determinant of the Identity Matrix proof
I have trouble proving that for all $n$, $\det(I_{n})=1$ $I_{n}$ is Identity Matrix $nxn$ I tried to use Inductive reasoning but without any progress
Apr 17, 2026
updates
Why every prime (>3) is represented as $6k\pm1$
Why is every prime (>3) representable as $6k\pm1$? Afterall, by putting values of k, we don't just get primes but also composites. Then why not $2k+1...
Apr 17, 2026
