updates
Intersection of two lines, each defined by a point and an angle
How to find a point where $L_1$ and $L_2$ intersect, given that $L_1$ goes through $(x_1,y_1)$ and it's slope is $\alpha_1$ and $L_2$ goes through $(...
Apr 18, 2026
Archive: Updates
updates
Split utilities among roommates give percent of month they occupied house
Let's say each month a utility bill comes and it needs to be split among a variable number of roommates. Let's say each person occupied the hous...
Apr 18, 2026
updates
Number of images formed by two plane mirrors formulae derivation.
Derive: Number of images formed by two plane mirrors inclined at an angle of $\theta$ is given by $$\frac{360}{\theta} -1 $$ What I think: Inclined mirror...
Apr 18, 2026
![How to find all irreducible polynomials in Z2 with degree 5? [duplicate]](https://news.conceivablytech.com/uploads/how-to-find-all-irreducible-polynomials-in-z2-with-degree-5-duplicate_720.jpg)
updates
How to find all irreducible polynomials in Z2 with degree 5? [duplicate]
I am totally lost on how to do this one. I am supposed to accomplish the following: Find all irreducible polynomials in $\mathbb{Z}_2[x]$ with degree $5$....
Apr 18, 2026
updates
Finding the mean and Std Dev from Geometric probability
Wasn't sure what to call this.. .But here goes I am having trouble solving the following questions, here is the first, and how I have gone about it T...
Apr 18, 2026
updates
Maximum number of circle packing into a rectangle
I'm asked to pack the maximum number of 10m^2 circle into a 257 x 157m rectangle. After a lot of research, I found out that there are no optimal solu...
Apr 18, 2026
updates
Proof that set is not a polyhedron.
Given following set $S = \{ \alpha \in \mathbf{R}^3 \mid \alpha _1 + \alpha _2e^{-t} + \alpha _3e^{-2t} \leq 1.1 \; \mbox{for}\; t \geq 1\}$. I more or le...
Apr 18, 2026
updates
Finding the matrix of a permutation
I am studying inverse permutations and I was given the following permutation sequence: 25413 I attempted to convert this permutation sequence into a permu...
Apr 18, 2026
updates
Finding the general Taylor Series of a function
I have to find the general Taylor Series Expansion, about $0$, of the following function. $$ \sqrt{x^4 -6x^2+1} $$ I have tried to use the identity $$ \le...
Apr 18, 2026
updates
Producing a recursive definition of the set of all positive integers not divisible by 5
Question Pretty basic problem here. Looking for some guidance on my train of thought. Give a recursive definition for the following set: the set of positi...
Apr 18, 2026
