news
Integrating to find mass and centre of mass
A component of a stone plinth has a square base with corners at coordinates $(0,0,0,)$, $(0,2,0)$, $(2,2,0)$ and $(2,0,0)$. The height of the top surface ...
Apr 10, 2026
Archive: News
news
A Christmas tree has the shape of the conical helix. Find the length of the Christmas tree.
A Christmas tree has the shape of the conical helix. The helix has the circular base of 1 foot diameter, and it rises three complete turns. Find the lengt...
Apr 10, 2026
news
Taylor expansion of $\arccos(1-x)$ around $x=0$ to two terms
Doing a normal Taylor expansion of $\arccos(1-x)$ around $x=0$ to two terms by taking derivatives doesn't work because of division by zero. I've...
Apr 10, 2026
news
Finding a linear factor and fully factorising polynomials
I have the following question: Question: Find a linear factor that will fully factorise $x^3 - 2x^2 - 5x + 6$. When I checked the solutions the linear fac...
Apr 10, 2026
news
Chromatic number of a graph
Construct a graph $G$ as follows: The vertices of $G$ are the edges of a complete graph $K_5$ on 5 vertices. The vertices of G are adjacent if and only if...
Apr 10, 2026
news
How to pronounce "L'Hospital"? [closed]
How to pronounce "L'Hospital"? Some people pronounce like "lapital". When I was in 12th standard, some teachers used to pronounce "lapital" and some ...
Apr 10, 2026
news
What is the necessary and sufficient conditions for a quadratic equation to have one positive root?
the equation $ax^2 + bx + c = 0$ has positive roots if $b^2-4ac > 0$ $-b/a > 0$ $c/a > 0$ I would like to know is there any necessary and suffici...
Apr 10, 2026
news
Sum of Sinusoids with Same Frequency = Sinusoid (proof)
I am studying Fourier analysis on my own, I realised that probably the first thing you want to proof in Fourier transform is that the sum of 2 sinuoids (n...
Apr 10, 2026
news
Limits to infinity of exponential functions
I am completly blocked trying to prove the solution of the limits below 1) $$ \lim _{m\to\infty}\left(\cos\left(\frac{x}{m}\right)\right)^m\\1 \quad \text...
Apr 10, 2026
news
Does SSA congruence criterion work if the non-included angle is obtuse?
I was trying to make some triangles when $2$ sides and the non-included angle was given. When the angle given was below $90$ degrees, there were two possi...
Apr 10, 2026
