general
Proving three lines are concurrent
In the triangle $ABC$ the segment $AD$ is altitude. $M$ is the midpoint of $BC$ and $N$ is the reflection of $M$ in $D$. The circumcircle of $ANM$ meets $...
Apr 15, 2026
Archive: General
general
Find the Nth derivative using Maclaurin series
The prompt is to find the 8th derivative of the function f(x) defined as, $$f(x) = \frac{3}{1+x-2x^2}$$ $$f^{(8)}(0) = ?$$ To find the maclaurin series, I...
Apr 15, 2026
general
Dimension of vector space in P3
I need help on the following question. I have no idea how to attempt it. Find the dimension of the vector space: $$ {p(x) = ax^3 + bx^2 + cx + d \in P_3:p...
Apr 15, 2026
general
Solving differential equation involving Heaviside's unit step function using Laplace Transform
$\ddot y(t)+2\dot y(t)+2y(t)=5H(t-2\pi)sint$ Also, $y(0)=1$ and $\dot y(0)=0$ I took the usual approach of solving an initial value problem but things get...
Apr 15, 2026
general
Find the surface area of a cone given height and the angle of the sector in the net
The problem is: The net of a cone is a sector with the angle 160 degrees, and the height (not slant height) of the cone is 2. Find the surface area. I hav...
Apr 15, 2026
general
What is the principal cubic root of $-8$?
According to my book it should be a real number, and according to WolframAlpha it should be $1+1.73i$ What is the correct answer?
Apr 15, 2026
![1 to the power i [duplicate]](https://news.conceivablytech.com/uploads/1-to-the-power-i-duplicate_720.jpg)
general
1 to the power i [duplicate]
Possible Duplicate: What is the value of $1^i$? I was thinking, what would 1^i be? Then I did: $e^{i\pi}=-1\rightarrow e^{i\pi}\cdot e^{i\pi}=e^{2i\pi}=-1...
Apr 15, 2026
general
Gauss' Lemma Proof Clarification
I am trying to follow a proof of Gauss' lemma in Number Theory by George Andrews. I have a few problems with a couple assumptions made. Let g.c.d.$(m...
Apr 15, 2026
general
How to symbol a sub-group?
If $G$ is a group and $H$ is subgroup of $G$, can I mark like this: $$K\prec G\;\;$$ Or I need to do this $$K<G\;\;$$ Thank you!
Apr 15, 2026
general
How to calculate the volume of an "icecream cone"?
How to calculate the volume of this shape? I've tried to do $2.5\cdot 2.5\cdot 3.14\cdot 12$ and then divide that with $3$ since the first part is a ...
Apr 15, 2026
