Coordinate-free notation for tensor contraction?
I am not sure if I can prevent this question from being too vague or with too large an overlap with other similar math.SE questions, but I will do my best...
Apr 18, 2026 1 VIEWS
Topic: General
5104 Articles 
Sixth root of -64 using Euler's formula and De Moivre's theorem
I am attempting to solve: $$(-64)^{\frac{1}{6}}$$ Using the relation: $$a+bi=re^{i(\tan^{-1}(\frac{b}{a})+2\pi n)}$$ And then applying De Moivre's th...
Apr 18, 2026 2 VIEWS
Units of a log of a physical quantity
So I have never actually found a good answer or even a good resource which discusses this so I appeal to experts here at stack exchange because this probl...
Apr 18, 2026 1 VIEWS
Factoring Quadratics: Asterisk Method
I'm teaching my students about factoring quadratics. We've done GCF, difference of two squares, squared binomials, and grouping. One of my colle...
Apr 18, 2026 1 VIEWS
Sleepwalking students on a 9x9 checkerboard [duplicate]
Each square of a 9x9 checkerboard is initially slept on by one of 81 students. At noon, each student will wake up and randomly sleepwalk to a valid adjace...
Apr 18, 2026 1 VIEWS
Calculate the new position of a point after rotating it around another point 2D
I have a point, whose location I know in Cartesian coordinates x and y. Now I need to calculate the coordinates of the point if it is rotated with another...
Apr 18, 2026 1 VIEWS
Solving $\tan 2x=1+2\sin 4x$
Solve: $$\tan 2x=1+2\sin 4x$$ My work: $$\left(\frac{\sin2x}{\cos2x}\right)(1+2\cos2x)(1-2\cos2x)=1$$ $$\frac{(\sin2x+\sin4x)(\sin2x-\sin4x)}{\cos2x}=1$$ ...
Apr 18, 2026 1 VIEWS
Derivative with a Square root in Denominator
$f(x) = \dfrac{-3}{\sqrt{3x^2 + 3}}$ I can't seem to figure this problem out. I think you would make the bottom(3x^2+3)^(1/2) and then use the chain ...
Apr 18, 2026 1 VIEWS
Doomsday Vs. Extinction - Population Growth Model
So the question goes something like this. Let $P(t)$ be the bunny population in a certain area after $t$ months. If $P(0)=200$, solve this IVP and show al...
Apr 18, 2026 1 VIEWS
Relation between chords length and radius of circle
Two chords of a circle, of lengths $2a$ and $2b$ are mutually perpendicular. If the distance of the point at which the chords intersect,from the centre of...
Apr 18, 2026 1 VIEWS
Find all $4$ digit numbers that are perfect squares and written with $4$ even integers
Find all $4$ digit numbers that are perfect squares and written with $4$ even integers. I let the digits be $2p,2q,2r,2s$, starting from the thousands pla...
Apr 18, 2026 1 VIEWS
How many years later the calendar of 2016 can be reused?
How many years later the calendar of 2016 can be reused? I was asked this question in an exam. I want to explain the term 'reuse' . If we ignore...
Apr 18, 2026 1 VIEWS