updates
Product of two distribution functions.
Let F and G be two distribution functions, does the product FG still a distribution function?
Apr 20, 2026
Archive: Updates
updates
Expansion of $\sin^5 \theta$ using the Complex Exponential
How do I expand $\sin^5\theta$ using the complex exponential, in order to obtain: $$\frac{1}{16}\sin 5\theta - \frac{5}{16}\sin 3\theta + \frac{5}{8}\sin\...
Apr 20, 2026
![volume of a parallelogram [duplicate]](https://news.conceivablytech.com/uploads/volume-of-a-parallelogram-duplicate_720.jpg)
updates
volume of a parallelogram [duplicate]
Possible Duplicate: Determinants and volume of parallelotopes Can you give me a direction about how to prove that $|det(UVW)|$ is the 3D volume of the par...
Apr 20, 2026
updates
Find the general solution of $\,y'' + 9y = 0$
$y'' + 9y = 0\,$ and $\,y(0) = 0, \; y'(0) = 3.$ Since this has real roots, I use the general solution $y_c = C_1 \mathrm{e}^{r_1 t} + C_2 ...
Apr 20, 2026
updates
Finding rank and nullity of 3X4 matrix
I am given \begin{bmatrix} 1 & 1 & 1 & 1 \\[0.3em] 1 & 2 & 4 & 2 \\[0.3em] 2 & 0 & -4 & 1 \end{bmatrix} I...
Apr 20, 2026
updates
Prove: $\cot x=\sin x\,\sin\left(\frac{\pi}{2}-x\right)+\cos^2x\,\cot x$
Prove: $$\cot x=\sin x\,\sin\left(\frac{\pi}{2}-x\right)+\cos^2x\,\cot x$$ Hi there! So this problem asks to prove this trigonometric identity. I am not s...
Apr 20, 2026
updates
When is tangent line horizontal?
When is the tangent line of the following function horizontal? $$y =\frac{\sin x}{e^x}$$ What steps or how can I draw a graph to figure this out or prove ...
Apr 20, 2026
updates
Given area of quadrilateral find missing coordinates
Can someone please explain how to proceed with this question, or maybe give me hints as to how to do it? I am not familiar with concave polygons at all, s...
Apr 20, 2026
updates
Quick way to determine if a rational function has a hole on the $x$-axis....
To sketch a rational function's graph, one step is to determine the sign $(+/-)$ of various intervals. I create intervals separated by the vertical a...
Apr 20, 2026
updates
What is the same as the inverse of a logarithm?
I am trying to simplify $f(n) = \frac{n}{\log(n)}$ into a more easily understandable function. Up until now, I got as far as $n\cdot(\left(\log(n)\right)^...
Apr 20, 2026
