What are the parameters of a parabola
In the following figure I understand the $bx+c$ part. It is simply the equation of a line. But I don't understand where did $ax^2$ came from? What ex...
22 Apr 2026 1 READS
Archive: News
How to put a system in the form x' = Ax + Bu
This question is from a feedback control lecture. I do not understand how to compute this, please explain interactively. Given this differential equation,...
22 Apr 2026 1 READS
How many solution does $1/a+1/b+1/c+1/d=1$ have?
From my friend, he gives me a competition question: "How many solution $(a,b,c,d)$ does $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{1}{d}=1$ have where $a,...
22 Apr 2026 1 READS
Examples of integration by parts that work both ways
Usually, integration by parts only works one way. For example, evaluating $\int xe^x\,dx$ can only be done by differentiating $x$ and integrating $e^x$, b...
22 Apr 2026 1 READS
![Are all uncountable infinities greater than all countable infinities? Are some uncountable infinities greater than other uncountable infinities? [duplicate]](https://edu.smbbmcl.edu.pk/uploads/are-all-uncountable-infinities-greater-than-all-countable-infinities-are-some-uncountable-infinities-greater-than-other-uncountable-infinities-duplicate_720.jpg)
Are all uncountable infinities greater than all countable infinities? Are some uncountable infinities greater than other uncountable infinities? [duplicate]
I recently finished a discrete mathematics class, and near the end of the semester, the prof (very superficially) touched on countable and uncountable inf...
22 Apr 2026 1 READS
How to prove rigorously that the series $1/(3n)$ diverges
How can I prove rigorously that the series $$\sum_{n=1}^\infty \frac{1}{3n}$$ Diverges, assuming that I know that the harmonic series when $p = 1$ diverge...
22 Apr 2026 1 READS
Inversion in circle
Let $C$ be a circle with the middle point $O$ and the radius $r$, we say that the points $P$ and $P'$ are inverse points with respect to $C$ if: $1.$...
22 Apr 2026 1 READS
Center of mass of a circular arc
I have an infinitesimally thin wire in the shape of a circular arc, with uniform mass distribution. I would like to know the location of the center of mas...
22 Apr 2026 1 READS
What are some interpretations of Von Neumann's quote?
John Von Neumann once said to Felix Smith, "Young man, in mathematics you don't understand things. You just get used to them." This was a response to...
22 Apr 2026 1 READS
Even degree polynomial.
I am trying to prove that if $p(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\cdot\cdot\cdot+a_{0}$ is an even degree polynomial with $a_{n}>0$ then its range is of th...
22 Apr 2026 1 READS
