Doubt on controllability and observability of a MIMO system
Suppose I have the a system of the type: $\dot{x}=\begin{bmatrix} -0.2152 & 3.9030\\ -1.2734& -4.7848 \end{bmatrix}\begin{bmatrix} 0.8\\ 0.5 \end{...
Apr 22, 2026 1 VIEWS
Topic: General
5104 Articles 
Marginal Distribution Calculation for use in Binomial Distribution.
[1 In the question I know how to calculate marginal distribution for X1 and X2. Like for X1 the marginal distribution for each column is the sum of each j...
Apr 22, 2026 2 VIEWS
How can I mathematically model and analyze an incremental game like Cookie Clicker?
Recently, I've been interested in the optimization of the infamous incremental game Cookie Clicker. From Wikipedia: The user initially clicks on a bi...
Apr 22, 2026 1 VIEWS
Direct proof of empty set being subset of every set
Recently I finished my first pure mathematics course but with some intrigue about some proofs of definitions by contradiction and contrapositive but not d...
Apr 22, 2026 1 VIEWS
Overflows in binary addition
This site has got 2 example for binary addition. The first, $0110 + 0111$ I can follow. The second, $1101 + 0101$ is being used as an example where overfl...
Apr 22, 2026 1 VIEWS
Arithmetic or Geometric sequence?
Given a sequence: $$1, \frac12, \frac13, \frac14, \frac15,...$$ Its explicit formula can be given as: $a(n) = \frac1n$ where $n \ge 1$. I actually want to...
Apr 22, 2026 2 VIEWS
Why is empty product defined to be $1$? [duplicate]
For example $\prod_{2 \le j < 1} 2^j= 1.$ How does that happen?
Apr 22, 2026 1 VIEWS
In general, what symbol should be used for time?
Is there a symbol which is generally recognized as a connotation for time? For example... Dollar Amount = $ Count = # Time = ??? In this context, I am sim...
Apr 22, 2026 2 VIEWS
Calculate the multiplicative inverse of $7$ in $\mathbb{Z}_{12}$
I'm not sure how to do this but I gave it a try: I know that $7$ must have an inverse because $\text{ gcd }(12,7)=1$ Now, on this, use euclidean algo...
Apr 22, 2026 1 VIEWS
Solve $2000x^6+100x^5+10x^3+x-2=0$
One of the roots of the equation $2000x^6+100x^5+10x^3+x-2=0$ is of the form $\frac{m+\sqrt{n}}r$, where $m$ is a non-zero integer and $n$ and $r$ are rel...
Apr 22, 2026 1 VIEWS
Using the distributivity law for propositional logic
I know how to use the standard rule $$p\vee (q\wedge r)\equiv (p\vee q)\wedge (p\vee r)$$ but what if I have a two by two statement like: $$(p\vee q)\wedg...
Apr 22, 2026 1 VIEWS
Chain rule of fractions
How can I use chain rule to find the derivative of $y=\frac{(3x-3)^2}{x}$? Should I multiply the derivative of whole $y$ with the derivative of $(3x-3)^2$...
Apr 22, 2026 1 VIEWS