Permutations and Combinations questions
Five separate awards are to be presented to select students from a class of 30. How many different outcomes are possible if: If a student can receive any ...
21 Apr 2026 1 READS
Archive: General
How to find an angle of a non-right angle triangle when given two sides and an area?
How would I go about finding an angles of a non-right angled triangle when given the area and two of its sides. For example: In the triangle $ABC$, $a = 5...
21 Apr 2026 1 READS
Prove $2^{1/3}$ is irrational.
Please correct any mistakes in this proof and, if you're feeling inclined, please provide a better one where "better" is defined by whatever criteria...
21 Apr 2026 1 READS
Proof of a statement about the continuity of polynomials and rational functions
My notes do not include a proof to the following: If $p$ is a polynomial, then $p$ is continuous at every point in $R$. If $r = \frac{p}{q}$ is a ratio of...
21 Apr 2026 1 READS
Inner regular measures and tight measures
On a Hausdorff topological space $X$ with a sigma algebra $ Σ$ at least as fine as the Borel sigma algebra, a measure $\mu$ is said to be inner regular, i...
21 Apr 2026 1 READS
![How write a periodic number as a fraction? [duplicate]](https://edu.smbbmcl.edu.pk/uploads/how-write-a-periodic-number-as-a-fraction-duplicate_720.jpg)
How write a periodic number as a fraction? [duplicate]
What I call as a periodic number is for exemple $$0.\underbrace{13}_{period}131313...$$ or $$42.\underbrace{465768}_{period}465768465768.$$ So how can we ...
21 Apr 2026 1 READS
What will be the form of the equation of a standing wave in circular form as shown below?
Following is the image of a 3D standing electron wave in circular form. Each of its loop moves up and down (while the adjacent loop is supposed to be $\pi...
21 Apr 2026 1 READS
What does "extension" mean in the Axiom of extension
I am learning Set Theory from the book Naive Set Theory by Halmos as part of my course. The first chapter is on the Axiom of Extension. I understand what ...
21 Apr 2026 1 READS
How to establish the identity
How do I establish the identity in this problem? Struggling with this one at the moment. $$\frac{\sin\theta\cos\theta}{\cos^2\theta-\sin^2\theta}=\frac{\t...
21 Apr 2026 1 READS
Why is it called the Fundamental Theorem of Arithmetic?
The Fundamental Theorem of Arithmetic is easy enough to understand, saying that every integer greater than 1 is either prime or is the product of a unique...
21 Apr 2026 1 READS
