Volume of a triangular prism with 2 different bases
How do I arrive at a formula to calculate the volume of the following 3D shape? Does this shape have a proper name? It kind of looks like an irregular tri...
Category: Updates
Prove that for one vertex of a convex pentagon, the sum of distances to the other four is greater than the perimeter
The problem is from the journal 'Crux Mathematicorum', originally proposed by Paul Erdős and Esther Szekeres for the case of a convex $n$-gon wi...
What is the best Classical Mechanics book for undergraduate?
I want to know which book is the best for undergraduate classical mechanics, given that I am well equipped with newtonian mechanics (From: University Phys...
how does $2*4*6....(2n)$ turn into $2^n* n! $ in this power series?
How do they change the denominator from the equation into $2^{n}n!$ in this case? Isn't it just $2n$ as $n$ approaches infinity?
Triangular arrays and almost sure convergence of row averages
Suppose we have the triangular array $\{\{X_{in},i=1,\ldots,n\},n=1,2,\ldots\}$: $$\begin{array}{ccccc} X_{11}&&&&\\ X_{12}&X_{22}&...
If $f(x) = x^5 + x^3 + x$ find $f^{-1}(3)$ and $f(f^{-1}(2))$
How do I go about solving a problem like this? Do I find the inverse formula first? If so I am stuck at $\frac{x}{y} = y^3(y^2+1)$. Help is welcomed.
Understanding a vacuously true statement through the following example.
I have the following logical implication If John is a dragon, then everyone in town gets 1000 gold coins. p = John is a dragon q = Everyone in town gets 1...
Derivative vs division
Suppose we have a function $s=16t^2$ now if we find $\frac{ds}{dt}$ we get $v=28t$ but when we simply divide we know $s/t=v$ so $s/t=16t$. Why classical d...
Solving a Recurrence Relation/Equation, is there more than 1 way to solve this?
1) Solve the recurrence relation $$T(n)=\begin{cases} 2T(n-1)+1,&\text{if }n>1\\ 1,&\text{if }n=1\;. \end{cases}$$ 2) Name a problem that also ...
Order of operations - why are they in the order they're in?
I understand the order of operations, but why are they ordered the way they're ordered? Is there a particular reason why multiplication should have a...
