formula for finding perimeter of half circle
i was looking for this problem http://www.majortests.com/gre/problem_solving_expl.php?exp=50313039243130243330 and was surprised if it is correct,we know ...
22 Apr 2026 1 READS
Archive: General
Laplace Transform of a Heaviside function
Find the Laplace transform. $$g(t)= (t-1) u_1(t) - 2(t-2) u_2(t) + (t-3) u_3(t)$$ I understand that the $\mathcal{L}\{u_c(t) f(t-c)\} = e^{-cs}*F(s)$ Find...
22 Apr 2026 1 READS
![Cartesian Product of Two Countable Sets is Countable [closed]](https://edu.smbbmcl.edu.pk/uploads/cartesian-product-of-two-countable-sets-is-countable-closed_720.jpg)
Cartesian Product of Two Countable Sets is Countable [closed]
How can I prove that the Cartesian product of two countable sets is also countable?
22 Apr 2026 1 READS
Symmetry functions and integration
I have this: Case 1) If f is a pair function $f(-x)=f(x)$ then $\int_{-a}^a f(x)dx=2\int_0^af(x)dx$ Case 2) If $f$ is a inpair function $f(-x)=-f(x)$ then...
22 Apr 2026 1 READS
Definition of arbitrarily large model in model theory
In 'A Mathematical Introduction to Logic' by Enderton, page $147,$ the author stated the following theorem. Theorem $26$A If a set $\Sigma$ of s...
22 Apr 2026 1 READS
Scaling the normal distribution?
I might just be slow (or too drunk), but I'm seeing a conflict in the equations for adding two normals and scaling a normal. According to page 2 of t...
22 Apr 2026 1 READS
What is the formal proof of AA similarity test?
It is a well-known fact that if any two triangles are equiangular then their sides are proportional and converse. But I am not sure how to prove it by usi...
22 Apr 2026 1 READS
How to solve $\sin^2 (2x) = 2 \sin (2x)$
I am not sure how to solve this: $$\sin^2 (2x) = 2 \sin (2x)$$ I thought I could rewrite it like this: $$4 \sin^2 (x) \cos^2 (x) = 4 \sin (x) \cos (x)$$ a...
21 Apr 2026 1 READS
Find the inverse of the cubic function
What is the resulting equation when $y=x^3 + 2x^2$ is reflected in the line $y=x$ ? I have tried and tried and am unable to come up with the answer. The f...
21 Apr 2026 1 READS
Is the sequence $\{\varphi^{(k)}(n)\}$ an eventually periodic sequence?
give a number $n \in \mathbb{Z}^+$，write it as $n = (\overbrace{a_1a_2\cdots a_{p_1}})_g$, it means $n$ as the $g$ base. for example: $n = (5)_{10} = (\o...
21 Apr 2026 1 READS
