Determine the exact arc length of the catenary curve $y = \cosh(x)$ spanning from …
A bead slides frictionlessly under gravity $g$ down a cycloid curve defined parametrically by …
Solve: $$\cos(x) = i$$ Format: [fraction] - i ln([term])
Find the residue of $f(z) = \frac{e^z}{(z-1)^2}$ at its pole $z=1$.
Calculate the principal value for: $$\sin(x) = 2$$ Format: X/Y - i*Z
A scheduler processes jobs on a 4x4 grid from $(0,0)$ to $(4,4)$. To maintain …
Find the expectation value of the slope between 2 random points strictly uniformly distributed …
Evaluate the definite integral analytically: $$\int_0^1 \frac{x^2 - 1}{\ln(x)} dx$$ Format: ln(X)
Calculate the exact number of trailing zeros in the decimal representation of $100!$ (100 …
In a fully developed, steady laminar pipe flow (Hagen-Poiseuille), the radial velocity profile is …
What is the expected area of a triangle whose three vertices are uniformly sampled …
Evaluate the exact sum of the infinite series: $$\sum_{n=1}^{\infty} \frac{1}{n^2}$$ Format: pi^2/X
Determine the explicit function $f(x)$ that satisfies the relation $f(x) + 2f\left(\frac{1}{x}\right) = 3x$ …
Determine the strictly largest eigenvalue $\lambda$ of the symmetric matrix $M = \begin{pmatrix} 2 …
A router dispatches 5 distinct data packets to 5 distinct MAC addresses. Due to …
Find the exact rational coefficient of the $x^4$ term in the Maclaurin series expansion …
Determine the least non-negative residue of $16! \pmod{17}$.