Solve for $x$: $$6x = 2^3 \cdot \frac{1}{3}$$
Expand: $$(a+b)^2$$
During a high-intensity interval, you perform $3x$ jumps in the first minute and $x …
A barbell is loaded for a $70$ kg deadlift. The olympic bar itself has …
Factorize: $$a^2 - 64$$
Simplify completely: $$\frac{a^2-b^2}{a+b}$$
Calculate: $$\log_2(8) + \log_3(27)$$
An alpinist hikes up a $12$ km mountain trail at a velocity of $v$ …
Determine the exact, strictly positive root of the quadratic equation: $$x^2 - x - …
Let $r_1$ and $r_2$ be the roots of the polynomial equation $3x^2 - 12x …
A dynamic system's energy decays according to $E(t) = E_0 e^{-k t}$. If the …
Simplify into a single logarithmic expression: $$\ln(a) + \ln(b)$$
Given the $2 \times 2$ matrix $A = \begin{pmatrix} x & 2 \\ 3 …
Evaluate the infinite nested radical: $x = \sqrt{6 + \sqrt{6 + \sqrt{6 + \dots}}}$
How many distinct real solutions exist for: $$(x^2+7x+11)^{(x^2+x-12)}=1$$
Let $\omega \in \mathbb{C}$ be a complex root of the polynomial $x^3 - 1 …
Let $r_1, r_2, r_3$ be the three roots of the cubic polynomial $2x^3 - …
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 …