A box contains 5 red and k blue balls. A ball is selected at random from the box. If the probability of selecting a blue ball is \(\frac{2}{3}\), find the value of k.
If \(\frac{x + P}{(x - 1)(x - 3)} = \frac{Q}{x - 1} + \frac{2}{x - 3}\), find the value of (P + Q).
Find the derivative of \(\sqrt[3]{(3x^{3} + 1}\) with respect to x.
If \(T = \begin{pmatrix} -2 & -5 \\ 3 & 8 \end{pmatrix}\), find \(T^{-1}\), the inverse of T.
A function is defined by \(h : x \to 2 - \frac{1}{2x - 3}, x \neq \frac{3}{2}\). Find \(h^-1\), the inverse of h.
