Find the least value of the function \(f(x) = 3x^{2} + 18x + 32\).
A force of 32 N is applied to an object of mass m kg which is at rest on a smooth horizontal surface. If the acceleration produced is 8\(ms^{-2}\), find the value of m.
Given that \(\begin{pmatrix} 1 & -3 \\ 1 & 4 \end{pmatrix} \begin{pmatrix} -6 \\ P \end{pmatrix} = \begin{pmatrix} 3 \\ -26 \end{pmatrix}\), find the value of P.
Find the coordinates of the centre of the circle \(4x^{2} + 4y^{2} - 5x + 3y - 2 = 0\).
A and B are two independent events such that \(P(A) = \frac{2}{5}\) and \(P(A \cap B) = \frac{1}{15}\). Find \(P(B)\).
