In a figure, PQR = 60o, PRS = 90o, RPS = 45o, QR = 8cm. Determine PS

Given that cos z = L , whrere z is an acute angle, find an expression for \(\frac{\cot z - \csc z}{\sec z + \tan z}\)

If 0.0000152 x 0.00042 = A x 10\(^{B}\), where 1 \(\leq\) A < 10, find A and B

If (x + 2) and (x - 1) are factors of the expression \(Lx^{3} + 2kx^{2} + 24\), find the values of L and k.

Make T the subject of the equation \(\frac{av}{1 - v}\) = \(\sqrt[3]{\frac{2v + T}{a + 2T}}\)