If \((x - 5)\) is a factor of \(x^3 - 4x^2 - 11x + 30\), find the remaining factors.

If \(^9C_x = 4[^7C_{x - 1}]\), find the values of \(x\)

The volume of a cube is increasing at the rate of \(3\frac{1}{2} cm ^3 s^{ -1}\). Find the rate of change of the side of the base when its length is 6 cm .

(a) The inverse of a function \(f\) is given by \(f^{-1}(x)=\frac{5x - 6}{4 - x},x ≠ 4\).Find the:

 function, \(f (x)\)

(b) The inverse of a function \(f\) is given by \(f^{-1}(x)=\frac{5x - 6}{4 - x},x ≠ 4\).Find the:

value of x for which \(f (x) = 5\)

(a) The first term of an Arithmetic Progression is -8, the last term is 52 and the sum of terms is 286. Find the:

number of terms in the series;

(b) The first term of an Arithmetic Progression is -8, the last term is 52 and the sum of terms is 286. Find the:

common difference.