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 .

P is the mid-point of \(\overline{NO}\) and equidistant from \(\overline{MN}\) and \(\overline{MO}\) . If \(\overline{MN}\) = 8i + 3j and \(\overline{MO}\) =...

(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...

There are 6 boys and 8 girls in a class. If five students are selected from the class, find the probability that more girls than boys are selected

(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 firs...

(a)The table shows the distribution of heights ( cm ) of 60 seedlings in a vegetable garden. Heights(cm) 0.1 - 0.3 0.4 - 0.6 0.7 - 0.9 1.0 - 1.4 1.5 - 1.9 2....

(a) Find the derivative of \(4x-\frac{7}{x^2}\)with respect to \(x\), from first principle. (b) Given that tan \(P =\frac{3}{x - 1}\) and tan \(Q\) =\frac{2}...

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

(a) A bus travels with a velocity of \(6 ms ^{-1}\). It then accelerates uniformly and travels a distance of 70 m. If the final velocity is \(20 ms ^{-1}\), ...