(a) A boy runs in a line and his displacement at time t seconds after leaving the start point O is X metres, where 20X = 4t\(^2\) + t\(^3\). Find the:
(i) velocity of the body when t = 15 seconds (ii) value of t for which the acceleration of the body is 8 times his initial acceleration
(b) A body of mass 6 kg moves with a velocity of 7 ms\(^{-1}\). It collides with a second body moving in the opposite direction with a velocity of 5 ms\(^{-1}\). After collision, the two bodies move together with a velocity of 4 ms\(^{-1}\). Find the mass of the second body.
If P = {x:1 ≤ x ≤ 6} and Q = {x: 2 < x < 9 },where x ∈ R, find P ∩ Q.
Solve the inequality 2x\(^2\) + 5x - 3 ≥ 0.
simplfy \(\sqrt{(\frac{1}{64}}\))\(^{\frac{-2}{3}}\).
If (x - 3)is a factor of 2x\(^3\) + 3x\(^2\) - 17x - 30, find the remaining factors.
