A car travelling at a velocity of 50kmh\(^{-1}\), covers a distance of 20km. If it was accelerating at 6kmh\(^{-1}\), calculate, correct to one decimal place, the time the car took to cover the distance.

The magnitude of a force \(xi + 15j\) is 17N. Find the :

(a) possible values of x ; 

(b) directions of the forces, correct to the nearest degree.

(a) The sum of the first n  terms of a sequence is given by \(S_{n} = \frac{5n^{2}}{2} + \frac{5n}{2}\). Write down the first four terms of the sequence and an expression for the nth term.

(b) The equation of a circle is given by \(x^{2} + y^{2} - 10x - 8y + 25 = 0\).

(i) Show that the circle touches the x- axis ; (ii) Find the coordinates of the point of contact.

(a) If \(\alpha\) and \(\beta\) are the roots of the equation \(2x^{2} + 5x - 6 = 0\), find the equation whose roots are \((\alpha - 2)\) and \((\beta - 2)\).

(b) Given that \(\int_{0} ^{k} (x^{2} - 2x) \mathrm {d} x = 4\), find the values of k.

(a) Express \(\frac{2x^{2} - 5x + 1}{x^{3} - 4x^{2} + 3x}\) in partial fractions.

(b) If \(\begin{vmatrix} x - 3 & -4 & 3 \\ 5 & 2 & 2 \\ 2 & -4 & 6 - x \end{vmatrix} = -24\), find the value of x.