Using the trapezium rule with seven ordinates, evaluate, correct to three decimal places, \(\int_{2.4}^{3.6} \frac{1}{\sqrt{x^2 - 2}}\)dx

If tan x = \(\frac{1}{3}\), where 180º < x < 270º evaluate \(\frac{sin2 x - cos x}{2 tan x + sin 2x}\), leaving the answer in surd form (radicals)

The table shows the distribution of distance (in km) of 60 villages from a state capital. Distance (in km) 0 - 19 20 - 29 30 - 39 40 - 49 50 - 59 70 - 99 100...

Two events M and N are such that P(M) = \(\frac{1}{2}\), P(N) = \(\frac{9}{20}\) and P(M ∩ N) = \(\frac{11}{50}\) (a) P(M ∩ N'): (b) P(M' ∩ N)

Find the equation of the normal to the curve y = 7x - 5x\(^2\) at x = 2

SECTION B (PART 1) A curve is given by y = 8x + \(\frac{27}{2x^2}\), FIND: (a) an expression for \(\frac{dy}{dx}\), (b) the coordinates of the stationary poi...

The magnitude of two vectors u and v are 10N and 12N respectively. If the magnitude of their resultant is 15N, calculate the angle between them.

A body of mass 40 kg is placed on a rough inclined plane which makes an angle of 30\(^0\) with the horizontal. If a force of 420 N is applied upwards paralle...

Find the sum of all natural numbers between 403 and 603 which are divisible by 7