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 parall...

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)

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

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.

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