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Q7. (a) The cost per hour in operating a vessel is £(2V² + 242), where V is the speed of the vessel in knots.

Calculate the speed of the vessel which will minimise the cost per nautical mile. (10)

Verify that the result obtained gives minimum cost per nautical mile.

(b) When a flywheel rotates through an angle of θ radians in t seconds, its angular velocity is given by

dθ/dt rads/s, and its angular acceleration is given by (d² θ)/dt² rads/s².

For a certain flywheel θ = 30t – 4t².

Determine EACH of the following for this flywheel:

(i) the angular velocity when t = 3; (3)

(ii) the angular acceleration; (1)

(iii) the time that elapses before the angular velocity is zero. (2)