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Q7. (a) The rate at which a particular vessel consumes fuel is given by:

rate = 10 + 0.000625V³ tonnes per hour (where V is the speed of the vessel in knots).

Calculate EACH of the following:

(i) the speed of the vessel which minimises the amount of fuel consumed on a passage of 1000 nautical miles; (10)

(ii) the amount of fuel consumed during the passage when the vessel sails at its most economical speed. (2)

(b) Determine the first and second derivatives of the function: (4)

P = sin θ + cos θ