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Q7. a. The rate R, in tonnes per hour, at which a particular vessel consumes fuel is given by:

R = 15 + 0.00048V³, where V is the speed of the vessel in knots.

Determine EACH of the following for this vessel when it embarks on a passage of 500 nautical miles:

i. the speed of the vessel which minimizes the amount of fuel consumed; (10)

ii. The minimum amount of fuel consumed. (2)

b. Determine ds/dt given s = 2(t² - t)/√t (4)