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Q7. (a) A liquid is evaporating from an open vessel such that the volume of the liquid remaining, V cm³, after x hours, is given by V = 15 c - (x^3⁄4 - x^1⁄2 ), where c is a constant. The liquid evaporates completely after exactly 16 hours.

Determine EACH of the following:

(i) The initial volume of the liquid; (4)

(ii) The rate of evaporation after exactly 8 hours. (6)

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

u = 2 sin θ + (1 - cos²θ)/(1 + cos θ) (6)