4. Find dry zug for the following set of parametric equations = a(t - cost) and y = a(1 - sint) [6] 5. Find - and dora if sin ' (x y) = vi -ry [6] 6. Verify that f(x, t) = Le-4x /t is a solution of the heat equation of 1 02 f at 16 0r2 [4] 7. The volume of water in a dam is determined by the formula V = 2#h(3d - 2h). In a 3 hour period of rain, water is flowing into the dam resulting in an increase in the height (h) from 6m to 6.3m while the diameter (d) increases from 23m to 24m. Using differentiation, determine the average rate of change of the volume in the same period. [5]