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Q7. (a) A car wash operates daily from 1000 hours to 1730 hours.

The average queuing time, q minutes, for customers arriving x hours after opening time is given by the function q = 0.2 (2.5 + 7.5x² - x³).

Calculate EACH of the following for this car wash:

(i) the busiest time of day;   (8)

(ii) the expected queuing time at the busiest time.         (2)

(b) Given u = (1 - sin² θ)/(1 - sinθ) - cosθ, determine  du/dq and (d² u)/(dq²)      (6)