A function h : [0,10] -> R, h(t) = 0.005t(t-10)" (2t + 5) models the height of liquid in a particular glass, measured in centimetres at time, t minutes. a. Find the average height of liquid in the glass. b. Find the maximum height of liquid in the glass. Give your answer in cm correct to one decimal place. c. Find the average rate of change of the height of liquid in the glass for the time it is filling. Give your answer correct to two decimal places in cm/min. d. Find the time when the height of liquid in the glass is increasing at its maximum rate. Give your answer in minutes correct to two decimal places. The glass is in the shape of a right circular cone with height 12 cm and radius 3 cm as shown below. / is the radius of the top surface of the liquid in centimetres and h is the height of the liquid in centimetres at time t minutes. 3cm 12cm e. Show that the volume, I em', of liquid in the glass is given by V= -h. T. Find the times when the glass is half full. Give your answers in minutes correct to two decimal places. Leth, :[a,10 + a]-> R, h, (t)= 0.005(t -a)(t-a-10) (2(t-a)+5) model the height of liquid in a similar glass, in centimetres at time, t minutes. a is positive real constant. g. Find the values of a such that the average rate of change of h, (t ) from t= a to t = 2 + a is equal to the gradient of the function h, (t ) at the first time when the original glass was half full. Give your answer correct to two decimal places