7. {5 marks}. An ant is sitting on the rim of a bike wheel suspended 0.5ft in the air (the circle shown below is meant to symbolize the bike wheel). The ant is initially at the point P on the wheel, but the wheel is spun at a constant speed so that it moves around in circles counterclockwise, making 1 full revolution each minute. As a result, the ants height as a function of time t (measured in minutes) can be modelled using an equation of the form Mt) = A + Bsin{21rt) + Ccos(2irt). {a} (1 mark). Identify the times during the rst minute of spinning at which the ant is at the points P, Q, R and 5'. (b) {1 mark). Given that the bike wheel has a radius of 1ft, identify the heights of the points Q, R and S. Then use this and your answer to (a) to nd the values of A, B and C so that Mt) models the ants height for all t. (c) (2 marks}. Find the rate of change of the ants height (is. the ant's vertical velocity]. {d} {1 mark). At what time(s:l [in the rst minute) is the ant's vertical velocity I]? Does your answer make sense based on the picture