Imagine a horse located on the outer edge of a merry go round, and a ticket booth located outside the merry go round, as pictured below. The function D(t) describes the distance D (in feet) between the horse and the ticket booth t seconds after the merry go round starts;
D(t) = 40 - 15 cos (Pi (t) / 10)
a. How far is the ticket booth from the nearest point on the merry go round?
b. What is the diameter of the circular deck of the merry go round?
c. How many revolutions will the merry go round complete in two minutes?
d.) D is not an invertible function. However, give the largest interval of time containing t - 2 on which the function D(t) is invertible?