An airplane is asked to stay within a holding pattern near Chicago’s O’Hare International Airport. The function d(x) = 70 sin(0.65x) + 150 represents the distance d, in miles, of the airplane from the airport at time x, in minutes.

(a) When the plane enters the holding pattern, x = 0 how far is it from O’Hare?

(b) During the first 20 minutes after the plane enters the holding pattern, at what time x is the plane exactly 100 miles from the airport?

(c) During the first 20 minutes after the plane enters the holding pattern, at what time x is the plane more than 100 miles from the airport?

(d) While the plane is in the holding pattern, will it ever be within 70 miles of the airport? Why?