Initially, a pendulum swings through an arc of 10 feet. On each successive swing, the length of the arc is 0.9 of the previous length. (a) What is the length of the arc of the eighth swing? (b) On which swing is the length of the arc first less than 5 feet? (c) After 15 swings, what total length will the pendulum have swung? (d) When it stops, what total length will the pendulum have swung?