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A clock sits on a desk so that its center is 35 inches from the floor. The MINUTE hand is 5 inches long. Let theta (θ) be the angle between the 12 o'clock position and the minute's hand position at any time (t) minutes after the hour.

a) Using a trigonometric function of theta (θ) write an expression for y the distance from the tip of the minute to the floor.

b) Express theta (θ) as a function of time (t).

c) In terms of θ, find an expression for dy/dt the rate at which y changes.

d) How many minutes after the hour is y increasing most rapidly? Use dy/dt to justify answer.