PLEASE HELP ME WITH THIS ARAMETRIC PROBLEM!?

You may use your calculator but all work must be shown.

Part of a cross–country skier′s path can be described with the vector function

r = ( 2 + 6t + 2cos(t), ( 15 – t )( 1 – sin(t) ) for 0 ≤ t ≤ 15 minutes, with x and y measured in meters.

The derivatives of these functions are given by

x ′(t) = 6 – 2 sin(t) and y′(t) = – 15cos(t) + tcos(t) – 1 + sin(t).

Find the slope of the path at time t = 4. Show the computations that lead to your answer.

Find the acceleration vector of the skier when the skier's horizontal position is x = 60.

Find the speed, in meters/min of the skier when he is at his maximum height.

Find the total distance in meters that the skier travels from t = 0 to t = 15 minutes.