Suppose that a boat is positioned at the origin with a water skier tethered to the boat at the point (19,0) on a rope 19 feet long. As the boat travels along the positive y-axis, the skier is pulled behind the boat along an unknown path, y f(x), as shown in the accompanying figure. 361-x y=fo0 path of skier a. Show that r'(x) (Hint Assume that the skier is always pointed directiy at the boat and the rope is on a line tangent to the path boa 19 rope y = f(x)) b. Solve the equation in part (a) for t(x), using f(19) =0. O) skier (19,0) Not to scale a. Start by writing the equation of the line formed by the rope between the boat and the water skier in terms of f(x), f'(x), and x

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