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 X a. Show that f'(x) = - path y = f(x).) b. Solve the equation in part (a) for f(x), using f(19) = 0. (Hint: Assume that the skier is always pointed directly at the boat and the rope is on a line tangent to the Ay boat y=f(x) path of skier f(x)-- 19 ft rope (x,f(x)) skier (19,0) Not to scale

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