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Unformatted text preview: The path of a water skier. Suppose that a boat is positioned at the origin with a water skier tethered to the boat at the point (30 , 0) on a rope 30 ft 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 Fgure. (a) [5 points] Show that f ( x ) =- 900-x 2 x . Hint: assume that the skier is always pointed di-rectly at the boat and the rope is on a line tangent to the path y = f ( x ) . (b) [5 points] Solve the equation in part (a) for f ( x ), using f (30) = 0. CONTINUE TO THE NEXT PAGE. Math 1120, Fall 2011 Homework 6 due 10/6 or 10/7 3 3. [10 points] (8.4: 40) Evaluate i e 4 t + 2 e 2 t-e t e 2 t + 1 dt. THIS IS THE LAST PAGE....
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