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homework6

homework6 - The path of a water skier Suppose that a boat...

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Math 1120 Homework 6 Due 10/6 or 10/7, 2011 Name: GRADES Book questions / 8 Presentation questions / 30 Print out these pages. Answer the “presentation questions” in the spaces provided. Include full explanations and write your answers in complete, mathematically and grammatically correct sentences. Your answers will be assessed for style and accuracy; you will be given written feedback on these prob- lems. Write your answers to the “book questions” on separate paper and staple to these pages. They will be assessed only for completeness. Always write neatly and legibly. Book questions — 8.3: 6, 8, 28, 38 8.4: 2, 14, 20, 22 Presentation questions 1. [10 points] (8.3: 54) Find the area enclosed by the ellipse x 2 a 2 + y 2 b 2 = 1 . CONTINUE TO THE NEXT PAGE.

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Math 1120, Fall 2011 Homework 6 — due 10/6 or 10/7 2 2. (8.3: 58)
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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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homework6 - The path of a water skier Suppose that a boat...

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