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
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
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 92E
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