Solved: The towers of the Golden Gate Bridge connecting San Francisco to Marin County

Chapter 10, Problem 88

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The towers of the Golden Gate Bridge connecting San Francisco to Marin County are 1280 meters apart and rise 140 meters above the road. The cable between the towers has the shape of a parabola and the cable just touches the sides of the road midway between the towers. The parabola is positioned in a rectangular coordinate system with its vertex at the origin. The point (640, 140) lies on the parabola, as shown. y x 1280 meters Parabolic Cable (640, 140) 160 meters a. Write an equation in the form y = ax2 for the parabolic cable. Do this by substituting 640 for x and 140 for y and determining the value of a. b. Use the equation in part (a) to find the height of the cable 200 meters from a tower. Round to the nearest meter.

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