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A suspension bridge has twin towers that are 1300 feet apart. Each tower extends 180 feet above the road surface. The cables are parabolic in shape and are suspended from the tops of the towers. The cables touch the road surface at the center of the bridge. Find the height of the cable at a point 200 feet from the center of the bridge.

Respuesta :

Answer:

[tex]y = 17.04 ft[/tex]

Explanation:

Since the cable touches the road at the mid point of two towers

so here we have vertex at that mid point taken to be origin

now the maximum height on the either side is given as

[tex]y = 180 ft[/tex]

horizontal distance of the tower from mid point is given as

[tex]x = \frac{1300}{2} = 650 ft[/tex]

now from the equation of parabola we have

[tex]y = k x^2[/tex]

[tex]180 = k(650^2)[/tex]

[tex]k = 4.26 \times 10^{-4}[/tex]

now we have

[tex]y = (4.26 \times 10^{-4})x^2[/tex]

now we need to find the height at distance of 200 ft from center

so we have

[tex]y = (4.26 \times 10^{-4})(200^2)[/tex]

[tex]y = 17.04 ft[/tex]

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