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Question 1072237: The cables of a suspension bridge are in the shape of a parabola. The towers supporting the cables are 500 feet apart and 60 feet high. If the cables touch the road surface midway between the towers, what is the height of the cable at a point 125 feet from the middle of the bridge?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The cables of a suspension bridge are in the shape of a parabola. The towers supporting the cables are 500 feet apart and 60 feet high. If the cables touch the road surface midway between the towers, what is the height of the cable at a point 125 feet from the middle of the bridge?
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Sketch that figure on an x/y coordinate plane.
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Let the cable touch the road at (0,0)
You have two points of the parabola:: (-250,60) and (250,60)
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Equation form of the parabola::
y = a*x^2
60 = a*250^2
a = 0.00096
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Equation of the parabola::
y = 0.00096x^2
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Your problem::
Height at 125 ft
y = 0.00096*125^2 = 15 ft
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Cheers,
Stan H.
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