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Question 1189231: t
he center of a suspension bridge forms a parabolic arc. The cable is suspended from the top of the support
towers, which are 800 ft apart. The top of the towers 170 ft above the road and the lowest point on the cable is
midway between the towers and 10 ft above the road. Find the height of the cable above the road at a distance of
100 ft from the towers
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! the center of a suspension bridge forms a parabolic arc. The cable is suspended from the top of the support towers, which are 800 ft apart.
The top of the towers 170 ft above the road and the lowest point on the cable is
midway between the towers and 10 ft above the road.
Find the height of the cable above the road at a distance of 100 ft from the towers
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A parabola has the form y = ax^2 + bx + c
Find the parabola with its vertex at (0,0) and the towers at (-400,0) and (400,0).
Add the 10 feet later.
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0 = 0*a + 0*b + c ---> c = 0
160 = a*(-400)^2 + b*(-400)
160 = a*(400)^2 + b*(400)
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160 = 160000a - 400b
160 = 160000a + 400b
--------------------------------- Subtract
0 = -800b ---> b = 0
----
160 = 160000a
a = 1/1000
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y = x^2/1000 + 10 is the equation of the cable
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For 100 feet from the towers and between the towers:
At x = 300:
y = 90000/1000 + 10 = 100 feet
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