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Question 1167631: The cables of a horizontal suspension bridge are supported by two towers
120 feet apart and 40 feet high. if the cable is 10 feet above the floor of the
bridge at the center, find the equation of the parabola using the midpoint
of the bridge as the origin. Note: - A suspension bridge cable hangs in a
parabolic arc if the weight is distributed uniformly along a horizontal.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! The cables of a horizontal suspension bridge are supported by two towers
120 feet apart and 40 feet high. if the cable is 10 feet above the floor of the
bridge at the center, find the equation of the parabola using the midpoint
of the bridge as the origin.
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You have 3 points: (-60,30), (0,10) and (60,30)
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y = ax^2 + bx + c
For (0,10): y = 10 = c
c = 10
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For (-60,30): y = 30 = a*(-60)^2 - 60b + 10
3600a - 60b = 20 --> 180a - 3b = 1
(60,30) ---> 180a + 3b = 1
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180a - 3b = 1
180a + 3b = 1
---------------------- Add
360a = 2
a = 1/180
b = 0
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---> y = x^2/180 + 10
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Note: - A suspension bridge cable hangs in a
parabolic arc if the weight is distributed uniformly along a horizontal.
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NOTE: A suspension bridge cable hangs in a catenary curve if the weight is distributed uniformly --- NOT a parabola.
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