SOLUTION: The cables of the horizontal suspension bridge are supported by two towers 120 ft. apart and 40 ft. high. If the cable is 10 ft. above the floor of the bridge at the center, find t
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Question 1187364: The cables of the horizontal suspension bridge are supported by two towers 120 ft. apart and 40 ft. high. If the cable is 10 ft. above the floor of the bridge at the center, find the equation of the parabola using midpoint of the bridge as the origin. (Note: A suspension bridge cable hangs in a parabolic arc if the weight is distributed uniformly along the horizontal.) Answer by ikleyn(52776) (Show Source):
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The cables of the horizontal suspension bridge are supported by two towers 120 ft. apart and 40 ft. high.
If the cable is 10 ft. above the floor of the bridge at the center, find the equation of the parabola
using midpoint of the bridge as the origin.
(Note: A suspension bridge cable hangs in a parabolic arc if the weight is distributed uniformly along the horizontal.)
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Since the midpoint of the bridge is the origin, we write the equation of gthe parabola in the form
y = ax^2 + 10.
The only unknown is the coefficient "a". We find it from the condition that y = 40 at x= 60 ft:
40 = a*60^2 + 10.
It gives a = = = = .
The final equation of the parabola is y = . ANSWER
