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Question 584079: The main cables of a suspension bridge are ideally parabolic. The cables over a bridge that is 400 feet long are attached to towers that are 100 feet tall. The lowest point of the cable is 40 feet above the bridge
a. Find the coordinatesof the vertex and the tops of the towers if the bridge represents the x-axis and the axis of symmetry is the y-axis
b. Find the equation that can be used to model the cables
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The main cables of a suspension bridge are ideally parabolic. The cables over a bridge that is 400 feet long are attached to towers that are 100 feet tall. The lowest point of the cable is 40 feet above the bridge
a. Find the coordinatesof the vertex and the tops of the towers if the bridge represents the x-axis and the axis of symmetry is the y-axis
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vertex: (0,40)
tower tops: (-200,100) and (200,100)
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b. Find the equation that can be used to model the cables
Form: ax^2 + bx + c = y
Using (0,40)::::::: 0....0...c = 40
Using (-200,100)::: 40000a - 200b + c = 100
Using (200,100):::: 40000a + 200b + c = 100
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Solve for a,b,c:
a = 0.0015
b = 0
c = 40
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Equation:
y = 0.0015x^2 + 40
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Cheers,
Stan H.
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