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Question 1167083: The tower supporting the cable of suspension bridge are 1200 meters apart and 170 meters above the bridge it supports.Suppose the cable hangs, following the shape of a parabola, with its lowest point 20 meters above the bridge. How high is the cable 120 meters away from the tower?
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! Let's place the coordinate system such that the parabola is symmetric about the y-axis. Then the coordinates of the vertex are (0,20).
The vertex form of a parabola is y = a(x-h)^2 + k , where (h,k) is the vertex.
The end points are (600,170) and (-600,170) since the suspension points are
1200/2 m away from the origin and 170 m high.
We can use one of the end points to determine a:
170 = a*600^2 + 20 -> a = 150/600^2 = 1/2400
So the equation for the parabola is: y = x^2/2400 + 20
At 120 m from the tower, x = 600 - 120 = 480 m
Thus y = 480^2/2400 + 20 = 116 m
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