math

In a suspension bridge, the shape of the suspension cables is parabolic. The bridge shown in the figure has towers that are 400 m apart, and the lowest point of the suspension cables is 100 m below the top of the towers. Find the equation of the parabolic part of the cables, placing the origin of the coordinate system at the lowest point of the cable.

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  1. Since the vertex is set at (0,0), you have a parabola

    y = ax^2
    where y(200) = 100
    a*40000 = 100
    a = 1/400

    y = 1/400 x^2

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  2. thank you steve

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  3. There are 2 towers that are each 10m high.  A rope that is 15m long is strung between the tops of the towers.  At its lowest point the rope sags 2.5m above the ground (see schematic diagram).  How far apart are the towers?

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