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# The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway which is horizontal and 100 m long is supported by vertical wires attached to the cable, the longest wire being 30 m and the shortest being 6 m. Find the length

3.  The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway which is horizontal and 100 m long is supported by vertical wires attached to the cable, the longest wire being 30 m and the shortest being 6 m Find the length of a supporting wire attached to the roadway 18 m from the middle

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Given,

The width of the parabolic cable = 100m

The length of the shorter supportive wire attached =  6m

The length of the longer supportive wire attached = 30m

Since the rope opens towards upwards, the equation will be of the form

Now if we consider origin at the centre of the rope, the equation of the curve will pass through points, (50,30-6)=(50,24)

Hence the equation of the parabola is

Now at a point, 18 m right from the centre of the rope, the x coordinate of that point will be 18, so by the equation, the y-coordinate will be

Hence the length of the supporting wire attached to roadway from the middle is 3.11+6=9.11m.

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