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What is the shape of the cable that supports the roadway of a suspension bridge?

What is the shape of the cable that supports the roadway of a suspension bridge? Our model is based on the following simplifying instructions:
A) the weight of the cable and suspension rods is negligible.
B) the weight of the roadway is uniform, x per unit length.
C) the suspension rods are so close together that the horizontal loading of the cable is the uniform weight of the roadway, x per unit length.

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