Question: A bead slides frictionlessly down a wire from the point ((1,0)) to ((0,0)). a. Determine the equation of the path (shape of the wire) such

A bead slides frictionlessly down a wire from the point \((1,0)\) to \((0,0)\).

a. Determine the equation of the path (shape of the wire) such that the bead takes the leat time between the given points.

b. How much time did it take the bead to follow this path?

c. If the path between these points is given by the line \(y=x\), then how much time does the bead take?

d. If the path between these points is given by \(y=x^{2}\), then how much time does the bead take? Explain your answer.

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