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1. Consider the brachistochrone problem of finding the curve of quickest descent as in the figure. (Note the convention: x denotes the vertical displacement, while
1. Consider the brachistochrone problem of finding the curve of quickest descent as in the figure. (Note the convention: x denotes the vertical displacement, while y denotes the horizontal displacement.) O y (a) Write down the expression for the total time T of the descent. (b) Determine the equation for y(x). (c) Show that the cycloid x = a(1 - cos 0), y = a(0 - sin 0) solves the equation
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