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Unformatted text preview: parametric equations. As your starting point, use the parametric equations of the cycloid x = a ( sin ) y = a (1cos ) 3) (10 points) Show that the shape of a wire loop (length l ) that encloses a maximum area is a circle. Note: consider only shapes that lie in a plane. 4) (15 points) Find the shortest mountain path around a volcano. Describe the surface of the volcano as a cone with z = 1 x 2 + y 2 and nd the shortest path between the points ( x, y, z ) = (0 ,1 , 0) and (0 , 1 , 0). Calculate the length of the path. TOTAL 50 points...
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 Fall '08
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 mechanics, Work

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