Suppose you decide to cut the wire into two pieces (not necessarily the same length) to shape into two circles. Write a function A ( x ) which models the total area of the two circles in terms of x , the length of one of the pieces of wire. (It may be helpful to use for a circle A = πr 2 and C = 2 πr ). Then find the length x that will minimize the total area.

Consider a double atwood machine constructed as follows: a mass 4m is suspended from a string that passes over a massless pulley on frictionless bearings. the other end of this string supports a second similar pulley, over which passes a second string supporting a mass of 3m at one end and m at the other. using two suitable generalized coordinates, set up the lagrangian and use the lagrange equations to find the acceleration of the mass 4m when the system is released. explain why the top pulley rotates even though it carries equal weights on each side.