Determine the following for a pair of standard spur gears in mesh:
(a) an equation for the center distance C as a function of the numbers of teeth and module;
(b) the various combinations of 20° gears that an be used to operate at a center distance of 120 mm with an angular velocity ratio of 3:1. The module is not to be less than 2, and the gears are not to be undercut. The gears are to be hobbed.