Atrivial oz code for returning the number of elements of a list can be given by: declare fun {length l} case l of nil then 0 [] h|t then 1+{length t} end end for example, the call {browse {length [1 f 2 3 s 5]}} will display 6. explain why this function is not tail recursive. write an equivalent tail recursive function. write also an invariant for this tail recursive function. using the invariant, prove the correctness for this program.

Asimple speed reducer is composed of 2 spur gears. the pinion gear has a pitch diameter of 0.75" and 36 teeth while the driven gear has a pitch diameter of 4.0" and 192 teeth. a)-what is the diametral pitch of each gear? b)-if an electric motor rotating ccw at 3000 rpm is coupled to the pinion, what is the rotational speed of the driven gear? c)-if the torque delivered to the pinion is 1 n-m, what is the torque on the driven gear? d)-what is the power transmitted by the gear train?