Decide whether the following statement is true of false. if it is true, give a short explanation, otherwise, give a counterexample. let g be an arbitrary flow network, with a source s, a sink t, and a positive integer capacity ce on every edge e; and let (a, b) be a minimum s − t cut with respect to these capacities ce : e ∈ e. now suppose we add 1 to every capacity; then (a, b) is still a minimum s − t cut with respect to these new capacities {1 + ce : e ∈ e}

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?