Illustrate the following theorems using circuits of switches:
(a) x + xy = x
(b) x + yz = (x + y)(x + z)
in each case, explain why the circuits are equivalent.

The force on a cutting tool are 2600n vertically downward and 2100 horizontal. determine the resultant force acting on the tool and the angle at which it acts.

Steel is coated with a thin layer of ceramic to protect against corrosion. what do you expect to happen to the coating when the temperature of the steel is increased significantly? explain.

Apump is used to circulate hot water in a home heating system. water enters the well-insulated pump operating at steady state at a rate of 0.42 gal/min. the inlet pressure and temperature are 14.7 lbf/in.2, and 180°f, respectively; at the exit the pressure is 60 lbf/in.2 the pump requires 1/15 hp of power input. water can be modeled as an incompressible substance with constant density of 60.58 lb/ft3 and constant specific heat of 1 btu/lb or. neglecting kinetic and potential energy effects, determine the temperature change, in °r, as the water flows through the pump.