1. write down the differential equation that vC(t) satisfies, keeping the L as an unknown. 2. Write down the characteristic equation of the differential equation you wrote in step 1. 3. Write down the discriminant of the characteristic equation in step 2. 4. The expression for vc(t) satisfies the differential equation you wrote in Step 1. From the format of vc(t), what can you conclude about the discriminant? What value should the discriminant be?

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.

During a steady flow process, the change of energy with respect to time is zero. a)- true b)- false

Different types of steels contain different elements that alter the characteristics of the steel. for each of the following elements, explain what the element does when alloyed with steel.