The current it in an electrical circuit is given by the

Question

1. A water tank contains 1000 gals of water in which 25 lbs of salt are dissolved. Ten gallons of brine, each contains 4 lb of dissolved salt, run into the tanks per minute. The mixture, kept uniform by stirring, runs out at the same rate. Model the above system into a differential equation. Also find the amount of salt dissolved v(t) in the tank at any time t.

2. Let R be the region enclosed by the x-axis, y = √x, and y = 2 - x. Rotate R about the y-axis and find the volume.

3. The current i(t) in an electrical circuit is given by the following differential Equation with initial conditions i(0) = 0, i'(0) = 0. Determine the current as a function of t.

d²i/dt² + 2.di/dt = e^2t.