Really need help with solving these question for an assignment. please thoroughly explain how you solve it

Stay Hydrated Torricelli's Law explains how fast water flows out of a tank. Imagine a cylindrical tank in which the water is filled up to height h meters (m), and suppose there is a hole in the bottom of the tank. Suppose that the tank has cross sectional area At and the hole has cross sectional area Ah, both in units m. The top of the tank is open. Torricelli's law tells us that the speed of the water leaving the tank is v= V2gh m/s, where g is a constant and h is, again, the height of the water in the tank. But there is also an open faucet above the tank, and water is flowing into the top of the tank at a constant rate of 1 m3/s. So water is flowing in and water is flowing out. Our goal is to be able to describe (1) the volume of water V(t) in the tank, and (2) the height of the water h(t) in the tank. 11. If water flows out according to v, and the area of the hole is Ay, what is the volume of water flowing out of the tank per second?! 12. If the tank is cylindrical, the height of the water is h, and the tank's cross sectional area is At, what is the volume of water in the tank as a function of the height of water h? 13. Draw a picture of the tank, the faucet above, and the flow out the bottom. Label the flows in and out, the height of the water in the tank, and anything else you know. Next to your drawing, draw a flow diagram for the volume of water in the tank V. 14. Write a differential equation for the rate of change of the volume of water in the tank with respect to time, dv/dt. 15. Use this to write a differential equation for the rate of change of the height of water in the tank with respect to time, dh/dt. 16. Find an equilibrium solution for the height of water in the tank and explain your results in words. Stay Hydrated Torricelli's Law explains how fast water flows out of a tank. Imagine a cylindrical tank in which the water is filled up to height h meters (m), and suppose there is a hole in the bottom of the tank. Suppose that the tank has cross sectional area At and the hole has cross sectional area Ah, both in units m. The top of the tank is open. Torricelli's law tells us that the speed of the water leaving the tank is v= V2gh m/s, where g is a constant and h is, again, the height of the water in the tank. But there is also an open faucet above the tank, and water is flowing into the top of the tank at a constant rate of 1 m3/s. So water is flowing in and water is flowing out. Our goal is to be able to describe (1) the volume of water V(t) in the tank, and (2) the height of the water h(t) in the tank. 11. If water flows out according to v, and the area of the hole is Ay, what is the volume of water flowing out of the tank per second?! 12. If the tank is cylindrical, the height of the water is h, and the tank's cross sectional area is At, what is the volume of water in the tank as a function of the height of water h? 13. Draw a picture of the tank, the faucet above, and the flow out the bottom. Label the flows in and out, the height of the water in the tank, and anything else you know. Next to your drawing, draw a flow diagram for the volume of water in the tank V. 14. Write a differential equation for the rate of change of the volume of water in the tank with respect to time, dv/dt. 15. Use this to write a differential equation for the rate of change of the height of water in the tank with respect to time, dh/dt. 16. Find an equilibrium solution for the height of water in the tank and explain your results in words