Controlling the flow from a draining tank Torricelli’s law says that if you drain a tank...

Controlling the flow from a draining tank Torricelli’s law says that if you drain a tank like the one in the figure shown, the rate y at which water runs out is a constant times the square root of the water’s depth x. The constant depends on the size and shape of the exit valve.

Suppose that    for a certain tank. You are trying to maintain a fairly constant exit rate by adding water to the tank with a hose from time to time. How deep must you keep the water if you want to maintain the exit rate

a. within 0.2 ft³/min of the rate y₀ = 1 ft³/min?

b. within 0.1 ft³/min of the rate y₀ = 1 ft³/min?