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5. A liquid flows into the top of a tank and exits via a hole at the base of the tank. The inlet and outlet flowrates (m3/s), along with the height of the liquid (m) in the tank vary with time and are denoted by the symbols Fin(t),Fout(t), and h(t) respectively. a) Prove that the open-loop dynamics can be described by the ordinary differential equation (ODE): Adtdh(t)=Fin(t)Fout(t) b) If the outlet flow is proportional to the height of the liquid in the tank, that is, Fout(t)h(t), determine the linear ODE. c) Put the linear ODE obtained from Part (b) in Standard Form and determine the process open-loop time constant (o) and process steady-state gain (Kp)