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ater tank with a hole of area Consider a w a in its base. The tank will drain through this hole, at a rate proportional to the height of the water (as this influences the pressure). Torricelli's Law describes this process: dh dtA where h(t) the height of water in the tank at time t in m, . Ais the cross-sectional area of the tank in m2, ·a-the area of the hole in the bottom of the tank in m, and g 9.81 m/s2 is the acceleration due to gravity For the following questions, use A 10 m2, a 0.1 m2, and h(0) 10 m 1. Solve the ODE using separation of variables 2. Use a first order Taylor series to show that when Torricelli's law is linearised about the initial height, we get dh = _ay2h(0)(h(t) + h(0)) dt AV 3. Solve the linearised ODE using the integrating factor method 4. Plot your solutions to Q1 and Q3 in the same figure. Discuss the accuracy of the linearised ODE solution