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Math 213 Name: Quiz 4 1. [12 points] Water is being drained from the bottom of an inverted conical tank. According to Torricelli’s law, the volume V of the water left in the tank obeys the differential equation dV = −kV 1/3 dt where k is a constant. (a) [4 pts] Find the general solution to the above equation. (b) [8 pts] Suppose the tank holds 1000 L of water, and that water initially drains from the tank at a rate of 0.20 L/sec. How long will it take for the tank to drain completely? 2. [5 points] Consider the following initial-value problem y0 = x + y2 − 3.6, y(0) = 2. Use Euler’s method with step size ∆x = 0.5 to estimate y(1). 3. [3 points] Which of the following graphs shows a solution to the equation y0 = x2 − y2 ? (Circle your answer.)