MATH 3000 Quiz: MATH 331 Mizzou Quiz 3 Solutions

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15 Feb 2019
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Also, /4 3/4, so the endpoints of the interval of de nition below are approximately 1/4 and 11/4. 2. 5 (c) (2 3 /4, 2 + /4). Solution: (a) the voltage drop across the capacitor is given by v = q/c = q/0. 02 where q = q(t) is the charge accumulated on the capacitor and c = 0. 02 is the capacitance. The voltage drop across the resistor is ir = 0. 3i where i = dq/dt is the current in the circuit and r = 0. 3 is the resistance of the resitor. We consider this equation with the initial conditions q(0) = 0. Multiplying the equation by 10/3 we have q + Multiply ng the equation by the integrating factor = e500t/3, we get (e500t/3q) = The voltage across the capacitor is therefore given by v = v(t) = 50q(t) = 10 10e 500t/3. (b) we wish to nd the time t for which v(t ) = 9:

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