Explanation Determine the general solution using the given equations and then determine the tank volume and salt concentration at the given time of t = 10 min Given: A 1000 L tank contains 500L of water with a salt concentration of 10g/L. Water with a salt concentration of 50 g/L flows into the tank at a rate of R i n = 80 L/minutes. The fluid mixes instantaneously and is pumped out at a specified rate R o u t . Let y ( t ) denote the quantity of salt in the tank at time t Calculation: Since the water outflows at the rate of 40 L / min , there are 500 − 40 t liters of water in the tank. Note that after 10 minutes, the volume of water in the tank is 100 l i t e r s . d y d t = s a l t i n − s a l t o u t = ( 80 ) ( 50 ) − ( 120 ) ( y 50 − 4 t ) = 4000 − 12 y 50 − 4 t This can be rewritten as d y d t + 6 y 25 − 2 t = 4000 Therefore, A ( t ) = 6 25 − 2 t , B ( t ) = 4000 The integrating factor is hence α ( t ) = e ∫ 6

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ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 10.5, Problem 36E

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$y (t)$ assuming that $R_{o u t} = 120$ L/min and then calculate the tank volume and the salt concentration at $t = 10 \min$

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Chapter 10.5, Problem 35E

Chapter 10.5, Problem 37E

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y ( t ) assuming that R o u t = 120 L/min and then calculate the tank volume and the salt concentration at t = 10 min

Solution Summary: The author explains how to determine the tank volume and salt concentration at the given time of t = 10 min.

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$y (t)$ assuming that $R_{o u t} = 120$ L/min and then calculate the tank volume and the salt concentration at $t = 10 \min$

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y ( t ) assuming that R o u t = 120 L/min and then calculate the tank volume and the salt concentration at t = 10 min

Solution Summary: The author explains how to determine the tank volume and salt concentration at the given time of t = 10 min.

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y(t) assuming that Rout=120 L/min and then calculate the tank volume and the salt concentration at t=10min

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Chapter 10 Solutions

$y (t)$ assuming that $R_{o u t} = 120$ L/min and then calculate the tank volume and the salt concentration at $t = 10 \min$