Mathematics, 24.07.2019 02:30 jorgereyes01
Atank contains 100 l of pure water. brine that contains 0.1 kg of salt per liter enters the tank at a rate of 10 l/min. the solution is kept thoroughly mixed and drains from the tank at the same rate. how much salt is in the tank after 6 minutes?
Answers: 1
be the amount of salt (in kg) after 
minutes. Then 
. The amount of liquid in the tank is 100 L at all times, so the concentration at time 
and ![\dfrac{dy}{dt} = \left( 0.1\dfrac{\mathrm{kg}}{\mathrm{L}}\right) \left( 10 \dfrac{\text{L} }{\text{ min}}\right)- \left[ \dfrac{y(t)}{100} \dfrac{\mathrm{kg}}{\mathrm{L}}\right] \left( 10 \dfrac{\text{L} }{\text{ min}}\right) \\ \\ \dfrac{dy}{dt} = 1 \dfrac{\mathrm{kg}}{\mathrm{min}}-\dfrac{y(t)}{10}\dfrac{\mathrm{kg}}{\mathrm{min}} \\ \\ \dfrac{dy}{dt} = 1 - \dfrac{y}{10} = \dfrac{10 - y}{10} \\ \displaystyle\int \dfrac{dy}{10 - y} = \int \frac{1}{10} dt \\ -\ln|10-y| = \frac{t}{10} + C](/tpl/images/0125/6401/669e6.png)
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Atank contains 100 l of pure water. brine that contains 0.1 kg of salt per liter enters the tank at...
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