Como se resuelve este problema 3{50-[6•2(9-5)+1]}
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Answer:
The mass of salt in the tank after t minutes is
The concentration of salt in the tank reach 0.02 kg/L when
Step-by-step explanation:
Let <em>y(t)</em> be the mass of salt (in kg) that is in the tank at any time, <em>t</em> (in minutes).
The main equation that we will be using to model this mixing process is:
Rate of change of = Rate of salt in - Rate of salt out
We need to determine the rate at which salts enters the tank. From the information given we know:
- The brine flows into the tank at a rate of
- The concentration of salt in the brine entering the tank is
The Rate of salt in = (flow rate of liquid entering) x (concentration of salt in liquid entering)
Next, we need to determine the output rate of salt from the tank.
The Rate of salt out = (flow rate of liquid exiting) x (concentration of salt in liquid exiting)
The concentration of salt in any part of the tank at time <em>t</em> is just <em>y(t) </em>divided by the volume. From the information given we know:
The tank initially contains 100 L and the rate of flow into the tank is the same as the rate of flow out.
At time t = 0, there is 0.5 kg of salt, so the initial condition is y(0) = 0.5. And the mathematical model for the mixing process is
Using the initial condition y(0)=0.5
The mass of salt in the tank after t minutes is
To determine when the concentration of salt is 0.02 kg/L, we solve for <em>t</em>