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Muskyboi

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- Homework Statement
- 9 gallons/hour entering with a salt concentration of 1/5(1+cos(t)) pounds/gallon (this is a function of time t).

15000 gallon capacity tank with 600 gallons of water with 5 pounds of salt dissolved inside.

6 gallons/hour leaving.

How much salt is the tank just before it overflows?

- Relevant Equations
- salt concentration= 1/5(1+cos(t)) pounds/gallon (this is a function of time t)

v(t)=600+(9-6)t

=600+3t

1500=600+3t

therefore t=300 hrs when tank is full

Cin=1/5(1 + cost)

ds/dt=Rate in - rate out = CinRin - Cout*S(t)/V(t)

=1/5(1 + cost)*9 - 6*S(t)/(600+3t)

S(0)=5 ib

Solving the first order linear ODE we get: https://www.desmos.com/calculator/l7iixzgyll

therefore S(300)=279.797 Ib

does my solution look right?

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