 #1
Muskyboi
 10
 0
 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+(96)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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