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Calculus and Beyond Homework Help
[Differential equations] Mixing problem.
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[QUOTE="Muskyboi, post: 6269388, member: 668864"] [B]Homework Statement:[/B] 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? [B]Relevant Equations:[/B] salt concentration= 1/5(1+cos(t)) pounds/gallon (this is a function of time t) [ATTACH type="full" alt="So You Want a Degree in Physics 7-14 screenshot.png"]253608[/ATTACH] 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: [URL]https://www.desmos.com/calculator/l7iixzgyll[/URL] therefore S(300)=279.797 Ib does my solution look right? [/QUOTE]
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[Differential equations] Mixing problem.
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