IVP: Initial-Value-Problem 1. Consider a 100L tank containing 50L of salt water with a concentration of 1kg/L. Suppose that each second,3L of pure water flows into the tank and 2L of the mixture flows out of the tank. The tank is kept wellmixed at all times.(a) Write an IVP that governs the salt content in the tank. Make sure to explain your equation.(b) Solve the IVP from part (a).2. Now consider the same model as in question 1, but with a "salt buffer" involved. This buffer will add saltif the concentration is below 1kg/L and will remove salt if the concentration is above 1kg/L.(a) Propose an ODE that would model the salt content in the tank and explain it. If you are using anyparameters for unknowns, explain what they mean.Note that there are many correct ways to set this up.(b) Without solving the ODE, answer the following: If at a certain moment there is a salt concentration of1kg/L in the tank, and taking into account all effects, is the amount of salt increasing or decreasingat that moment?

1. Consider a 100L tank containing 50L of salt water with a concentration of 1kg/L. Suppose that each second, 3L of pure water flows into the tank and 2L of the mixture flows out of the tank. The tank is kept well mixed at all times. (a) Write an IVP that governs the salt content in the tank. Make sure to explain your equation. (b) Solve the IVP from part (a).

1. Consider a 100L tank containing 50L of salt water with a concentration of 1kg/L. Suppose that each second, 3L of pure water flows into the tank and 2L of the mixture flows out of the tank. The tank is kept well mixed at all times. (a) Write an IVP that governs the salt content in the tank. Make sure to explain your equation. (b) Solve the IVP from part (a).

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter12: Quadratic Functions

Section12.8: Joint And Combined Variation

Problem 11P

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