Karla is an industrial engineer working with a chemical producer studying a process involving how a large tank fills and empties. At the start of the process the tank contains 40 liters of fluid. Valves connected to the tank are opened allowing more of the fluid to enter the tank at a rate of 24.5 liters per minute. At the same time another valve is controlled in such a way to allow 14% of the fluid in the tank to drain each minute. A. Introduce appropriate variables: Let t represent the independent variable. What should t represent in this situation? (input a phrase or sentence with appropriate units) t: Let a represent the dependent variable. What should a represent in this situation? (input a phrase or sentence with appropriate units x: B. Write a differential equation, along with initial condition (so an initial value problem), that models the situation. Initial Value Problem: Equation: dx dt - Initial Condition: ( C. Solve the initial value problem. Then use the solution curve to determine the volume of the liquid in the tank after 6 minutes (round your response to one decimal place). Volume of the liquid in the tank: D. Assuming that Karla allows the process to continue for a "long time", how large of a tank is needed to contain the fluid exchange? Size of tank that will contain the fluid exchange:
Karla is an industrial engineer working with a chemical producer studying a process involving how a large tank fills and empties. At the start of the process the tank contains 40 liters of fluid. Valves connected to the tank are opened allowing more of the fluid to enter the tank at a rate of 24.5 liters per minute. At the same time another valve is controlled in such a way to allow 14% of the fluid in the tank to drain each minute. A. Introduce appropriate variables: Let t represent the independent variable. What should t represent in this situation? (input a phrase or sentence with appropriate units) t: Let a represent the dependent variable. What should a represent in this situation? (input a phrase or sentence with appropriate units x: B. Write a differential equation, along with initial condition (so an initial value problem), that models the situation. Initial Value Problem: Equation: dx dt - Initial Condition: ( C. Solve the initial value problem. Then use the solution curve to determine the volume of the liquid in the tank after 6 minutes (round your response to one decimal place). Volume of the liquid in the tank: D. Assuming that Karla allows the process to continue for a "long time", how large of a tank is needed to contain the fluid exchange? Size of tank that will contain the fluid exchange:
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Karla is an industrial engineer working with a chemical producer studying a process involving how a large
tank fills and empties. At the start of the process the tank contains 40 liters of fluid. Valves connected to the
tank are opened allowing more of the fluid to enter the tank at a rate of 24.5 liters per minute. At the same
time another valve is controlled in such a way to allow 14% of the fluid in the tank to drain each minute.
A. Introduce appropriate variables:
Let t represent the independent variable. What should t represent in this situation? (input a phrase or
sentence with appropriate units)
t:
Let a represent the dependent variable. What should a represent in this situation? (input a phrase or
sentence with appropriate units
x:
B. Write a differential equation, along with initial condition (so an initial value problem), that models the
situation.
Initial Value Problem:
Equation:
dx
dt
Initial Condition: (
C. Solve the initial value problem. Then use the solution curve to determine the volume of the liquid in
the tank after 6 minutes (round your response to one decimal place).
Volume of the liquid in the tank:
D. Assuming that Karla allows the process to continue for a "long time", how large of a tank is needed to
contain the fluid exchange?
Size of tank that will contain the fluid exchange:
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