: a very large tank initially contains 15 gallons of saltwater Recall the salty tank containing 6 pounds of salt. Saltwater containing 1 pound of salt per gallon is pumped into the top of the tank at a rate of 2 gallons per minute, while a well-mixed solution leaves the bottom of the tank at a rate of 1 gallon per minute. Let's call this salty tank from class Tank A. Consider the following modifications: • Tank B is the same basic scenario as Tank A, but pure water is being pumped into Tank B instead of saltwater. • Tank C is the same basic scenario as Tank A, but the rates are switched: saltwater enters Tank C at a rate of 1 gallon per minute, and leaves at a rate of 2 gallons per minute. (a) Set up and solve initial value problems that correspond to individual Tanks B and C. (b) Use a plot to compare the three solution curves (including the solution for Tank A) and discuss how these curves predict or represent outcomes you would expect from the description of each scenario.

Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.4: Hyperbolas
Problem 5ECP: Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.
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9. Recall the salty tank
containing 6 pounds of salt. Saltwater containing 1 pound of salt per gallon is pumped into the top of the
tank at a rate of 2 gallons per minute, while a well-mixed solution leaves the bottom of the tank at a rate of
1 gallon per minute. Let's call this salty tank from class Tank A. Consider the following modifications:
: a very large tank initially contains 15 gallons of saltwater
• Tank B is the same basic scenario as Tank A, but pure water is being pumped into Tank B instead of
saltwater.
• Tank C is the same basic scenario as Tank A, but the rates are switched: saltwater enters Tank C at a
rate of 1 gallon per minute, and leaves at a rate of 2 gallons per minute.
(a) Set up and solve initial value problems that correspond to individual Tanks B and C.
(b) Use a plot to compare the three solution curves (including the solution for Tank A) and discuss how
these curves predict or represent outcomes you would expect from the description of each scenario.
Transcribed Image Text:9. Recall the salty tank containing 6 pounds of salt. Saltwater containing 1 pound of salt per gallon is pumped into the top of the tank at a rate of 2 gallons per minute, while a well-mixed solution leaves the bottom of the tank at a rate of 1 gallon per minute. Let's call this salty tank from class Tank A. Consider the following modifications: : a very large tank initially contains 15 gallons of saltwater • Tank B is the same basic scenario as Tank A, but pure water is being pumped into Tank B instead of saltwater. • Tank C is the same basic scenario as Tank A, but the rates are switched: saltwater enters Tank C at a rate of 1 gallon per minute, and leaves at a rate of 2 gallons per minute. (a) Set up and solve initial value problems that correspond to individual Tanks B and C. (b) Use a plot to compare the three solution curves (including the solution for Tank A) and discuss how these curves predict or represent outcomes you would expect from the description of each scenario.
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