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7. A 100-gal tank contains 40 gal of an alcohol-water solution 2 gal of which is alcohol. A solution con- taining 0.5 gal alcohol/gal runs into the tank at a rate of 3 gal/min and the well-stirred mixture leaves the tank at a rate of 2 gal/min. a) How many gallons of alcohol are in the tank after 10 minutes? b) How many gallons of alcohol are in the tank when it overflows?

7. A 100-gal tank contains 40 gal of an alcohol-water solution 2 gal of which is alcohol. A solution con- taining 0.5 gal alcohol/gal runs into the tank at a rate of 3 gal/min and the well-stirred mixture leaves the tank at a rate of 2 gal/min. a) How many gallons of alcohol are in the tank after 10 minutes? b) How many gallons of alcohol are in the tank when it overflows?

Advanced Engineering Mathematics
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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Number 7 part a and b modeling with differential equations ?
s section can be found in Exercises 17-22. equations not covered in eneur re- io worth 10% per thdraws live on, 5. Cesium 137 has a half-life of approximately 30 years. If cesium 137 is entering a cesium-free pond at a rate of 1 lb/year, approximately how many pounds of cesium 137 will be in the pond after 30 years? ey? 6. A drum contains 30 g of radioactive cobalt 60 sus- pended in liquid. Because the drum has a small leak, 0.1 g of radioactive cobalt 60 escapes from the drum each mploy- est rate ployee 00 per ave in year. If the half-life of radioactive cobalt 60 is about 5.3 years, about how many grams of radioac- tive cobalt 60 are left in the drum after 10 years? rts at T this n the 7. A 100-gal tank contains 40 gal of an alcohol-water solution 2 gal of which is alcohol. A solution con- taining 0.5 gal alcohol/gal runs into the tank at a rate of 3 gal/min and the well-stirred mixture leaves the tank at a rate of 2 gal/min. con- on in a) How many gallons of alcohol are in the tank after 10 minutes? lion b) How many gallons of alcohol are in the tank when it overflows? our. 8. A 500-gal tank contains 200 gal fresh water. Salt wa- ter containing 0.5 lb/gal enters the tank at 4 gal/min. The well-stirred solution leaves the tank at the same pac- tin- any rate.
Transcribed Image Text:s section can be found in Exercises 17-22. equations not covered in eneur re- io worth 10% per thdraws live on, 5. Cesium 137 has a half-life of approximately 30 years. If cesium 137 is entering a cesium-free pond at a rate of 1 lb/year, approximately how many pounds of cesium 137 will be in the pond after 30 years? ey? 6. A drum contains 30 g of radioactive cobalt 60 sus- pended in liquid. Because the drum has a small leak, 0.1 g of radioactive cobalt 60 escapes from the drum each mploy- est rate ployee 00 per ave in year. If the half-life of radioactive cobalt 60 is about 5.3 years, about how many grams of radioac- tive cobalt 60 are left in the drum after 10 years? rts at T this n the 7. A 100-gal tank contains 40 gal of an alcohol-water solution 2 gal of which is alcohol. A solution con- taining 0.5 gal alcohol/gal runs into the tank at a rate of 3 gal/min and the well-stirred mixture leaves the tank at a rate of 2 gal/min. con- on in a) How many gallons of alcohol are in the tank after 10 minutes? lion b) How many gallons of alcohol are in the tank when it overflows? our. 8. A 500-gal tank contains 200 gal fresh water. Salt wa- ter containing 0.5 lb/gal enters the tank at 4 gal/min. The well-stirred solution leaves the tank at the same pac- tin- any rate.
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