One thing of which hobbits are particularly fond (besides 'Old Tobey') are their ales, and Merry and Pippin enjoyed many different ones on their journeys abroad. Even though they still preferred their flagons from the Green Dragon the most, Pippin asked some Men along the way how they made their brews. This is all he remembered for one of the steps: To mix the barley and water, they use a pair of barrels connected by pipes as shown below: Suppose the barrels A and B are filled to their capacities of 30 gallons and 20 gallons, respectively. Moreover, water with barley concentration 1 oz/gal flows into Barrel A at a rate of 1.5 gal/min. Water with barley concentration 3 oz/gal flows into Barrel B at a rate of 1 gal/min. Water flows from Barrel A to Barrel B at a rate of 3 gal/min. Water flows from Barrel B to Barrel A at a rate of 1.5 gal/min. Water drains from Barrel B at a rate of 2.5 gal/min. If we let r(t) and y(t) denote the amount of barley (in ounces) in barrels A and B respectively, we obtain the following system of differential equations: (-)-(0.1 = 0-02) (+) + (¹³) (¹:5). 3 -0.1 0.075
One thing of which hobbits are particularly fond (besides 'Old Tobey') are their ales, and Merry and Pippin enjoyed many different ones on their journeys abroad. Even though they still preferred their flagons from the Green Dragon the most, Pippin asked some Men along the way how they made their brews. This is all he remembered for one of the steps: To mix the barley and water, they use a pair of barrels connected by pipes as shown below: Suppose the barrels A and B are filled to their capacities of 30 gallons and 20 gallons, respectively. Moreover, water with barley concentration 1 oz/gal flows into Barrel A at a rate of 1.5 gal/min. Water with barley concentration 3 oz/gal flows into Barrel B at a rate of 1 gal/min. Water flows from Barrel A to Barrel B at a rate of 3 gal/min. Water flows from Barrel B to Barrel A at a rate of 1.5 gal/min. Water drains from Barrel B at a rate of 2.5 gal/min. If we let r(t) and y(t) denote the amount of barley (in ounces) in barrels A and B respectively, we obtain the following system of differential equations: (-)-(0.1 = 0-02) (+) + (¹³) (¹:5). 3 -0.1 0.075
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:4. One thing of which hobbits are particularly fond (besides 'Old Tobey') are their ales, and
Merry and Pippin enjoyed many different ones on their journeys abroad. Even though they
still preferred their flagons from the Green Dragon the most, Pippin asked some Men along
the way how they made their brews. This is all he remembered for one of the steps:
To mix the barley and water, they use a pair of barrels connected by pipes as shown below:
in
Suppose the barrels A and B are filled to their capacities of 30 gallons and 20 gallons,
respectively. Moreover, water with barley concentration 1 oz/gal flows into Barrel A at a
rate of 1.5 gal/min. Water with barley concentration 3 oz/gal flows into Barrel B at a rate
of 1 gal/min. Water flows from Barrel A to Barrel B at a rate of 3 gal/min. Water flows
from Barrel B to Barrel A at a rate of 1.5 gal/min. Water drains from Barrel B at a rate of
2.5 gal/min. If we let r(t) and y(t) denote the amount of barley (in ounces) in barrels A
and B respectively, we obtain the following system of differential equations:
(~) = (-0.1¹
-0.1 0.075)
-0.2/
075) (3) + (¹:5).
3
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