40 30- 20 15- 5 1 y = b(r) 2 y = a(t) 3 (a) How much water will be in tank A at time t = 4.5 ? 4 5 2 sin f 2. During the time interval 0 ≤ i ≤ 4.5 hours, water flows into tank A at a rate of a(1) = (21 − 5) + 5e² liters per hour. During the same time interval, water flows into tank B at a rate of b(1) liters per hour. Both tanks are empty at time 1 = 0. The graphs of y = a(t) and y = b(t), shown in the figure above, intersect at t = k and t = 2.416. (b) During the time interval 0 ≤ t ≤ k hours, water flows into tank 6 at a constant rate of 20 5 liters per
40 30- 20 15- 5 1 y = b(r) 2 y = a(t) 3 (a) How much water will be in tank A at time t = 4.5 ? 4 5 2 sin f 2. During the time interval 0 ≤ i ≤ 4.5 hours, water flows into tank A at a rate of a(1) = (21 − 5) + 5e² liters per hour. During the same time interval, water flows into tank B at a rate of b(1) liters per hour. Both tanks are empty at time 1 = 0. The graphs of y = a(t) and y = b(t), shown in the figure above, intersect at t = k and t = 2.416. (b) During the time interval 0 ≤ t ≤ k hours, water flows into tank 6 at a constant rate of 20 5 liters per
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:40
30-
on
15-
1
2!!
y = b(r)
2
y = a(t)
3
(a) How much water will be in tank A at time t = 4.5 ?
4
5
2. During the time interval 0 ≤ ≤ 4.5 hours, water flows into tank A at a rate of a(1) = (21 − 5) + 5e² 2 sin f
liters per hour. During the same time interval, water flows into tank B at a rate of b(1) liters per hour. Both
tanks are empty at time 1 = 0. The graphs of y = a(t) and y = b(t), shown in the figure above, intersect at
ƒ = k and t = 2.416.
(b) During the time interval 0 ≤ t ≤ k hours, water flows into tank B at a constant rate of 20.5 liters per
hour. What is the difference between the amount of water in tank A and the amount of water in tank B at
time t = k ?
Transcribed Image Text:(c) The area of the region bounded by the graphs of y = a(t) and y = b(1) for k≤1 ≤ 2.416 is 14.470. How
much water is in tank B at time t = 2.416 ?
(d) During the time interval 2.7 ≤ ≤ 4.5 hours, the rate at which water flows into tank B is modeled by
liters per hour. Is the difference w(t) - a(t) increasing or decreasing at time
30t
(18)²
t = 3.5 ? Show the work that leads to your answer.
w(1) =
= 21
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