Water is poured into a cylindrical tank, and then a spout at the base of the tank is opened so that the water can drain out. The volume of water in the tank after t minutes is given by V = f(t) m³, where t is measured in minutes. A graph of f is given to the right. 5 5 (a) How long does it take to fill the tank, and how fast is it being filled during this time? (b) About how fast is water draining from the tank at t = 7 minutes? Include units with your answer. (c) Sketch a graph of f'(t), the derivative of f, on the axes below. Choose a reasonable scale for the vertical axis, and label the vertical axis with the appropriate units. V' 10 V 15 5₁ 4 3 2 1 20 10 15 20

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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1. Water is poured into a cylindrical tank, and then a spout at the base
of the tank is opened so that the water can drain out. The volume of
water in the tank after t minutes is given by V = f(t) m³, where t is
measured in minutes. A graph of f is given to the right.
5
(a) How long does it take to fill the tank, and how fast is it being filled during this time?
(b) About how fast is water draining from the tank at t = 7 minutes? Include units with your answer.
(c) Sketch a graph of f'(t), the derivative of f, on the axes below. Choose a reasonable scale for the vertical
axis, and label the vertical axis with the appropriate units.
V'
..........
5
..….…........
10
************
**************
15
V
5
4
3
2
1
...........
20
10
15
20
Transcribed Image Text:1. Water is poured into a cylindrical tank, and then a spout at the base of the tank is opened so that the water can drain out. The volume of water in the tank after t minutes is given by V = f(t) m³, where t is measured in minutes. A graph of f is given to the right. 5 (a) How long does it take to fill the tank, and how fast is it being filled during this time? (b) About how fast is water draining from the tank at t = 7 minutes? Include units with your answer. (c) Sketch a graph of f'(t), the derivative of f, on the axes below. Choose a reasonable scale for the vertical axis, and label the vertical axis with the appropriate units. V' .......... 5 ..….…........ 10 ************ ************** 15 V 5 4 3 2 1 ........... 20 10 15 20
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