Using the graph and the statement below to answer (a): The wave heights h in the open sea depend on the speed v of the wind and the length of time t that the wind has been blowing at that speed. Different values of the function h = f (v, t) are recorded (in feet) in the following table. NOTE: v is the first variable listed and t is the second variable listed in h = f(v,t). (a) What are the meanings of the partial derivatives ∂h/∂v and ∂h/∂t?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Using the graph and the statement below to answer (a):

The wave heights h in the open sea depend on the speed v of the wind and the length of time t that the wind has been blowing at that speed. Different values of the function h = f (v, t) are recorded (in feet) in the following table.

NOTE: v is the first variable listed and t is the second variable listed in h = f(v,t).

(a) What are the meanings of the partial derivatives ∂h/∂v and ∂h/∂t?

Duration (hours)
10
15
20
30
40
50
10
21
2
15
14
5.
5
20
ト
9.
9.
30
13
16
17
18
19
19
40
14
25
28
31
33
33
50
19
29
36
40
45
48
50
60
24
37
47
54
62
67
69
2.
2.
21
Wind speed (knots)
Transcribed Image Text:Duration (hours) 10 15 20 30 40 50 10 21 2 15 14 5. 5 20 ト 9. 9. 30 13 16 17 18 19 19 40 14 25 28 31 33 33 50 19 29 36 40 45 48 50 60 24 37 47 54 62 67 69 2. 2. 21 Wind speed (knots)
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