2. 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. Values of the function h = f(v, t) are recorded in feet in the following table. Wind speed (km/h) V 20 30 40 5 60 0.6 1.2 10 Duration (hours) 15 20 0.6 0.6 0.6 0.6 1.3 1.5 1.5 1.5 1.5 2.2 2.4 30 6.4 2.8 80 4.3 100 5.8 120 7.4 11.3 14.4 16.6 19.0 4.0 4.9 5.2 5.5 2.5 2.7 8.9 11.0 40 0.6 1.6 5.8 7.7 8.6 9.5 10.1 12.2 13.8 14.7 50 0.6 1.6 2.8 2.8 5.9 10.2 15.3 20.5 21.1 (a) What are the meanings of the partial derivatives əh/av and əh/at? (b) Estimate the values of f(40, 15) and f(40, 15). What are the practical interpretations of these values?

2. 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. Values of the function h = f(v, t) are recorded in feet in the following table. Wind speed (km/h) V 20 30 40 5 60 0.6 1.2 10 Duration (hours) 15 20 0.6 0.6 0.6 0.6 1.3 1.5 1.5 1.5 1.5 2.2 2.4 30 6.4 2.8 80 4.3 100 5.8 120 7.4 11.3 14.4 16.6 19.0 4.0 4.9 5.2 5.5 2.5 2.7 8.9 11.0 40 0.6 1.6 5.8 7.7 8.6 9.5 10.1 12.2 13.8 14.7 50 0.6 1.6 2.8 2.8 5.9 10.2 15.3 20.5 21.1 (a) What are the meanings of the partial derivatives əh/av and əh/at? (b) Estimate the values of f(40, 15) and f(40, 15). What are the practical interpretations of these values?

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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Question

2c) (FOR IMAGE) Estimate the values of f_vv(30, 20), f_tt(30, 20), f_vt(30, 20), and
f_tv(30, 20).

d) Use the answers you found in Problem 2 to find a linear approximation to the wave height
function when v is near 30 knots and t is near 20 hours.

2. 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. Values of the function h = f(v, t) are
recorded in feet in the following table.
Wind speed (km/h)
V
20
30
40
60
80
t
100
5 10 15
0.6
1.2
5.8
Duration (hours)
20
0.6 0.6 0.6
1.5 1.5
1.3
1.5 2.2
2.8 4.0
4.3 6.4
2.4
4.9
30
2.5
40
0.6
0.6
1.5 1.6
7.7 8.6 9.5
50
2.7
5.2 5.5 5.8 5.9
10.1
2.8
0.6
1.6
2.8
10.2
8.9 11.0
12.2 13.8 14.7
15.3
120 7.4 11.3 14.4 16.6 19.0 20.5 21.1
(a) What are the meanings of the partial derivatives əh/av
and əh/at?
(b) Estimate the values of f(40, 15) and fi(40, 15). What are
the practical interpretations of these values?

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