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
Related questions
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.
Transcribed Image Text: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?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 4 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
