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?
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.4: Definition Of The Derivative
Problem 50E
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
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell