1. The wave heights h in the open sea depends 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 Table 1. (a) What is the value of f(40,15) ? What is its meaning? (b) What is the meaning of the function h = f(30,t)? Describe the behaviour of the function. (c) What is the meaning of the function h = f(v,30)? Describe the behaviour of the function. Table 1 Duration (hours) 10 15 20 30 40 50 10 2 2 2 2 15 4 4 5 5 5 5 5 Wind Speed (Knots) 20 5 8 8 9 9. 9 30 9 13 16 17 18 19 19 40 14 21 25 28 31 33 33 50 19 29 36 40 45 48 50 60 24 37 47 54 62 67 69 21 2. 2) un
1. The wave heights h in the open sea depends 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 Table 1. (a) What is the value of f(40,15) ? What is its meaning? (b) What is the meaning of the function h = f(30,t)? Describe the behaviour of the function. (c) What is the meaning of the function h = f(v,30)? Describe the behaviour of the function. Table 1 Duration (hours) 10 15 20 30 40 50 10 2 2 2 2 15 4 4 5 5 5 5 5 Wind Speed (Knots) 20 5 8 8 9 9. 9 30 9 13 16 17 18 19 19 40 14 21 25 28 31 33 33 50 19 29 36 40 45 48 50 60 24 37 47 54 62 67 69 21 2. 2) un
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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Question
Transcribed Image Text:1. The wave heights h in the open sea depends 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 Table 1.
(a) What is the value of f(40,15) ? What is its meaning?
(b) What is the meaning of the functionh = f(30, t) ?
Describe the behaviour of the function.
(c) What is the meaning of the function h = f(v,30)?
Describe the behaviour of the function.
Table 1
Duration (hours)
5
10
15
20
30
40
50
10
2
2
2
2
15
4
4
5
5
5
5
Wind Speed (Knots)
5
7
8.
8.
30
13
16
17
18
19
19
40
14
21
25
28
31
33
33
19 29
45 48
50
36
40
50
60
24
37
47
54
62
67
69
x*y²-8x+y
2. a) Find the local maximum and minimum values and saddle point(s) of the function f(x,y):
xy
Graph the factors (roughly) with a domain of view point that reveal all the important aspects of the
Factors.
fx = y - x-2 = 0
fy = x + 8y-2 = 0
b) A cardboard box without a lid is to have a volume of 32,000 cm3. Find the dimensions that minimize
the amount of cardboard used.
2.
6,
9,
20
Transcribed Image Text:3. a) Use the figure to estimate Duf (2,2)
(0,2)
at (2,2)
b) If f(x, y) = x(x² + y²)esin(x²y)
find fr (1,0)
4. a) Draw an example of a region that is
i) Both type I and type II.
ii) Neither type I nor type II.
b) Calculate the iterated integral by first reversing the order of integration.
Apxp
5. Use polar coordinates to combine the sum
Lixy dydx + S, xy dydx + ** xy dydx
V4-x2
into one double integral. Then evaluate the double integral.
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