The speed v ( L ) (in m/sec) of an ocean wave in deep water is approximated by V ( L ) = 1.2 L , where L (in meters) is the wavelength of the wave. (The wavelength is the distance between two consecutive wave crests.) a. Find the average rate of change in speed between waves that are between 1 m and 4 m in length. b. Find the average rate of change in speed between waves that are between 4 m and 9 m in length. c. Use a graphing utility to graph the function. Using the graph and the results from parts (a) and (b), what does the difference in the rates of change mean?
The speed v ( L ) (in m/sec) of an ocean wave in deep water is approximated by V ( L ) = 1.2 L , where L (in meters) is the wavelength of the wave. (The wavelength is the distance between two consecutive wave crests.) a. Find the average rate of change in speed between waves that are between 1 m and 4 m in length. b. Find the average rate of change in speed between waves that are between 4 m and 9 m in length. c. Use a graphing utility to graph the function. Using the graph and the results from parts (a) and (b), what does the difference in the rates of change mean?
(in m/sec) of an ocean wave in deep water is approximated by
V
(
L
)
=
1.2
L
, where L (in meters) is the wavelength of the wave. (The wavelength is the distance between two consecutive wave crests.)
a. Find the average rate of change in speed between waves that are between 1 m and 4 m in length.
b. Find the average rate of change in speed between waves that are between 4 m and 9 m in length.
c. Use a graphing utility to graph the function. Using the graph and the results from parts (a) and (b), what does the difference in the rates of change mean?
1) Express these large and small numbers from the Read and Study section in scientific
notation:
(a) 239,000 miles
(b) 3,800,000,000,000 sheets of paper
(c) 0.0000000000000000000000167 grams
2) Find all values for the variable x that make these equations true.
(a) 5x = 1
(b) 3x = 1/1
9
(c) 4* = 11/
4
(e) 4* = 64
(g) 10x = 1,000,000
(d) 3x=-3
(f) 2x =
=
8
(h) 10x = 0.001
(b)
4) Find an equation to fit each of the following graphs:
(a)
20
20
18
16
14
12
10
8
6
4
2
24
22
20
18
16
14
12
10
8
16
A
2
-3 -2
-1-0
2
3
4.
-1
0
1
2
3.
-2
-2
3) Which of the following are equivalent to 3? (There may be more than one that is
equivalent!)
-1
(a) (9)¯¹
3.
(b) (-3)-1
(c) (-3)
-1
(d) -(¯3)
(e) 11
3-1
(f) 3-4
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