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?
Solution Summary: The author calculates the average rate of change in speed between the ocean waves that are 1m and 4m in length.
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?
rmine the immediate settlement for points A and B shown in
figure below knowing that Aq,-200kN/m², E-20000kN/m², u=0.5, Depth
of foundation (DF-0), thickness of layer below footing (H)=20m.
4m
B
2m
2m
A
2m
+
2m
4m
sy = f(x)
+
+
+
+
+
+
+
+
+
X
3
4
5
7
8
9
The function of shown in the figure is continuous on the closed interval [0, 9] and differentiable on the open
interval (0, 9). Which of the following points satisfies conclusions of both the Intermediate Value Theorem
and the Mean Value Theorem for f on the closed interval [0, 9] ?
(A
A
B
B
C
D
=
Q6 What will be the allowable bearing capacity of sand having p = 37° and ydry
19 kN/m³ for (i) 1.5 m strip foundation (ii) 1.5 m x 1.5 m square footing and
(iii)1.5m x 2m rectangular footing. The footings are placed at a depth of 1.5 m
below ground level. Assume F, = 2.5. Use Terzaghi's equations.
0
Ne
Na
Ny
35 57.8 41.4 42.4
40 95.7 81.3 100.4
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