Concept explainers
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
Duration (hours) | ||||||||
Wind speed (knots) | v\t | 5 | 10 | 15 | 20 | 30 | 40 | 50 |
10 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | |
15 | 4 | 4 | 5 | 5 | 5 | 5 | 5 | |
20 | 5 | 7 | 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 |
(a) What are the meanings of the partial derivatives
(b) Estimate the values of
(c) What appears to be the value of the following limit?
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Chapter 14 Solutions
Calculus (MindTap Course List)
- Let f(x)=1x . Find a number c such that the average rate of change of the functionfon the interval (1,c) is 14arrow_forwardTsunami Waves and BreakwatersThis is a continuation of Exercise 16. Breakwaters affect wave height by reducing energy. See Figure 5.30. If a tsunami wave of height H in a channel of width W encounters a breakwater that narrows the channel to a width w, then the height h of the wave beyond the breakwater is given by h=HR0.5, where R is the width ratio R=w/W. a. Suppose a wave of height 8 feet in a channel of width 5000feet encounters a breakwater that narrows the channel to 3000feet. What is the height of the wave beyond the breakwater? b. If a channel width is cut in half by a breakwater, what is the effect on wave height? 16. Height of Tsunami WavesWhen waves generated by tsunamis approach shore, the height of the waves generally increases. Understanding the factors that contribute to this increase can aid in controlling potential damage to areas at risk. Greens law tells how water depth affects the height of a tsunami wave. If a tsunami wave has height H at an ocean depth D, and the wave travels to a location with water depth d, then the new height h of the wave is given by h=HR0.25, where R is the water depth ratio given by R=D/d. a. Calculate the height of a tsunami wave in water 25feet deep if its height is 3feet at its point of origin in water 15,000feet deep. b. If water depth decreases by half, the depth ratio R is doubled. How is the height of the tsunami wave affected?arrow_forwardIn Example 7, find the average speed of the car (a) from t1=0tot2=1 second and (b) from t1=1 second to t2=4 seconds.arrow_forward
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