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ch00_02

# ch00_02 - 20 CHAPTER 0 Preliminaries 0-20 76 The spin rate...

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20 CHAPTER 0 . . Preliminaries 0-20 76. The spin rate of a golf ball hit with a 9 iron has been measured at 9100 rpm for a 120-compression ball and at 10,000 rpm for a 60-compression ball. Most golfers use 90-compression balls. If the spin rate is a linear function of compression, find the spin rate for a 90-compression ball. Professional golfers often use 100-compression balls. Estimate the spin rate of a 100-compression ball. 77. The chirping rate of a cricket depends on the temperature. A species of tree cricket chirps 160 times per minute at 79 F and 100 times per minute at 64 F. Find a linear function relating temperature to chirping rate. 78. When describing how to measure temperature by counting cricket chirps, most guides suggest that you count the number of chirps in a 15-second time period. Use exercise 77 to explain why this is a convenient period of time. 79. A person has played a computer game many times. The statis- tics show that she has won 415 times and lost 120 times, and the winning percentage is listed as 78%. How many times in a row must she win to raise the reported winning percentage to 80%? EXPLORATORY EXERCISES 1. Suppose you have a machine that will proportionally enlarge a photograph. For example, it could enlarge a 4 × 6 photograph to 8 × 12 by doubling the width and height. You could make an 8 × 10 picture by cropping 1 inch off each side. Explain how you would enlarge a 3 1 2 × 5 picture to an 8 × 10 . A friend returns from Scotland with a 3 1 2 × 5 picture showing the Loch Ness monster in the outer 1 4 on the right. If you use your proce- duretomakean8 × 10 enlargement,doesNessiemakethecut? 2. Solve the equation | x 2 | + | x 3 | = 1 . (Hint: It’s an unusual solution, in that it’s more than just a couple of numbers.) Then, solve the equation x + 3 4 x 1 + x + 8 6 x 1 = 1. (Hint: If you make the correct substitution, you can use your solution to the previous equation.) 0.2 GRAPHING CALCULATORS AND COMPUTER ALGEBRA SYSTEMS The relationships between functions and their graphs are central topics in calculus. Graphing calculators and user-friendly computer software allow you to explore these relationships for a much wider variety of functions than you could with pencil and paper alone. This section presents a general framework for using technology to explore the graphs of functions. Recall that the graphs of linear functions are straight lines and the graphs of quadratic polynomials are parabolas. One of the goals of this section is for you to become more familiar with the graphs of other functions. The best way to become familiar is through experience, by working example after example. EXAMPLE 2.1 Generating a Calculator Graph Use your calculator or computer to sketch a graph of f ( x ) = 3 x 2 1 . y x 4 2 4 2 20 40 60 FIGURE 0.26a y = 3 x 2 1 y x 2 1 1 2 4 8 FIGURE 0.26b y = 3 x 2 1 Solution You should get an initial graph that looks something like that in Figure 0.26a. This is simply a parabola opening upward. A graph is often used to search for important points, such as x -intercepts, y -intercepts or peaks and troughs. In this case,

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