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**Unformatted text preview: **nd the square of the distance as r2 . We have F
varies directly with mM and inversely with r2 , so that F = kmM .
r2
In many of the formulas in the previous example, more than two varying quantities are related. In
practice, however, usually all but two quantities are held constant in an experiment and the data
collected is used to relate just two of the variables. Comparing just two varying quantities allows
us to view the relationship between them as functional, as the next example illustrates. 274 Rational Functions Example 4.3.5. According to this website the actual data relating the volume V of a gas and its
pressure P used by Boyle and his assistant in 1662 to verify the gas law that bears his name is
given below.
V
P 48
46
44
42
40
38
36
34
32
30
28
26
24
29.13 30.56 31.94 33.5 35.31 37 39.31 41.63 44.19 47.06 50.31 54.31 58.81 V
P 23
61.31 22
21
20
19
18
17
16
15
14
13
12
64.06 67.06 70.69 74.13 77.88 82.75 87.88 93.06 100.44 107.81 117.56 1. Use your calculator to generate a scatter diagram for these data using V as the independent
variable and P as the dependent variable. Does it appear from the graph that P is inversely
proportional to V ? Expla...

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