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Section 2.5 Introduction to Relations 187 3. Applications Involving Relations Analyzing a Relation Example 5 The data in Table 2-5 depict the length of a woman’s femur and her corresponding height. Based on these data, a forensics specialist can find a linear relationship between height y (in inches) and femur length x (in centimeters): y 0.91x 24 40 x 55 From this type of relationship, the height of a woman can be inferred based on skeletal remains. a. Find the height of a woman whose femur is 46.0 cm. b. Find the height of a woman whose femur is 51.0 cm. c. Why is the domain restricted to 40 x 55 ? Solution: a. y 0.91x 24 0.91146.02 x 46.0 cm. 24 Substitute The woman is approximately 65.9 in. tall. b. Substitute x 51.0 cm. 65.86 y 0.91x 24 0.91151.02 24 70.41 The woman is approximately 70.4 in. tall. c. The domain restricts femur length to values between 40 cm and 55 cm inclusive.These values are within the normal lengths for an adult female and are in the proximity of the observed data (Figure 2-31). Height of an Adult Female Based y on the Length of the Femur 80 y 0.91x 24 70 60 50 40 30 20 10 0 0 5 10 15 20 25 30 35 40 45 50 55 60 Skill Practice The linear equation, for relates the weight of a car, x (in pounds), to its gas mileage, y (in mpg). 8. Find the gas mileage in miles per gallon for a car weighing 2550 lb. 9. Find the gas mileage for a car weighing 2850 lb. 10. Why is the domain restricted to 1500 x 4000? y 0.014x64.5, 1500 x 4000, Height (in.) Length of Femur (cm) x Figure 2-31 Table 2-5 Length of Height Femur (cm) (in.) x y 45.5 65.5 48.2 68.0 41.8 62.2 46.0 66.0 50.4 70.0 Answers 8. 28.8 mpg 9. 24.6 mpg 10. The relation is valid only for cars weighing between 1500 lb and 4000 lb, inclusive.


miller_intermediate_algebra_4e_ch1_3
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