By James Stewart; L Redlin; Saleem Watson
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Distance is always positive or zero, so we have Ȋa Ȋ Ն 0 for every number a. Remembering that Ϫa is positive when a is negative, we have the following definition. Definition of Absolute Value If a is a real number, then the absolute value of a is a if a Ն 0 Ȋ a Ȋ ϭ Ϫa if a Ͻ 0 Ά 20 CHAPTER P Prerequisites Example 7 Evaluating Absolute Values of Numbers (a) Ȋ3Ȋ ϭ 3 (b) ȊϪ3Ȋ ϭ ϪÓϪ3Ô ϭ 3 (c) Ȋ0Ȋ ϭ 0 (d) Ȋ œ2ෆ Ϫ 1Ȋ ϭ œ2ෆ Ϫ 1 Ósince œ2ෆ Ͼ 1 ⇒ œ2ෆ Ϫ 1 Ͼ 0Ô (e) Ȋ 3 Ϫ pȊ ϭ ϪÓ3 Ϫ pÔ ϭ p Ϫ 3 Ósince p Ͼ 3 ⇒ 3 Ϫ p Ͻ 0Ô ■ When working with absolute values, we use the following properties.
RϪ5sqϪ8 2a 2b 50. ᎏᎏ @ c3 70. 01582Ô 73. 542 ϫ 10Ϫ6Ô9 74. 05 ϫ 104Ô12 30 CHAPTER P Prerequisites 75. Let a, b, and c be real numbers with a Ͼ 0, b Ͻ 0, and c Ͻ 0. Determine the sign of each expression. 9, while a person with body-mass index B Ն 30 is considered obese. (a) Calculate the body-mass index for each person listed in the table, then determine whether he or she is of normal weight, underweight, overweight, or obese. 76. Prove the given Laws of Exponents for the case in which m and n are positive integers and m Ͼ n.
Find its gas mileage. ■ Thinking about the problem. Let’s try a simple case. If a car uses 2 gallons to drive 100 miles, we easily see that 100 gas mileage ϭ ᎏᎏ ϭ 50 mi/gal 2 So gas mileage is the number of miles driven divided by the number of gallons used. 5 in the formula. 9 mi/gal. Example 5 Finding a Formula for Area (a) Find a formula for the area of a rectangle whose length is twice its width. (b) A manufacturing company requires a rectangular sheet of metal whose length is twice its width and whose total area is 50 ft2.