By James Stewart, Lothar Redlin, Saleem Watson
This top promoting writer crew explains innovations easily and obviously, with no glossing over tricky issues. challenge fixing and mathematical modeling are brought early and strengthened all through, delivering scholars with an exceptional origin within the rules of mathematical pondering. entire and flippantly paced, the ebook presents whole insurance of the functionality inspiration, and integrates an important quantity of graphing calculator fabric to aid scholars advance perception into mathematical rules. The authors' recognition to aspect and readability, just like present in James Stewart's market-leading Calculus publication, is what makes this booklet the marketplace chief.
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Extra info for Algebra and Trigonometry , Third Edition
If you spent at the same rate, how many years would it take you to empty a suitcase filled with a billion (10 9 ) dollars? 102. 320 ϫ 1013 dollars. How much was each person’s share of the debt? 103. Number of Molecules A sealed room in a hospital, measuring 5 m wide, 10 m long, and 3 m high, is filled with pure oxygen. 02 ϫ 1023 molecules (Avogadro’s number). How many molecules of oxygen are there in the room? 104. Body-Mass Index The body-mass index is a measure that medical researchers use to determine whether a person is overweight, underweight, or of normal weight.
Find the sign of each expression. (a) Ϫa (b) Ϫc (c) bc (d) a Ϫ b (e) c Ϫ a (f) a Ϫ bc (g) c 2 (h) Ϫabc 65. Mailing a Package The post office will accept only packages for which the length plus the “girth” (distance around) is no more than 108 inches. Thus for the package in the figure, we must have (a) Will the post office accept a package that is 6 in. wide, 8 in. deep, and 5 ft long? What about a package that measures 2 ft by 2 ft by 4 ft? (b) What is the greatest acceptable length for a package that has a square base measuring 9 in.
1Ϫa2 1Ϫb2 ϭ ab 1Ϫ42 1Ϫ32 ϭ 4 # 3 3. 1Ϫa2b ϭ a1Ϫb2 ϭ Ϫ1ab2 1Ϫ527 ϭ 51Ϫ72 ϭ Ϫ15 # 72 5. Ϫ1a ϩ b2 ϭ Ϫa Ϫ b Ϫ13 ϩ 52 ϭ Ϫ3 Ϫ 5 6. Ϫ1a Ϫ b2 ϭ b Ϫ a Ϫ15 Ϫ 82 ϭ 8 Ϫ 5 Property 6 states the intuitive fact that a Ϫ b and b Ϫ a are negatives of each other. Property 5 is often used with more than two terms: Ϫ1a ϩ b ϩ c2 ϭ Ϫa Ϫ b Ϫ c EXAMPLE 4 Using Properties of Negatives Let x, y, and z be real numbers. (a) Ϫ13 ϩ 22 ϭ Ϫ3 Ϫ 2 (b) Ϫ1x ϩ 22 ϭ Ϫx Ϫ 2 (c) Ϫ1x ϩ y Ϫ z 2 ϭ Ϫx Ϫ y Ϫ 1Ϫz2 ϭ Ϫx Ϫ y ϩ z NOW TRY EXERCISE 9 Property 5: –(a + b) = –a – b Property 5: –(a + b) = –a – b Property 5: –(a + b) = –a – b Property 2: –(–a) = a ■ ▼ Multiplication and Division The number 1 is special for multiplication; it is called the multiplicative identity because a и 1 ϭ a for any real number a.