By Earl W. Swokowski, Jeffery A. Cole
Transparent factors, an uncluttered and attractive structure, and examples and routines that includes numerous real-life purposes have made this article renowned between scholars 12 months after 12 months. This most modern version of Swokowski and Cole's ALGEBRA AND TRIGONOMETRY WITH ANALYTIC GEOMETRY keeps those positive factors. the issues were constantly praised for being at simply the correct point for precalculus scholars such as you. The ebook additionally offers calculator examples, together with particular keystrokes that aid you use numerous graphing calculators to resolve difficulties extra fast. probably so much important-this ebook successfully prepares you for extra classes in arithmetic.
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Extra info for Algebra and Trigonometry with Analytic Geometry
Some special cases of this definition are given in the following illustration. ILLUS TRATION The Absolute Value Notation ͉ a ͉ ͉ 3 ͉ ϭ 3, since 3 Ͼ 0. ͉Ϫ3͉ ϭ Ϫ͑Ϫ3͒, since Ϫ3 Ͻ 0. Thus, ͉ Ϫ3 ͉ ϭ 3. ͉ 2 Ϫ ͙2 ͉ 2 Ϫ ͙2, since 2 Ϫ ͙2 Ͼ 0. ͉ ͙2 Ϫ 2 ͉ Ϫ͑ ͙2 Ϫ 2 ͒, since ͙2 Ϫ 2 Ͻ 0. Thus, ͉ ͙2 Ϫ 2 ͉ 2 Ϫ ͙2. In the preceding illustration, ͉ 3 ͉ ͉ Ϫ3 ͉ and ͉ 2 Ϫ ͙2 ͉ ͉ ͙2 Ϫ 2 ͉. In general, we have the following: ͉ a ͉ ͉ Ϫa ͉, for every real number a TI-83/4 Plus Absolute Value ᭟ MATH TI-86 1 Ϫ3 ) ENTER 2nd MATH abs(F5) Ϫ3 NUM(F1) ENTER 576 STO ᭟ 927 STO ᭟ ᭟ MATH A Ϫ ALPHA A ALPHA B 1 ALPHA ALPHA B : ALPHA ENTER ALPHA A ALPHA B 2nd ) ENTER ALPHA ALPHA ϭ 576 2nd ALPHA ϭ 927 ENTER MATH A NUM(F1) Ϫ ( abs(F5) B ALPHA : ) ENTER On the TI-86, note that ALPHA A ALPHA ϭ 576 and 576 STO ᭟ A are equivalent.
24 CHAPTER 1 FUNDAMENTAL CONCEPTS OF ALGEBRA n To complete our terminology, the expression 2 a is a radical, the number a is the radicand, and n is the index of the radical. The symbol 2 is called a radical sign. 3 If 2a ϭ b, then b2 ϭ a; that is, ͑ 2a͒2 ϭ a. If 2 a ϭ b, then b3 ϭ a, or 3 3 ͑ 2 a ͒ ϭ a. Generalizing this pattern gives us property 1 in the next chart. n Properties of 2a (n is a positive integer) Property (1) (2) (3) (4) Illustrations ͑ 25͒2 ϭ 5, ͑ 23 Ϫ8 ͒3 ϭ Ϫ8 n 2͑Ϫ2͒3 ϭ Ϫ2, 2 ͑Ϫ2͒5 ϭ Ϫ2 n 2͑Ϫ3͒2 ϭ ͉ Ϫ3 ͉ ϭ 3, 2 ͑Ϫ2͒4 ϭ ͉ Ϫ2 ͉ ϭ 2 ͑ 2n a ͒n ϭ a if 2n a is a real number n 2 an ϭ a if a Ն 0 2 52 ϭ 5, 2 an ϭ a if a Ͻ 0 and n is odd 3 3 2 2 ϭ2 3 2 an ϭ ͉ a ͉ if a Ͻ 0 and n is even 5 4 If a Ն 0, then property 4 reduces to property 2.
1 Exercises Exer. 1–2: If x < 0 and y > 0, determine the sign of the real number. 1 (a) xy 2 (a) x y (b) x 2y (c) ̈ (b) xy 2 (c) x ϩx y (d) y Ϫ x xϪy xy (d) y͑ y Ϫ x͒ 1 1 (d) c is between 5 and 3 . (e) p is not greater than Ϫ2. (f ) The negative of m is not less than Ϫ2. (g) The quotient of r and s is at least 15 . (h) The reciprocal of f is at most 14. Exer. 3–6: Replace the symbol ᮀ with either <, >, or ؍to make the resulting statement true. 143 22 7 ᮀ Exer. 7–8: Express the statement as an inequality.