By Earl Swokowski, Jeffery A. Cole
The most recent version within the hugely revered Swokowski/Cole precalculus sequence keeps the weather that experience made it so well liked by teachers and scholars alike: its exposition is obvious, the time-tested workout units characteristic quite a few purposes, its uncluttered structure is attractive, and the trouble point of difficulties is suitable and constant. Mathematically sound, ALGEBRA AND TRIGONOMETRY WITH ANALYTIC GEOMETRY, vintage version, 12E, successfully prepares scholars for extra classes in arithmetic via its first-class, time-tested challenge units
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Additional info for Algebra and Trigonometry with Analytic Geometry, Classic Edition
3 ϫ 10Ϫ10 Figure 6 2. 025 I3 or 2. 025 E I3 or 2. 48 ϫ 10Ϫ4 Many calculators use scientific form in their display panels. For the number c ϫ 10n, the 10 is suppressed and the exponent is often shown preceded by the letter E. For example, to find ͑4,500,000͒2 on a scientific calculator, we could enter the integer 4,500,000 and press the x 2 (or squaring) key, obtaining a display similar to one of those in Figure 6. 025 ϫ 1013. Thus, ͑4,500,000͒2 ϭ 20,250,000,000,000. Calculators may also use scientific form in the entry of numbers.
9–14: Rewrite the number without using the absolute value symbol, and simplify the result. 9 (a) ͉ Ϫ3 Ϫ 2 ͉ (b) ͉ Ϫ5 ͉ Ϫ ͉ 2 ͉ (c) ͉ 7 ͉ ϩ ͉ Ϫ4 ͉ (c) q is less than or equal to . 10 (a) ͉ Ϫ11 ϩ 1 ͉ (b) ͉ 6 ͉ Ϫ ͉ Ϫ3 ͉ (c) ͉ 8 ͉ ϩ ͉ Ϫ9 ͉ (d) d is between 4 and 2. 11 (a) ͑Ϫ5͉͒ 3 Ϫ 6 ͉ (b) ͉ Ϫ6 ͉͑͞Ϫ2͒ (c) ͉ Ϫ7 ͉ ϩ ͉ 4 ͉ (e) t is not less than 5. 12 (a) ͑4͉͒ 6 Ϫ 7 ͉ (b) 5͉͞ Ϫ2 ͉ (c) ͉ Ϫ1 ͉ ϩ ͉ Ϫ9 ͉ (b) y is nonnegative. 7 Ϫ 23 ͉ (c) ͉ 51 Ϫ 13 ͉ Exer. 15 – 18: The given numbers are coordinates of points A, B, and C, respectively, on a coordinate line.
Thus, ͑am͒n ϭ amn. The cases m Յ 0 and n Յ 0 can be proved using the definition of nonpositive exponents. The remaining three laws can be established in similar fashion by counting factors. In laws 4 and 5 we assume that denominators are not 0. Laws of Exponents for Real Numbers a and b and Integers m and n Law Illustration (1) a a ϭ a (2) ͑am͒n ϭ amn (3) ͑ab͒n ϭ anbn a n an ϭ n (4) b b am (5) (a) n ϭ amϪn a am 1 (b) n ϭ nϪm a a m n ͩͪ mϩn 2 и 2 ϭ 2 ϭ 27 ϭ 128 ͑23͒4 ϭ 23и4 ϭ 212 ϭ 4096 ͑20͒3 ϭ ͑2 и 10͒3 ϭ 23 и 103 ϭ 8 и 1000 ϭ 8000 8 2 3 23 ϭ 3ϭ 5 5 125 25 ϭ 25Ϫ3 ϭ 22 ϭ 4 23 1 1 1 23 5 ϭ 5Ϫ3 ϭ 2 ϭ 2 2 2 4 3 4 3ϩ4 ͩͪ We usually use 5(a) if m Ͼ n and 5(b) if m Ͻ n.
Algebra and Trigonometry with Analytic Geometry, Classic Edition by Earl Swokowski, Jeffery A. Cole