By Earl Swokowski, Jeffery A. Cole
The newest 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 apparent, the time-tested workout units characteristic numerous functions, its uncluttered format is beautiful, and the trouble point of difficulties is acceptable and constant. Mathematically sound, ALGEBRA AND TRIGONOMETRY WITH ANALYTIC GEOMETRY, vintage variation, 12E, successfully prepares scholars for additional classes in arithmetic via its very good, time-tested challenge units.
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Additional resources for Algebra and Trigonometry with Analytic Geometry, Classic 12th Edition
A b c 48 Rational approximations to square roots can be found using a formula discovered by the ancient Babylonians. Let x 1 be the first rational approximation for 2n. If we let x2 ϭ 1 2 ͩ x1 ϩ ͪ n , x1 then x 2 will be a better approximation for 2n, and we can repeat the computation with x 2 replacing x 1. Starting with x 1 ϭ 32, find the next two rational approximations for 22. Exer. 49–50: Express the number in scientific form. 000 005 5 (c) 24,900,000 Exer. 51–52: Express the number in decimal form.
The largest documented halibut weighed 230 kilograms. Estimate its length. 43, where W is in tons and L is in feet. Estimate the weight of a whale that is 25 feet long. 99 Weight lifters’ handicaps O’Carroll’s formula is used to handicap weight lifters. If a lifter who weighs b kilograms lifts w kilograms of weight, then the handicapped weight W is given by w Wϭ 3 . 2 b Ϫ 35 Suppose two lifters weighing 75 kilograms and 120 kilograms lift weights of 180 kilograms and 250 kilograms, respectively.
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) ͑ 2n a ͒n ϭ a if 2n a is a real number n 2 an ϭ a if a Ն 0 n 2 a ϭ a if a Ͻ 0 and n is odd n n 2 an ϭ ͉ a ͉ if a Ͻ 0 and n is even Illustrations ͑ 25͒2 ϭ 5, ͑ 23 Ϫ8 ͒3 ϭ Ϫ8 2͑Ϫ2͒ ϭ Ϫ2, 2 ͑Ϫ2͒5 ϭ Ϫ2 2͑Ϫ3͒2 ϭ ͉ Ϫ3 ͉ ϭ 3, 2 ͑Ϫ2͒4 ϭ ͉ Ϫ2 ͉ ϭ 2 2 52 ϭ 5, 3 3 3 3 2 2 ϭ2 5 4 If a Ն 0, then property 4 reduces to property 2.