Algebra and Trigonometry with Analytic Geometry by Earl W. Swokowski, Jeffery A. Cole

By Earl W. Swokowski, Jeffery A. Cole

Transparent reasons, an uncluttered and beautiful format, and examples and routines that includes quite a few real-life functions have made this article well known between scholars 12 months after yr. This most up-to-date 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 perfect point for precalculus scholars such as you. The ebook additionally offers calculator examples, together with particular keystrokes that assist you use quite a few graphing calculators to resolve difficulties extra quick. possibly so much important-this booklet successfully prepares you for additional classes in arithmetic.

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Sample text

2 Exponents and Radicals 19 If n is a positive integer, the exponential notation an, defined in the following chart, represents the product of the real number a with itself n times. We refer to an as a to the nth power or, simply, a to the n. The positive integer n is called the exponent, and the real number a is called the base. 2 Exponents and Radicals Exponential Notation General case (n is any positive integer) a ෇ a и a и a и иии и a n factors of a u n Special cases a ෇a a2 ෇ a и a a3 ෇ a и a и a a6 ෇ a и a и a и a и a и a 1 The next illustration contains several numerical examples of exponential notation.

Use scientific form to approximate the number of offspring that live to age 3. 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. 000 000 000 000 000 000 000 001 7 gram. Express this number in scientific form. 1 ϫ 10Ϫ31 kilogram. Express this number in decimal form. 55 Light year In astronomy, distances to stars are measured in light years. One light year is the distance a ray of light travels in one year. If the speed of light is approximately 186,000 miles per second, estimate the number of miles in one light year.

To prove law 2, we may write, for m and n positive, ͑am͒n ϭ am и am и am и и и и и am ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ 20 n factors of am and count the number of times a appears as a factor on the right-hand side. Since am ϭ a и a и a и и и и и a, with a occurring as a factor m times, and since the number of such groups of m factors is n, the total number of factors of a is m и n. 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.

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