Mathematical Applications for the Management, Life, and by James J. Reynolds Ronald J. Harshbarger

By James J. Reynolds Ronald J. Harshbarger

MATHEMATICAL purposes FOR THE administration, existence, AND SOCIAL SCIENCES, ninth version is meant for a two-semester utilized calculus or mixed finite arithmetic and utilized calculus direction. The book's concept-based process, a number of presentation tools, and fascinating and appropriate purposes continue scholars who usually take the course--business, economics, lifestyles sciences, and social sciences majors--engaged within the fabric. This variation broadens the book's real-life context by way of including a couple of environmental technology and fiscal purposes. using modeling has been improved, with modeling difficulties now basically categorized within the examples. additionally integrated within the 9th variation is a quick overview of algebra to arrange scholars with assorted backgrounds for the fabric in later chapters.

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This process is called rationalizing the denominator. ● EXAMPLE 9 Rationalizing Denominators Express each of the following with no radicals in the denominator. ) (a) 15 (b) 1x 2x 118xy (x, y Ͼ 0) (c) 3x 1 2x2 3 (x 0) Solution (a) We wish to create a perfect square under the radical in the denominator. 15 ؒ 1x (b) 2x ؒ 1x 15 1x ϭ x 1x 12xy 2x 12xy 2x 12xy 12xy ϭ ϭ ϭ 2 2 6xy 3y 12xy 136x y 118xy (c) We wish to create a perfect cube under the radical in the denominator. 3x 3 1 2x2 ● Checkpoint 6. Simplify: 7 7 (a) 1 x ؒ 3 3 3 3 1 4x 3x 1 4x 3x 1 4x 31 4x ϭ ϭ ϭ 3 3 2x 2 1 4x 1 8x3 5 (b) 3 1 (x2 ϩ 1)2 4 5 7.

09)Ϫ7. Calculations such as this are often done directly with a calculator. Using the definitions of zero and negative exponents enables us to extend the rules of exponents to all integers and to express them more simply. 3 Integral Exponents ● Rules of Exponents 17 For real numbers a and b and integers m and n, 1. 3. 5. 7. am ؒ an ϭ amϩn (ab)m ϭ ambm (a͞b)m ϭ am͞bm aϪn ϭ 1͞an (a (b 0) 2. 4. 6. 8. 0) am͞an ϭ amϪn (a 0) (am)n ϭ amn a0 ϭ 1 (a 0) (a͞b)Ϫn ϭ (b͞a)n (a, b 0) Throughout the remainder of the text, we will assume all expressions are defined.

95. (a) With cell A2 as 49, what entry in cell A3 (referenced to A2) could be used to fill column A with the possible lengths? (b) Because the sum of the length and width must be 50, what rule would we use to find the width if we knew the length? (c) Use your result from (b) to write an entry for cell B2 that is referenced to A2 and that could be used to fill column B with the correct widths for each of the lengths in column A. (d) What entry in cell C2 (appropriately referenced) could be used to fill column C with the area for any pair of lengths and widths?

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