By Harshbarger
Mathematical functions: For the administration, existence, and Social Sciences via H...
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XϪ1͞2 64. 2 3 2 2 A P P L I C AT I O N S 65. Richter scale The Richter scale reading for an earthquake measures its intensity (as a multiple of some min- imum intensity used for comparison). 5 on the Richter scale would be severe. Express the intensity of such a quake in exponential form and in radical form. 5. 25. Calculate the ratio of these intensities (larger to smaller). 66. Sound intensity The intensity of sound I (as a multiple of the average minimum threshold of hearing intensity) is related to the decibel level D (or loudness of sound) according to I ϭ 10D͞10 (a) Express 10D͞10 using radical notation.
72. The half-life of carbon-14 is 5600 years. 0 g. 5 27 73. 5)ht where P0 is the population of the city at the present time and P is the population t years from now. 03 and P0 ϭ 30,000, find P when t ϭ 10. 74. 1x) where S is in dollars and x is the number of days after the campaign ends. What are the daily sales 10 days after the end of the campaign? 75. 7 t where t is the number of years the company has been in existence and N is the number of employees. (a) What is the number of employees when t ϭ 0?
Remove parentheses and combine like terms: 9x Ϫ 5x(x ϩ 2) ϩ 4x2 2. Find the following products. (a) (2x ϩ 1)(4x2 Ϫ 2x ϩ 1) (b) (x ϩ 3)2 (c) (3x ϩ 2)(x Ϫ 5) (d) (1 Ϫ 4x)(1 ϩ 4x) All algebraic expressions can represent real numbers, so the techniques used to perform operations on polynomials and to simplify polynomials also apply to other algebraic expressions. ● EXAMPLE 9 Operations with Algebraic Expressions Perform the indicated operations. (a) (b) (c) (d) 3 13 ϩ 4x 1y Ϫ 5 13 Ϫ 11x 1y Ϫ ( 13 Ϫ x 1y) x3͞2(x1͞2 Ϫ xϪ1͞2) (x1͞2 Ϫ x1͞3)2 ( 1x ϩ 2)( 1x Ϫ 2) Solution (a) We remove parentheses and then combine the terms containing 13 and the terms containing x 1y.