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Pre-Calc Homework Solutions 12

Pre-Calc Homework Solutions 12 - 12 Section 1.2(d Since f...

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60. continued (b) 61. (a) (b) 62. (a) (b) 63. (a) Since ( f + g )( x ) 5 ˇ g w ( x w ) w 2 w 5 w 5 ˇ x 2 w 2 w 5 w , g ( x ) 5 x 2 . (b) Since ( f + g )( x ) 5 1 1 } g ( 1 x ) } 5 x , we know that } g ( 1 x ) } 5 x 2 1, so g ( x ) 5 } x 2 1 1 } . (c) Since ( f + g )( x ) 5 f 1 } 1 x } 2 5 x , f ( x ) 5 } 1 x } . (d) Since ( f + g )( x ) 5 f ( ˇ x w ) 5 ) x ) , f ( x ) 5 x 2 . The completed table is shown. Note that the absolute value sign in part (d) is optional. 64. (a) Note that the data in the table begins at x 5 20. (We do not include the initial investment in the data.) The power regression equation is y 5 27.1094 x 2.651044 . (b) [0, 30] by [ 2 20,000, 180,000] (c) When x 5 30, y < 223,374. According to the power regression equation, the investment will grow to approximately $223,374. (d) The linear regression equation is y 5 12,577.97 x 2 177,275.52. When x 5 30, y < 200,064. According to the linear regression equation, the investment will grow to approximately $200,064. 65. (a) Because the circumference of the original circle was 8 p and a piece of length x was removed. (b) r 5 } 8 p 2 p 2 x } 5 4 2 } 2 x p } (c) h 5 ˇ 1 w 6 w 2 w r w 2 w 5 ! 1 § 6
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