Pre-Calculus Homework Solutions 190

Pre-Calculus Homework Solutions 190 - 32 12 x x 8 x2 40...

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32. } 1 x 2 } 5 ¬ } 8 x } x 2 5 ¬ 96 x 5 ¬ Ï 96 w or 4 Ï 6 w x < ¬ 9.8 } 12 y 2 8 } 5 ¬ } 8 y } y 2 5 ¬ 32 y 5 ¬ Ï 32 w or 4 Ï 2 w y < ¬ 5.7 } 1 z 2 } 5 ¬ } 12 z 2 8 } z 2 5 ¬ 48 z 5 ¬ Ï 48 w or 4 Ï 3 w z < ¬ 6.9 33. } Ï a 17 w } 5 ¬ } Ï b 17 w } ab 5 ¬ 17 7 b 5 ¬ 17 b 5 ¬ } 1 7 7 } 34. } Ï x 12 w } 5 ¬ } Ï y 12 w } xy 5 ¬ 12 x Ï 3 w 5 ¬ 12 x 5 ¬ } Ï 12 3 w } or 4 Ï 3 w x < ¬ 6.9 35. Never; let x and x 1 1 be consecutive positive integers. The average of the numbers is } x 1 ( x 2 1 1) } or } 2 x 2 1 1 } 0 ¬ x 2 1 x 0 ¬ } 4 x 2 1 4 4 x 1 1 } x 2 1 x 0 ¬ x 2 1 x 1 } 1 4 } 0 Þ ¬ } 1 4 } Since 0 Þ ¬ } 1 4 } ,the first equation is never true. The average of the numbers is not the geometric mean of the numbers. 36. Always; let a and b be positive integers, and let x be the geometric mean of a 2 and b 2 . } a x 2 } 5 ¬ } b x 2 } a 2 b 2 5 ¬ x 2 ( ab ) 2 5 ¬ x 2 ab 5 ¬ x Because a and b are positive integers, their product x is a positive integer. 37.
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