Pre-Calculus Homework Solutions 138

# Pre-Calculus Homework Solutions 138 - 40 Given ABC Prove AC...

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40. Given: n ABC Prove: AC 1 BC . AB Proof: 41. AB 5 ¬ Ï (2 2 5 w ) 2 1 ( 2 w 4 2 8) w 2 w 5 ¬ Ï 9 1 14 w 4 w 5 ¬ Ï 153 w < ¬ 12.4 BC 5 ¬ Ï ( 2 3 2 w 2 ) 2 1 w [ 2 1 2 w ( 2 4)] w 2 w 5 ¬ Ï 25 1 9 w 5 ¬ Ï 34 w < ¬ 5.8 AC 5 ¬ Ï ( 2 3 2 w 5 ) 2 1 w ( 2 1 2 w 8) 2 w 5 ¬ Ï 64 1 8 w 1 w 5 ¬ Ï 145 w < ¬ 12.0 AB 1 BC ¬ . ? AC AB 1 AC ¬ . ? BC 12.4 1 5.8 ¬ . ? 12.0 12.4 1 12.0 ¬ . ? 5.8 18.2 ¬ . 12.0 24.4 ¬ . 5.8 AC 1 BC ¬ . ? AB 12.0 1 5.8 ¬ . ? 12.4 17.8 ¬ . 12.4 All of the inequalities are true, so the coordinates can be the vertices of a triangle. 42. LM 5 ¬ Ï [ 2 22 w 2 ( 2 2 w 4)] 2 1 w [20 2 w ( 2 19 w )] 2 w 5 ¬ Ï 4 1 15 w 21 w 5 ¬ Ï 1525 w < ¬ 39.1 MN 5 ¬ Ï [ 2 5 2 w ( 2 22 w )] 2 1 ( w 2 7 2 w 20) 2 w 5 ¬ Ï 289 1 w 729 w 5 ¬ Ï 1018 w < ¬ 31.9 LN 5 ¬ Ï [ 2 5 2 w ( 2 24 w )] 2 1 [ w 2 7 2 w ( 2 19) w ] 2 w 5 ¬ Ï 361 1 w 144 w 5 ¬ Ï 505 w < ¬ 22.5 LM 1 MN ¬ . ? LN
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