Pre-Calculus Homework Solutions 180

Pre-Calculus Homework Solutions 180 - 21. Given: ABC is...

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21. Given: n ABC is equilateral. CD 5 } 1 3 } CB and CE 5 } 1 3 } CA Prove: n CED , n CAB Proof: 22. 23. Yes; the smaller and smaller details of the shape have the same geometric characteristics as the original form. 24. Stage 1: 6 Stage 2: 36 25. Stage Number of Segments Pattern 014 0 144 1 21 64 2 36 44 3 The formula is 4 to the power of the stage number: A n 5 4 n . So in Stage 8 there are 4 8 5 65,536 segments. 26. Stage 0: 1 unit, Stage 1: } 1 3 } unit, Stage 2: } 1 9 } unit, Stage 3: } 2 1 7 } unit; as the stages increase, the length of the segments will approach zero. 27. Stage 0: 3 units, Stage 1: 3 ? } 4 3 } or 4 units, Stage 2: 3 1 } 4 3 } 21 } 4 3 } 2 5 3 1 } 4 3 } 2 2 or 5 } 1 3 } units, Stage 3: 3 1 } 4 3 } 2 3 or 7 } 1 9 } units 28. P 5 3 1 } 4 3 } 2 n ; as the stages increase, the perimeter increases and approaches infinity. 29. The original triangle and the new triangles are equilateral and thus, all of the angles are equal to 60. By AA Similarity, the triangles are similar. 30. The numbers converge to 1.
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This note was uploaded on 12/19/2011 for the course MAC 1140 taught by Professor Dr.zhan during the Fall '10 term at UNF.

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