Pre-Calculus Homework Solutions 181

Pre-Calculus Homework Solutions 181 - 41. Sample answer:...

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41. Sample answer: The leaves in the tree and the branches of the trees are self-similar. These self- similar shapes are repeated throughout the painting. 42a. The flower and mountain are computer- generated; the feathers and moss are real. 42b. The fractals exhibit self-similarity and iteration. 43. See students’ work. 44. In Stage 1, the shaded triangle has legs 3 and 4 units. The hypotenuse has length c ,where c 2 5 3 2 1 4 2 , or c 5 Ï 9 1 16 w or 5. So, the perimeter of the triangle is 3 1 4 1 5 or 12 units. In Stage 2, there are three small shaded triangles and the larger shaded triangle from Stage 1. Each of the small shaded triangles has legs 2 and 1.5 units. The hypotenuse has length d d 2 5 2 2 1 1.5 2 , or d 5 Ï 4 1 2. w 25 w or 2.5. So, the perimeter of all shaded triangles in Stage 2 is 3(2 1 1.5 1 2.5) 1 12 or 30 units. 45. Sample answer: Fractal geometry can be found in the repeating patterns of nature. Answers should include the following.
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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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