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Pre-Calculus Homework Solutions 181

# Pre-Calculus Homework Solutions 181 - 41 Sample answer The...

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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 3 2 4 2 , or c 9 16 or 5. So, the perimeter of the triangle is 3 4 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 , where d 2 2 2 1.5 2 , or d 4 2.25 or 2.5. So, the perimeter of all shaded triangles in Stage 2 is 3(2 1.5 2.5) 12 or 30 units. 45. Sample answer: Fractal geometry can be found in the repeating patterns of nature. Answers should include the following. • Broccoli is an example of fractal geometry because the shape of the florets is repeated
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