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Written by:
Lisa K
Date added:
August 10, 2013
Level:
University
Grade:
B
No of pages / words:
2 / 298
Was viewed:
1327 times
Rating of current essay:
Essay content:
We were already given that 1 cut creates at most 2 pieces, 2 cuts create at most 4 pieces, and 3 cuts create at most 7 pieces. However, since these 3 sets of data are not enough to show us the pattern, we decided to obtain more data by drawing circles with 4 and 5 cuts.
Solution:
From our experimentation, we were able to finish the data table
Number of Cuts (C) Number of Pieces (P)
1 2
2 4
3 7
4 11
5 16
We notice that P is increasing in each case by C...
displayed 300 characters
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For example, with C=2, P=The previous number + 2, and with C=3, P=The previous number + 3, and so on. So when C=10, P= 16+6+7+8+9+10 = 56.
This pattern makes sense because of the observation that we made earlier. For example, when we added the fifth cut, it intersected the first four lines. Four lines in a figure makes five areas, and so drawing a line through the four lines creates 5 additional areas:
Evaluation:
However, since using addition isn’t very practical for finding P when C is large, we need a general function explaining P in terms of C...
displayed 300 characters
General issues of this essay:
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