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Solutions for Session 4, Part C
See solutions for Problems: C1 | C2 | C3 | C4 | C5 | C6| C7 | C8 | C9
C10 | C11 | C12
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Problem C1 | |
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The "after" Quadperson has the same scale to its facial features; the nose is still four times as wide as it is tall, and so forth.
<< back to Problem C1
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Problem C2 | |
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This "after" Quadperson does not have the same shape as the original. In particular, the nose becomes a flat line, but other features are scaled differently from "before."
<< back to Problem C2
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Problem C3 | |
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Problem C1 is the relative comparison. Think about the angles and measurements in the body; we expect, for example, the head to be a certain fraction of the size of the torso, and so forth.
<< back to Problem C3
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Problem C4 | |
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The change in Problem C1, a relative comparison, keeps these measurements in proportion, while the change in Problem C2, an absolute comparison, does not. In Problem C2, short lengths are made way too short (the nose, for example) by giving an absolute change in length, rather than a proportional change in length.
<< back to Problem C4
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Problem C7 | |
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Both graphs are straight lines. The graph of y1 goes through the origin (0, 0), while the graph of y2 does not. Additionally, the graph of y2 becomes negative if x < 1/2, not a good thing when measuring lengths.
a.  | b.  |
<< back to Problem C7
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Problem C8 | |
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Yes, the graph of y1 is proportional, since the input is always twice the output. Or, the output is half the input. (Compare that to the formula y1 = x / 2.) The graph of y2 is not proportional; try finding the outputs for two different values of x, then determine if they are proportional. This produces the different shape of Quadperson in Problem C2.
<< back to Problem C8
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Problem C10 | |
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The equation for this table is y3 = 2x.
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X | | Y3 |
1 | | 2 |
2 | | 4 |
3 | | 6 |
4 | | 8 |
5 | | 10 |
6 | | 12 |
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<< back to Problem C10
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Problem C11 | |
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It is a proportional relationship because every output is twice the input, and if we multiply the input by any number, we multiply the output by the same number. This graph, like the last proportional graph, passes through the origin (0, 0).
<< back to Problem C11
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Problem C12 | |
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All proportional relationships have the equation y = kx, where k is some constant number. A line graph represents a proportional relationship only when the line goes through the origin (0, 0).
<< back to Problem C12
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