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Question
The length L (in centimeters) of a copper rod is a linear function of its celsius temperature C. In an experiment, if L = 124.942 when C = 20 and L = 125.134 when C = 110, express L in terms of C.
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Solution
Assuming C along the x-axis and L along the y-axis, we have two points, (20, 124.942) and (110, 125.134), in CL-plane.
As L is a linear function of C, the equation of the line passing through (20, 124.942) and (110, 125.134) is
\[L - 124 . 942 = \frac{125 . 134 - 124 . 942}{110 - 20}\left( C - 20 \right)\]
\[ \Rightarrow L - 124 . 942 = \frac{0 . 192}{90}\left( C - 20 \right)\]
\[ \Rightarrow L - 124 . 942 = \frac{0 . 032}{15}\left( C - 20 \right)\]
\[ \Rightarrow L = \frac{0 . 032}{15}C + 124 . 942 - \frac{20 \times 0 . 032}{15}\]
\[ \Rightarrow L = \frac{0 . 032}{15}C + 124 . 942 - 0 . 04267\]
\[ \Rightarrow L = \frac{4}{1875}C + 124 . 899\]
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