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NCERT Class XI Mathematics - Straight Lines - Solutions

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Question : 30 of 74
Marks: +1, -0
The length L (in centimetre) 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.
Solution:  
Assuming L along x-axis and C along y-axis, we have two points (124.942, 20) and (125.134, 110). By two point form, the point (L, C) satisfies the equation
C−20L−124.942\frac{C-20}{L-124.942} = (110−20125.134−124.942)\left(\frac{110-20}{125.134-124.942}\right) ⇒ C - 20 = 900.192\frac{90}{0.192} (L - 124.942)
⇒ 0.192C – 3.84 = 90L – 11244.78 ⇒ 0.192(C – 20) + 11244.78 = 90 L
⇒ L = 0.19290\frac{0.192}{90} (C - 20) + 124.942
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