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The length $L$ (in centimeters) of a coppper 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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$L$ is linear function of $C$
$\therefore \quad L=a+b C$
For $L=124.942, C=20$,
$124.942=a+20 b \quad \ldots(i)$
For $L=125.134, C=110$,
$125.134=a+110 b \quad \ldots(ii)$
Subtracting (i) from (ii), $0.192=90 b$
$\therefore \quad b=\frac{0.192}{90}=0.00213$
from (i) $124.942=a+20 \times 0.00213$
$\Rightarrow \quad 124.942=a+0.0426$
$a=124.942-0.0426=124.8994$
Now $L$ in term of $C$ is $L=a+b C$
$\Rightarrow \quad L=124.8994+0.00213 C$
$\therefore \quad L=a+b C$
For $L=124.942, C=20$,
$124.942=a+20 b \quad \ldots(i)$
For $L=125.134, C=110$,
$125.134=a+110 b \quad \ldots(ii)$
Subtracting (i) from (ii), $0.192=90 b$
$\therefore \quad b=\frac{0.192}{90}=0.00213$
from (i) $124.942=a+20 \times 0.00213$
$\Rightarrow \quad 124.942=a+0.0426$
$a=124.942-0.0426=124.8994$
Now $L$ in term of $C$ is $L=a+b C$
$\Rightarrow \quad L=124.8994+0.00213 C$
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