The equation $\displaystyle F = \frac{9}{5} C + 32$ represents the relationship between Fahrenheit $(F)$ and Celsius $(C)$ temperature scales.
a.) Complete the table to compare the two scales at the given values.
b.) Find the temperature at which the scales agree.
a.)
$
\begin{array}{|c|c|}
\hline\\
C & F \\
\hline\\
-30^{\circ} & \underline{-22^{\circ}} \\
-20^{\circ} & \underline{-4^{\circ}} \\
-10^{\circ} & \underline{14^{\circ}} \\
0^{\circ} & \underline{32^{\circ}} \\
\underline{10^{\circ}} & 50^{\circ} \\
\underline{20^{\circ}} & 68^{\circ} \\
\underline{30^{\circ}} & 86^{\circ}\\
\hline
\end{array}
$
$
\begin{equation}
\begin{aligned}
F =& \frac{9}{5} C + 32
\\
\\
C =& \frac{5}{9} (^{\circ} F - 32)
\end{aligned}
\end{equation}
$
b.) If we set $F = T$ and $C = T$, then
$
\begin{equation}
\begin{aligned}
T =& \frac{9}{5}T + 32
\\
\\
T - \frac{9}{5} T =& 32
\\
\\
\frac{-4}{5} T =& 32
\\
\\
-4T =& 160
\\
\\
T =& -40^{\circ}
\end{aligned}
\end{equation}
$
It means that the temperature scales are equal at $-40^{\circ}$
No comments:
Post a Comment