# Question 9456d

Mar 13, 2017

${124.2}^{\circ} \text{F}$

#### Explanation:

All you have to do here is to convert the two temperatures from degrees Celsius to degrees Fahrenheit by using the conversion factor

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{t \left[\text{^@"F"] = 1.8 * t[""^@"C}\right] + 32}}}$

Now, you know that the record-low temperature for Hawaii is equal to $- {11}^{\circ} \text{C}$. Plug this value into the above equation but do not calculate the equivalent temperature in degrees Fahrenheit yet

$t \left[\text{^@"F"]_"Hawaii" = 1.8 * (-11^@"C}\right) + 32$

t[""^@"F"]_"Hawaii" = 1.8 * (-11) + 32

Now do the same for Alaska, which had a record-low temperature of $- {80}^{\circ} \text{C}$

$t \left[\text{^@"F"]_"Alaska" = 1.8 * (-80^@"C}\right) + 32$

t[""^@"F"]_"Alaska" = 1.8 * (-80) + 32

The problem wants you to find the difference in degrees Fahrenheit between the record-low temperature in Hawaii and the record-low temperature in Alaska

${\Delta}_{\text{temp" = t[""^@"F"]_ "Hawaii" - t[""^@"F"]_ "Alaska}}$

Notice what happens when you subtract the two temperatures

${\Delta}_{\text{temp}} = 1.8 \cdot \left(- 11\right) + 32 - \left[1.8 \cdot \left(- 80\right) + 32\right]$

${\Delta}_{\text{temp}} = 1.8 \cdot \left(- 11\right) + \textcolor{red}{\cancel{\textcolor{b l a c k}{32}}} - 1.8 \cdot \left(- 80\right) - \textcolor{red}{\cancel{\textcolor{b l a c k}{32}}}$

This is equivalent to

${\Delta}_{\text{temp}} = 1.8 \cdot \left(- 11 + 80\right)$

which gets you

Delta_"temp" = 1.8 * 69 = color(darkgreen)(ul(color(black)(124.2^@"F")))#

I'll leave the answer rounded to three sig figs, but keep in mind that you only have one significant figure for the record-low temperature in Alaska.

Finally, notice that you cannot get the same answer by calculating the difference between the two temperature in degrees Celsius

${\Delta}_{\text{temp C" = - 11^@"C" - (-80^@"C") = 69^@"C}}$

then converting it to degrees Fahrenheit

$\textcolor{red}{\cancel{\textcolor{b l a c k}{{\Delta}_{\text{temp F" = 1.8 * 69^@"C" + 32 = 156.2^@"F}}}}}$