Question

Question #9456d

Answer 1

`124.2^@"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

`color(blue)(ul(color(black)(t[""^@"F"] = 1.8 * t[""^@"C"] + 32)))`

Now, you know that the record-low temperature for Hawaii is equal to `-11^@"C"`. Plug this value into the above equation but do not calculate the equivalent temperature in degrees Fahrenheit yet

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

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

Now do the same for Alaska, which had a record-low temperature of `-80^@"C"`

`t[""^@"F"]_"Alaska" = 1.8 * (-80^@"C") + 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_"temp" = t[""^@"F"]_ "Hawaii" - t[""^@"F"]_ "Alaska"`

Notice what happens when you subtract the two temperatures

`Delta_"temp" = 1.8 * (-11) + 32 - [1.8 * (-80) + 32]`

`Delta_"temp" = 1.8 * (-11) + color(red)(cancel(color(black)(32))) - 1.8 * (-80) - color(red)(cancel(color(black)(32)))`

This is equivalent to

`Delta_"temp" = 1.8 * (-11 + 80)`

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_"temp C" = - 11^@"C" - (-80^@"C") = 69^@"C"`

then converting it to degrees Fahrenheit

`color(red)(cancel(color(black)(Delta_"temp F" = 1.8 * 69^@"C" + 32 = 156.2^@"F")))`