Question #9456d

1 Answer
Mar 13, 2017

Answer:

#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")))#