Each of the following temperature ranges is in degrees Fahrenheit. Use the formula F=#9/5C+32# to find the corresponding temperature range in degrees Celsius (using interval notation and assume inclusion)?

Ask for:
a). Below 23°
b). Above 41°
c). Below 14°
d). Above 32°

1 Answer
smendyka
Feb 20, 2018

See a solution process below:

Explanation:

First, we need to convert the formula to solve for #C#:

#F = 9/5C + 32#

#F - color(red)(32) = 9/5C + 32 - color(red)(32)#

#F - 32 = 9/5C + 0#

#F - 32 = 9/5C#

#color(red)(5)/color(blue)(9)(F - 32) = color(red)(5)/color(blue)(9) xx 9/5C#

#5/9(F - 32) = cancel(color(red)(5))/cancel(color(blue)(9)) xx color(blue)(cancel(color(black)(9)))/color(red)(cancel(color(black)(5)))C#

#5/9(F - 32) = C#

#C = 5/9(F - 32)#

a) #"Below "23^o#

First, we need to convert the Fahrenheit temperature to Celsius degrees using the formula above:

#C = 5/9(43 - 32)#

#C = 5/9 xx 11#

#C = 55/9#

#C = 6.1#

Because the problem is Below, this is less than or equal to this temperature so we can write the interval notation, assuming inclusion, as:

#(-oo, 6.1^o]#

b) #"Above "41^o#

Again, we need to convert the Fahrenheit temperature to Celsius degrees using the formula above:

#C = 5/9(43 - 41)#

#C = 5/9 xx 21#

#C = 10/9#

#C = 1.1#

Because the problem is Above, this is greater than or equal to this temperature so we can write the interval notation, assuming inclusion, as:

#[1.1^o, +oo)#

#c# and #d# can be done using the same process.

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