[Different Ask] 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). -22° to -13°
b). -4° to 59°
c). -40° to -31°
d). 104° to 140°

1 Answer
Feb 22, 2018

See the explanation

Explanation:

We are changing Fahrenheit into Centigrade so we need to change the given formula

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

Subtract #color(red)(32)# from both sides

#color(green)(F=9/5C+32 color(white)("ddd")->color(white)("ddd")Fcolor(red)(-32)=9/5C+ubrace(32color(red)(-32)))#
#color(white)("dddddddddddddddddddddddddd.dddddddd")darr#
#color(green)(color(white)("dddddddddddddd")->color(white)("ddd")F-32=9/5C+color(white)("dd")0)#

Multiply both sides by #color(red)(5/9)#
This turns the #9/5# from #9/5C# into 1

#color(green)(color(white)("dddddddddddddd")->color(white)("ddd")color(red)(5/9)(F-32)=ubrace(color(red)(5/9xx)9/5C))#

#color(green)(color(white)("dddddddddddddd")->color(white)("ddd")5/9(F-32)=C#

Using the above formula we have:

Tony B

#{F:Fin[-22,-13]} ->{C:C in[-30,-25])#
#{F:Fin[-color(white)("d")4,-59]} ->{C:C in[-20,color(white)("dd.")15])#
#{F:Fin[-40,-31]} ->{C:C in[-40,color(white)(".dd")15])#
#color(red)("unexpected "-40F = -40C)#
#{F:Fin[-104,140]} ->{C:C in[40,color(white)(".dd")60]}#

I checked -40F = -40C several times. I even asked my wife to check it.