Question

[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°

Answer 1

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:

`{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.