Each of the following temperature ranges is in degrees Fahrenheit. Use the formula F=95 C+32 to find the corresponding temperature range in degrees Celsius (using interval notation and assume inclusion).
a. below 32∘
b.above 122∘
c. below 5∘
d. above -31∘
above and below are the same for both scales.
For the temperatures, just plug in an F value and crank out the C value
For example, if F=98.6,
C = 5/9 (F-32) = 5/9 (66.6) = 37
To find the corresponding temperature range in degrees Celsius, we can use the formula F=9/5 C+32. We will solve for C using the given temperature ranges in degrees Fahrenheit.
a. Below 32∘:
Plug in the value for F as 32 in the formula:
32 = 9/5 C + 32
Subtract 32 from both sides:
0 = 9/5 C
Multiply both sides by 5/9 to isolate C:
0 = C
The corresponding temperature range in degrees Celsius is (-∞, 0].
b. Above 122∘:
Plug in the value for F as 122 in the formula:
122 = 9/5 C + 32
Subtract 32 from both sides:
90 = 9/5 C
Multiply both sides by 5/9 to isolate C:
50 = C
The corresponding temperature range in degrees Celsius is (50, ∞).
c. Below 5∘:
Plug in the value for F as 5 in the formula:
5 = 9/5 C + 32
Subtract 32 from both sides:
-27 = 9/5 C
Multiply both sides by 5/9 to isolate C:
-15 = C
The corresponding temperature range in degrees Celsius is (-∞, -15].
d. Above -31∘:
Plug in the value for F as -31 in the formula:
-31 = 9/5 C + 32
Subtract 32 from both sides:
-63 = 9/5 C
Multiply both sides by 5/9 to isolate C:
-35 = C
The corresponding temperature range in degrees Celsius is (-35, ∞).