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).
a. below 32 degrees
b. above 122 degrees
c. below 5 degrees
d. above −31 degrees
I will do one as an example
F=9/5 C + 32
5/9 F=C+5/9 *32
C=5/9 (F-32)
so F<5
C<5/9 (5-32)
C<5/9 (-27)
C<-15 deg
To find the corresponding temperature range in degrees Celsius, we need to use the formula F = 9/5C + 32 and solve for the range of temperature in Celsius.
a. Below 32 degrees Fahrenheit:
To find the corresponding temperature range below 32 degrees Fahrenheit, we start by substituting the value of F = 32 into the formula:
32 = (9/5)C + 32
Next, we subtract 32 from both sides of the equation:
0 = (9/5)C
To solve for C, we divide both sides of the equation by (9/5):
C = 0
So, the corresponding temperature range in Celsius below 32 degrees Fahrenheit is (-∞, 0] in interval notation.
b. Above 122 degrees Fahrenheit:
To find the corresponding temperature range above 122 degrees Fahrenheit, we start by substituting the value of F = 122 into the formula:
122 = (9/5)C + 32
Next, we subtract 32 from both sides of the equation:
90 = (9/5)C
To solve for C, we divide both sides of the equation by (9/5):
C = 50
So, the corresponding temperature range in Celsius above 122 degrees Fahrenheit is (50, +∞) in interval notation.
c. Below 5 degrees Fahrenheit:
To find the corresponding temperature range below 5 degrees Fahrenheit, we start by substituting the value of F = 5 into the formula:
5 = (9/5)C + 32
Next, we subtract 32 from both sides of the equation:
-27 = (9/5)C
To solve for C, we divide both sides of the equation by (9/5):
C = -15
So, the corresponding temperature range in Celsius below 5 degrees Fahrenheit is (-∞, -15] in interval notation.
d. Above -31 degrees Fahrenheit:
To find the corresponding temperature range above -31 degrees Fahrenheit, we start by substituting the value of F = -31 into the formula:
-31 = (9/5)C + 32
Next, we subtract 32 from both sides of the equation:
-63 = (9/5)C
To solve for C, we divide both sides of the equation by (9/5):
C = -35
So, the corresponding temperature range in Celsius above -31 degrees Fahrenheit is (-35, +∞) in interval notation.