Each of the following temperature ranges is in degrees Fahrenheit. Use the formulaF=9/5C+32 to find the corresponding temperature range in degrees Celsius (using interval notation and assume inclusion).
a.23∘ to 50 ∘
b.68∘ to 86∘
c. -4∘ to 14∘
d. 104∘ to 140∘
a. The corresponding temperature range in degrees Celsius is (-5°C to 10°C).
b. The corresponding temperature range in degrees Celsius is (20°C to 30°C).
c. The corresponding temperature range in degrees Celsius is (-20°C to -10°C).
d. The corresponding temperature range in degrees Celsius is (40°C to 60°C).
To find the corresponding temperature range in degrees Celsius for each given range in degrees Fahrenheit, we can use the formula F = (9/5)C + 32 and solve for C.
a. 23∘ to 50∘:
First, we substitute 23 for F in the formula:
23 = (9/5)C + 32
Next, we solve for C:
(9/5)C = 23 - 32
(9/5)C = -9
C = (-9)(5/9)
C = -5
Therefore, the corresponding temperature range in degrees Celsius is -5∘ to -5∘, or [-5, -5].
b. 68∘ to 86∘:
Substituting 68 for F in the formula:
68 = (9/5)C + 32
Next, we solve for C:
(9/5)C = 68 - 32
(9/5)C = 36
C = (36)(5/9)
C = 20
Therefore, the corresponding temperature range in degrees Celsius is 20∘ to 20∘, or [20, 20].
c. -4∘ to 14∘:
Substituting -4 for F in the formula:
-4 = (9/5)C + 32
Next, we solve for C:
(9/5)C = -4 - 32
(9/5)C = -36
C = (-36)(5/9)
C = -20
Therefore, the corresponding temperature range in degrees Celsius is -20∘ to -20∘, or [-20, -20].
d. 104∘ to 140∘:
Substituting 104 for F in the formula:
104 = (9/5)C + 32
Next, we solve for C:
(9/5)C = 104 - 32
(9/5)C = 72
C = (72)(5/9)
C = 40
Therefore, the corresponding temperature range in degrees Celsius is 40∘ to 40∘, or [40, 40].
To find the corresponding temperature range in degrees Celsius for each given range in degrees Fahrenheit, we'll use the formula F = (9/5)C + 32. Let's solve each range one by one.
a. To find the temperature range in Celsius for 23∘F to 50∘F, we'll use the formula F = (9/5)C + 32 and plug in the Fahrenheit values:
23 = (9/5)C + 32
Subtract 32 from both sides:
23 - 32 = (9/5)C
-9 = (9/5)C
Simplify:
-9 = (9/5)C
-9 * (5/9) = C
-5 = C
So the temperature range in Celsius is -5∘C to -5∘C in interval notation.
b. To find the temperature range in Celsius for 68∘F to 86∘F, we'll again use the formula F = (9/5)C + 32:
68 = (9/5)C + 32
Subtract 32 from both sides:
68 - 32 = (9/5)C
36 = (9/5)C
Simplify:
36 = (9/5)C
36 * (5/9) = C
20 = C
So the temperature range in Celsius is 20∘C to 20∘C in interval notation.
c. To find the temperature range in Celsius for -4∘F to 14∘F, using the formula:
-4 = (9/5)C + 32
Subtract 32 from both sides:
-4 - 32 = (9/5)C
-36 = (9/5)C
Simplify:
-36 = (9/5)C
-36 * (5/9) = C
-20 = C
So the temperature range in Celsius is -20∘C to -20∘C in interval notation.
d. To find the temperature range in Celsius for 104∘F to 140∘F:
104 = (9/5)C + 32
Subtract 32 from both sides:
104 - 32 = (9/5)C
72 = (9/5)C
Simplify:
72 = (9/5)C
72 * (5/9) = C
40 = C
So the temperature range in Celsius is 40∘C to 40∘C in interval notation.
To summarize:
a. The temperature range in Celsius for 23∘F to 50∘F is -5∘C to -5∘C.
b. The temperature range in Celsius for 68∘F to 86∘F is 20∘C to 20∘C.
c. The temperature range in Celsius for -4∘F to 14∘F is -20∘C to -20∘C.
d. The temperature range in Celsius for 104∘F to 140∘F is 40∘C to 40∘C.
Since you want your answers in Celsius, we have to convert our formula
F=9/5C+32
F - 32 = (9/5)C
(5/9)(F - 32) = C
I will do b), you do the rest
when F = 68, C = (5/9)(68-32) = 20° C
when F = 86, C = (5/9)(86-32) = 30° C