Question

The formula for converting Fahrenheit temperature, F, to celsius temperature, C, is C= 5/9(F-32). If the celsius temperature ranges from 10 degrees to 50

degrees, inclusive, what is the range for the Fahrenheit temperature? use the interval notation to express the range for the Fahrenheit temperature.

Answer 1

The range for the Fahrenheit temperature, when the Celsius temperature ranges from 10 degrees to 50 degrees inclusive, is [50, 122].

Step-by-step explanation:

The formula for converting Fahrenheit temperature, F, to Celsius temperature, C, is C = 5/9(F-32). We are given that the Celsius temperature ranges from 10 degrees to 50 degrees, inclusive.

To find the range for the Fahrenheit temperature, we can use the formula and substitute the minimum and maximum values of Celsius temperature:

For the minimum Celsius temperature (10 degrees):

C = 5/9(F-32)

10 = 5/9(F-32)

Multiplying both sides by 9:

90 = 5(F-32)

Dividing both sides by 5:

18 = F-32

Adding 32 to both sides:

F = 50

For the maximum Celsius temperature (50 degrees):

C = 5/9(F-32)

50 = 5/9(F-32)

Multiplying both sides by 9:

450 = 5(F-32)

Dividing both sides by 5:

90 = F-32

Adding 32 to both sides:

F = 122

Therefore, the range for the Fahrenheit temperature is [50, 122] (inclusive) in interval notation.