15. 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).
it is 9C/5 + 32. Use the formula.
To convert a temperature range from Fahrenheit to Celsius, we can use the formula F = (9/5)C + 32. Let's go through each temperature range and use the formula to find the corresponding range in degrees Celsius.
1. Range: [-40, 40] °F
To find the corresponding range in Celsius, we'll substitute the values into the formula:
F = (9/5)C + 32
-40 = (9/5)C + 32
Subtract 32 from both sides:
-72 = (9/5)C
Multiply both sides by 5/9 to solve for C:
C = -72 * (5/9)
C = -40
So, the corresponding temperature range in degrees Celsius is [-40, 40] °C.
2. Range: [32, 212] °F
Using the formula:
F = (9/5)C + 32
32 = (9/5)C + 32
Subtract 32 from both sides:
0 = (9/5)C
Multiply both sides by 5/9 to solve for C:
C = 0 * (5/9)
C = 0
So, the corresponding temperature range in degrees Celsius is [0, 100] °C.
In summary:
- Range [-40, 40] °F is equivalent to the range [-40, 40] °C.
- Range [32, 212] °F is equivalent to the range [0, 100] °C.