Question

The lowest temperature for the day was 63 degrees Fahrenheit. Later on the day, the temperature increased to 81.5 degrees Fahrenheit. By how many degrees Fahrenheit did the temperature increase?

a) 18.5
b) 17.5
c) 19.5
d) 20.5

Answer 1

The temperature increased by 18.5 degrees Fahrenheit when it went from 63 degrees Fahrenheit to 81.5 degrees Fahrenheit. In the context of temperature conversion, a 40.0°F decrease is equivalent to a 22.2°C decrease, affirming that the Fahrenheit change is nine-fifths that of Celsius.

Step-by-step explanation:

The question is asking by how many degrees Fahrenheit did the temperature increase if it went from 63 degrees Fahrenheit to 81.5 degrees Fahrenheit. To find this, we subtract the lower temperature from the higher temperature:

81.5 °F (higher temperature) - 63 °F (lower temperature) = 18.5 °F (increase in temperature).

Therefore, the temperature increased by 18.5 degrees Fahrenheit.

To address the additional questions provided:

1. To convert a decrease in temperature from Fahrenheit to Celsius, use the formula for temperature conversion: C = (F - 32) × (5/9), where F is the Fahrenheit temperature. For a 40.0 °F decrease, the Celsius decrease would be the same proportion, so 40.0 °F × (5/9), which is approximately 22.2 °C.
2. To show that any change in temperature in Fahrenheit degrees is nine-fifths the change in Celsius degrees, use the derivative of the temperature conversion formula mentioned above. Since the rate of change of Fahrenheit to Celsius is 5/9, when you reverse it, it becomes 9/5. Therefore, any change in Fahrenheit (F) equals the change in Celsius (C) times 9/5.