Final answer:
To convert a 40.0°F temperature decrease to Celsius, use the formula C = (F - 32) x 5/9, which yields a decrease of approximately 4.44°C. To show the relationship between Fahrenheit and Celsius changes, the formula ΔF = 9/5 × ΔC can be used. Without specific timing information, the rate of the temperature drop in hours cannot be determined.
Step-by-step explanation:
To answer the student's question, we will convert the temperature change from Fahrenheit to Celsius and determine the rate of temperature drop over time. Starting with part (a), a drop in temperature by 40.0 Fahrenheit degrees can be converted to Celsius degrees using the formula:
C = (F - 32) × 5/9
Here, C is the change in Celsius and F is the change in Fahrenheit. Plugging in the numbers gives us:
C = (40.0°F - 32) × 5/9
C = 8 × 5/9
C = 40/9
C = 4.44°C
For part (b), to demonstrate the relationship between Fahrenheit and Celsius temperature changes, we have:
ΔF = 9/5 × ΔC
Where ΔF is the change in Fahrenheit and ΔC is the change in Celsius. The equation shows that a change in Fahrenheit is nine-fifths the change in Celsius degrees.
As for the time component, the information provided does not offer specifics on the number of hours over which the temperature drop occurs. However, one of the passages mentions Alaska's average daylight duration, which could hint at a timeframe, although it is unrelated to a specific temperature change event. To determine the rate of temperature drop, you would need the exact number of hours during which the 40.0°F drop occurred.