Final answer:
The temperature decrease of 40.0°F is equivalent to approximately 22.2°C. Additionally, the relationship between Fahrenheit and Celsius temperature changes is such that a change in Fahrenheit is nine-fifths of a change in Celsius degrees.
Step-by-step explanation:
The student asks about how a temperature decrease in Fahrenheit relates to the respective change in Celsius. To answer this question, two parts need to be addressed: (a) the conversion of a temperature decrease from Fahrenheit to Celsius, and (b) to show the relationship between the changes in these temperature scales.
Part (a): Conversion from Fahrenheit to Celsius
When the temperature decreases by 40.0°F, we can find out how much it decreases in Celsius by using the formula for converting Fahrenheit to Celsius, which is C = (F - 32) × 5/9. A decrease of 40.0°F would therefore be a decrease of (40.0°F - 32) × 5/9, which simplifies to 40.0 × 5/9 or about 22.2°C.
Part (b): Relationship Between Fahrenheit and Celsius Changes
To show that a change in temperature in Fahrenheit is nine-fifths of a change in Celsius degrees, we can use the fact that the Fahrenheit scale has a 9/5 ratio relative to the Celsius scale. This comes from the conversion formulas where F = C × 9/5 + 32 and C = (F - 32) × 5/9. Thus, a change in Fahrenheit, say ΔF, corresponds to a change in Celsius, ΔC, in the following way: ΔF = ΔC × 9/5.