Final answer:
The difference in temperature in Fahrenheit for a 5 degrees Celsius increase is 9 degrees Fahrenheit. The conversion from Celsius to Fahrenheit for a change in temperature does not involve adding the 32 degrees used to convert a specific temperature reading, hence none of the provided options accurately reflect the correct expression for the temperature difference. The correct expression is simply the Celsius difference multiplied by 1.8, which in this case is 9.
Step-by-step explanation:
To determine the expression for the temperature difference in Fahrenheit when the temperature today is 5 degrees Celsius more than yesterday, we need to use the formula for converting Celsius to Fahrenheit. The formula is F = C × 1.8 + 32, where F is the temperature in degrees Fahrenheit and C is the temperature in degrees Celsius.
Let yesterday's temperature in Celsius be C. The temperature today in Celsius would then be C + 5. Converting both to Fahrenheit:
- Yesterday: F1 = C × 1.8 + 32
- Today: F2 = (C + 5) × 1.8 + 32
To find the difference in Fahrenheit:
ΔF = F2 - F1
Substitute the expressions for F1 and F2:
ΔF = [(C + 5) × 1.8 + 32] - [C × 1.8 + 32]
The '32' cancels out because it is subtracted and then added, simplifying the expression to:
ΔF = (C + 5) × 1.8 - C × 1.8
Further simplify by distributing the 1.8 and combining like terms:
ΔF = C × 1.8 + 9 - C × 1.8
The terms involving C cancel each other out, leaving:
ΔF = 9
Therefore, the difference in temperature in Fahrenheit when today's temperature is 5 degrees Celsius more than yesterday is 9 degrees Fahrenheit. None of the options a) 5C, b) 5C + 32, c) 37C, d) 37C + 32 are correct.