Final answer:
The Fahrenheit and Celsius scales have the same numerical value at -40 degrees. The Fahrenheit and Kelvin scales never have the same numerical value because they are offset by a constant when converting from one to the other.
Step-by-step explanation:
To determine at what temperature the Fahrenheit and Celsius scales have the same numerical value, we can compare the formulas that define conversions between these two scales. The formula for converting Fahrenheit to Celsius is C = (F - 32) × 5/9, and the formula for converting Celsius to Fahrenheit is F = C × 9/5 + 32. We are looking for the point where C = F, so setting the two equal to each other and solving the resulting equation, we find that -40°C = -40°F. This is the temperature where the numerical values on both scales match.
For the question about the temperature at which the Fahrenheit and Kelvin scales have the same numerical value, it's important to understand the relationship between these two scales. The Kelvin scale is an absolute scale based on the concept of absolute zero, and the formula to convert Fahrenheit to Kelvin is K = (F + 459.67) × 5/9.
There is no temperature where the Fahrenheit and Kelvin scales have the same numerical value, because they are offset by the constant 459.67 when Fahrenheit is converted to Kelvin. Hence, there is no answer for part (b) in conventional terms.