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Answer :
Final answer:
The Fahrenheit and Celsius scales share the same numerical value at -40 degrees, proven by temperature conversion formulas. However, Fahrenheit and Kelvin scales do not share a common value as Kelvin begins at absolute zero.
Explanation:
The main answer to the question is that the Fahrenheit and Celsius scales have the same numerical value at -40 degrees. This occurs because the two scales intersect at this point due to the way they are defined and converted from one to the other.To show this, we can use the formula for converting Fahrenheit to Celsius: C = (F - 32) × 5/9. By setting C equal to F and solving for the variable, we can find the temperature where both scales match. -40°C = (-40°F - 32) × 5/9. Simplifying this, we find that it indeed checks out that -40°C = -40°F.As for part (b) of your question regarding the Fahrenheit and Kelvin scales having the same numerical value, that situation is not practically possible because the Kelvin scale starts at absolute zero (0 K), which corresponds to -459.67°F, and the values of Fahrenheit and Kelvin do not intersect at a common value.
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