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The equation \( F = \frac{9}{5}C + 32 \) gives the Fahrenheit temperature \( F \) corresponding to the Celsius temperature \( C \).

Find the Fahrenheit temperature equivalent to \(-15\) degrees Celsius.

Answer :

A decrease of 40.0 Fahrenheit degrees corresponds to a decrease of 22.22 Celsius degrees, which demonstrates the nine-fifths relationship between the temperature scales.

Temperature Conversion from Fahrenheit to Celsius

When dealing with a decrease of 40.0 Fahrenheit degrees, we can calculate the equivalent decrease in Celsius. For conversion, we know that 1 Fahrenheit degree equals 5/9 Celsius degrees. Therefore, a decrease of 40.0 Fahrenheit degrees is:

40.0 × (5/9) = 22.22 Celsius degrees (rounded to two decimal places).

To show that any change in temperature in Fahrenheit is nine-fifths the change in Celsius degrees, we can use the ratio of degree sizes: 1 Fahrenheit degree is 5/9 of a Celsius degree. This ratio can be expressed as:

( Change in Fahrenheit / Change in Celsius ) = (9/5)

Thus, for a change of 40.0 Fahrenheit degrees, the Celsius change is:

40.0 × (5/9) = 22.22 Celsius degrees, demonstrating the nine-fifths relationship.

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