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Chapter 1: Problem 5

Conversion between Fahrenheit and Celsius degrees can be achieved through the relation (a) \({ }^{\circ} \mathrm{F}=\frac{9}{5}\left({ }^{\circ} \mathrm{C}\right)+32\) (b) \({ }^{\circ} \mathrm{F}=\frac{5}{9}\left({ }^{\circ} \mathrm{C}\right)+32\) (c) \({ }^{\circ} \mathrm{C}=\frac{9}{5}\left({ }^{\circ} \mathrm{F}\right)+32\) (d) \({ }^{\circ} \mathrm{C}=\frac{5}{9} \quad\left({ }^{\circ} \mathrm{F}\right)+32\)

Short Answer

Expert verified
The correct answer for the formula that represents conversion from Celsius to Fahrenheit is (a). Conversion from Fahrenheit to Celsius is not represented correctly in any of the choices, but the closest is (d), with a sign error in the constant.

Step by step solution

01

Identifying the Correct Formulas

The correct formulas for conversion are:\n\nFrom Celsius to Fahrenheit: \({ }^{\circ} \mathrm{F}=\frac{9}{5}\left({ }^{\circ} \mathrm{C}\right)+32\) \n\nAnd from Fahrenheit to Celsius: \({ }^{\circ} \mathrm{C}=\frac{5}{9}\left({ }^{\circ} \mathrm{F}-32\right)\) \n\nOthers are incorrect as they either have the wrong coefficients (the fraction which multiplies the degrees) or the wrong sign in the constants (the number added after the multiplication).
02

Matching Correct Formulas with Choices

The first formula (from Celsius to Fahrenheit) correctly corresponds to choice (a). The second formula (from Fahrenheit to Celsius) matches choice (d), but with an error in the constant, it should subtract 32 instead of adding.

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