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Pretest: Functions

Select the correct answer.

In the field of thermodynamics, Rankine is the unit used to measure temperature. One can convert temperature from Celsius into Rankine using the formula [tex]C=\frac{R}{1.8}-273[/tex]. What is the temperature in Celsius corresponding to [tex]R[/tex] degrees Rankine?

A. [tex]\frac{9}{5}(C-273)[/tex]

B. [tex]\frac{9}{5}(C+273)[/tex]

C. [tex]\frac{5}{9}(C-273)[/tex]

D. [tex]\frac{5}{9}(C+273)[/tex]

Sagot :

GinnyAnsweridn
To convert temperature from Rankine (R) to Celsius (C), we start with the given formula:

[tex]\[ C = \frac{R}{1.8} - 273 \][/tex]

Our goal is to solve for [tex]\( R \)[/tex] when given [tex]\( C \)[/tex]. Let's rearrange the equation to isolate [tex]\( R \)[/tex]:

1. Start by isolating [tex]\(\frac{R}{1.8}\)[/tex] on one side of the equation:
[tex]\[ C + 273 = \frac{R}{1.8} \][/tex]

2. Now, multiply both sides by 1.8 to solve for [tex]\( R \)[/tex]:
[tex]\[ R = 1.8 (C + 273) \][/tex]

Now we substitute the correct result which, according to our calculation, simplifies the relation between Rankine and Celsius temperatures:

[tex]\[ \boxed{R = 1.8 (C + 273)} \][/tex]

Thus, the temperature in Celsius corresponding to [tex]\( R \)[/tex] degrees Rankine is:

[tex]\[ \boxed{R = \frac{5}{9}(C+273)} \][/tex]

This can be matched to the answer choice:

D. [tex]\(\frac{5}{9}(C + 273)\)[/tex]

Hence, it is the temperature in Celsius corresponding to [tex]\( R \)[/tex] degrees Rankine.
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