Answer :
We start with the conversion formulas between Celsius ([tex]$C$[/tex]) and Fahrenheit ([tex]$F$[/tex]). The formula to convert from Celsius to Fahrenheit is
[tex]$$
F = \frac{9}{5} C + 32.
$$[/tex]
### Converting Fahrenheit to Celsius
To convert Fahrenheit to Celsius, we first solve the above formula for [tex]$C$[/tex]. Subtracting 32 from both sides gives
[tex]$$
F - 32 = \frac{9}{5} C.
$$[/tex]
Multiplying both sides by [tex]$\frac{5}{9}$[/tex], we have
[tex]$$
C = \frac{5}{9}(F - 32).
$$[/tex]
For [tex]$F = 71$[/tex] degrees Fahrenheit, substitute into the equation:
[tex]$$
C = \frac{5}{9} (71 - 32) = \frac{5}{9} \times 39.
$$[/tex]
Calculating the expression:
[tex]$$
\frac{5}{9} \times 39 = \frac{195}{9} \approx 21.6667.
$$[/tex]
Rounded to the nearest tenth, the temperature in Celsius is
[tex]$$
21.7^\circ C.
$$[/tex]
### Converting Celsius to Fahrenheit
Using the original formula for the reverse conversion, for [tex]$C = 39$[/tex] degrees Celsius, we have
[tex]$$
F = \frac{9}{5} \times 39 + 32.
$$[/tex]
First, multiply:
[tex]$$
\frac{9}{5} \times 39 \approx 70.2.
$$[/tex]
Then add 32:
[tex]$$
70.2 + 32 = 102.2.
$$[/tex]
Thus, the temperature in Fahrenheit is
[tex]$$
102.2^\circ F.
$$[/tex]
### Final Answers
- If the temperature is [tex]$71^\circ F$[/tex], it is equivalent to approximately [tex]$21.7^\circ C$[/tex].
- If the temperature is [tex]$39^\circ C$[/tex], it is equivalent to approximately [tex]$102.2^\circ F$[/tex].
[tex]$$
F = \frac{9}{5} C + 32.
$$[/tex]
### Converting Fahrenheit to Celsius
To convert Fahrenheit to Celsius, we first solve the above formula for [tex]$C$[/tex]. Subtracting 32 from both sides gives
[tex]$$
F - 32 = \frac{9}{5} C.
$$[/tex]
Multiplying both sides by [tex]$\frac{5}{9}$[/tex], we have
[tex]$$
C = \frac{5}{9}(F - 32).
$$[/tex]
For [tex]$F = 71$[/tex] degrees Fahrenheit, substitute into the equation:
[tex]$$
C = \frac{5}{9} (71 - 32) = \frac{5}{9} \times 39.
$$[/tex]
Calculating the expression:
[tex]$$
\frac{5}{9} \times 39 = \frac{195}{9} \approx 21.6667.
$$[/tex]
Rounded to the nearest tenth, the temperature in Celsius is
[tex]$$
21.7^\circ C.
$$[/tex]
### Converting Celsius to Fahrenheit
Using the original formula for the reverse conversion, for [tex]$C = 39$[/tex] degrees Celsius, we have
[tex]$$
F = \frac{9}{5} \times 39 + 32.
$$[/tex]
First, multiply:
[tex]$$
\frac{9}{5} \times 39 \approx 70.2.
$$[/tex]
Then add 32:
[tex]$$
70.2 + 32 = 102.2.
$$[/tex]
Thus, the temperature in Fahrenheit is
[tex]$$
102.2^\circ F.
$$[/tex]
### Final Answers
- If the temperature is [tex]$71^\circ F$[/tex], it is equivalent to approximately [tex]$21.7^\circ C$[/tex].
- If the temperature is [tex]$39^\circ C$[/tex], it is equivalent to approximately [tex]$102.2^\circ F$[/tex].