To find the formula for the temperature [tex]\( F(v) \)[/tex] in degrees Fahrenheit in terms of the Kelvin temperature [tex]\( v \)[/tex], we need to perform a step-by-step substitution.
1. Starting with the given formulas:
- The temperature in Fahrenheit [tex]\( T \)[/tex] as a function of Celsius [tex]\( d \)[/tex] is:
[tex]\[
T(d) = \frac{9}{5} d + 32
\][/tex]
- The temperature in Celsius [tex]\( C \)[/tex] as a function of Kelvin [tex]\( v \)[/tex] is:
[tex]\[
C(v) = v - 273
\][/tex]
2. Substitute [tex]\( d = C(v) \)[/tex] into [tex]\( T(d) \)[/tex]:
- Here we replace [tex]\( d \)[/tex] with [tex]\( v - 273 \)[/tex]:
[tex]\[
T(v - 273) = \frac{9}{5} (v - 273) + 32
\][/tex]
3. Express [tex]\( F(v) \)[/tex] as the formula in terms of Kelvin [tex]\( v \)[/tex]:
- Thus, the formula for the temperature [tex]\( F(v) \)[/tex] in degrees Fahrenheit in terms of the Kelvin temperature [tex]\( v \)[/tex] is:
[tex]\[
F(v) = \left( \frac{9}{5} \right) (v - 273) + 32
\][/tex]
So, the formula is:
[tex]\[
F(v) = \left( \frac{9}{5} \right) (v - 273) + 32
\][/tex]
