Question

The temperature T(d) in degrees Fahrenheit in terms of the Celsius temperature d is given by T(d) = 9/5 * d + 32

Answer 1

Answer:

$\displaystyle F(v) = \frac{9}{5}(v-273)+32$

Step-by-step explanation:

The temperature T(d) in degrees Fahrenheit in terms of Celsius d is given by:

$\displaystyle T(d)=\frac{9}{5}d+32$

And the temperature C(v) in degrees Celsius in terms of Kelvin v is given by:

$C(v)=v-273$

We want the formula for the temperature F(v) in degrees Fahrenheit in terms of the Kelvin temperature.

So, we can use a composition of functions. Since T(d) outputs the temperature in Fahrenheit and C(v) inputs the temperature in Kelvin, T(C(v)) will be the temperature in Fahrenheit given the temperature in Kelvin. So:

$\displaystyle T(C(v))=\frac{9}{5}(C(v)))+32$

Substitute:

$\displaystyle T(C(v)) = F(v) = \frac{9}{5}(v-273)+32$

Therefore:

$\displaystyle F(v) = \frac{9}{5}(v-273)+32$