Problem

The temperature $T(d)$ in degrees Fahrenheit in terms of the Celsius temperature $d$ is given by $T(d)=\frac{9}{5} d+32$. The temperature $C(v)$ in degrees Celsius in terms of the Kelvin temperature $v$ is given by $C(v)=v-273$. Write a formula for the temperature $F(v)$ in degrees Fahrenheit in terms of the Kelvin temperature $v$. It is not necessary to simplify. \[ F(v)= \]

Solution

Step 1 :We are given two formulas, one that converts Celsius to Fahrenheit and another that converts Kelvin to Celsius. We are asked to find a formula that converts Kelvin to Fahrenheit. We can do this by substituting the Celsius to Fahrenheit formula into the Kelvin to Celsius formula.

Step 2 :Given the formula for Celsius to Fahrenheit: \(T(d) = 1.8d + 32\)

Step 3 :And the formula for Kelvin to Celsius: \(C(v) = v - 273\)

Step 4 :We substitute the Kelvin to Celsius formula into the Celsius to Fahrenheit formula to get the formula for Kelvin to Fahrenheit.

Step 5 :Final Answer: The formula for the temperature \(F(v)\) in degrees Fahrenheit in terms of the Kelvin temperature \(v\) is \(\boxed{F(v)=1.8v - 459.4}\)

From Solvely APP
Source: https://solvelyapp.com/problems/20087/

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