the function f gives the temperature, in degrees fahrenheit, that corresponds to a temperature of x kelvins…

the function f gives the temperature, in degrees fahrenheit, that corresponds to a temperature of x kelvins. f(x)=\\frac{9}{5}(x - 273.15)+32. if a temperature increased by 9.10 kelvins, by how much did the temperature increase, in degrees fahrenheit? a. 16.38 b. 48.38 c. 475.29 d. 507.29

the function f gives the temperature, in degrees fahrenheit, that corresponds to a temperature of x kelvins. f(x)=\\frac{9}{5}(x - 273.15)+32. if a temperature increased by 9.10 kelvins, by how much did the temperature increase, in degrees fahrenheit? a. 16.38 b. 48.38 c. 475.29 d. 507.29

Answer

Explanation:

Step1: Identify the function for Fahrenheit - Kelvin conversion

The function is $F(x)=\frac{9}{5}(x - 273.15)+32$.

Step2: Let the initial temperature be $x$ and the new temperature be $x + 9.10$.

The initial Fahrenheit temperature is $F(x)=\frac{9}{5}(x - 273.15)+32$. The new Fahrenheit temperature is $F(x + 9.10)=\frac{9}{5}((x + 9.10)-273.15)+32=\frac{9}{5}(x - 273.15)+\frac{9}{5}\times9.10+32$.

Step3: Find the increase in Fahrenheit temperature

Subtract the initial Fahrenheit temperature from the new one: $F(x + 9.10)-F(x)=\left(\frac{9}{5}(x - 273.15)+\frac{9}{5}\times9.10+32\right)-\left(\frac{9}{5}(x - 273.15)+32\right)$. The $\frac{9}{5}(x - 273.15)$ and $32$ terms cancel out, leaving $\frac{9}{5}\times9.10$.

Step4: Calculate the value of the increase

$\frac{9}{5}\times9.10 = 1.8\times9.10=16.38$.

Answer:

A. 16.38