Question

The temperature in degrees Fahrenheit, F, is related to the temperature in degrees Celsius,C, by the equationF-*c+32a. In the Sahara desert, temperatures often reach 50 degrees Celsius. How many degreesFahrenheit is this?b. In parts of Alaska, the temperatures can reach -60 degrees Fahrenheit. How manydegrees Celsius is this?c. There is one temperature where the degrees Fahrenheit and degrees Celsius are thesame, so that C = F. Use the expression from the equation, where Fis expressed interms of C to solve for this temperature,

Answer 1

Given the relation between The temperature in degrees Fahrenheit, F, is related to the temperature in degrees Celsius, C, by the equation:

`F=(9)/(5)C+32`

a) If C = 50 , F = ??

So, substitute with C at the given equation :

`\begin{gathered} F=(9)/(5)\cdot50+32 \\ F=9\cdot10+32 \\ F=122 \end{gathered}`

b) When F = -60 , We need to find C = ?

So, substitute with F and find C

`\begin{gathered} -60=(9)/(5)C+32 \\ -60-32=(9)/(5)C \\ -92=(9)/(5)C \\ C=(5)/(9)\cdot-92=-(460)/(9)=-51(1)/(9)=-51.1 \end{gathered}`

c) when need to solve the equation in case of : C = F

So, Substitute with F = C , then solve for C

`\begin{gathered} C=(9)/(5)C+32 \\ C-(9)/(5)C=32 \end{gathered}`

Multiply the all terms by 5 :

`\begin{gathered} 5\cdot C-5\cdot(9)/(5)C=5\cdot32 \\ 5C-9C=160 \\ -4C=160 \\ \\ C=(160)/(-4)=-40 \end{gathered}`

In the case of F = C , Both of them will be equal -40

`F=C=-40`