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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,

Respuesta :

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

[tex]F=\frac{9}{5}C+32[/tex]

a) If C = 50 , F = ??

So, substitute with C at the given equation :

[tex]\begin{gathered} F=\frac{9}{5}\cdot50+32 \\ F=9\cdot10+32 \\ F=122 \end{gathered}[/tex]

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

So, substitute with F and find C

[tex]\begin{gathered} -60=\frac{9}{5}C+32 \\ -60-32=\frac{9}{5}C \\ -92=\frac{9}{5}C \\ C=\frac{5}{9}\cdot-92=-\frac{460}{9}=-51\frac{1}{9}=-51.1 \end{gathered}[/tex]

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

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

[tex]\begin{gathered} C=\frac{9}{5}C+32 \\ C-\frac{9}{5}C=32 \end{gathered}[/tex]

Multiply the all terms by 5 :

[tex]\begin{gathered} 5\cdot C-5\cdot\frac{9}{5}C=5\cdot32 \\ 5C-9C=160 \\ -4C=160 \\ \\ C=\frac{160}{-4}=-40 \end{gathered}[/tex]

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

[tex]F=C=-40[/tex]

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