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The temperature in degrees Fahrenheit, [tex]F[/tex], is related to the temperature in degrees Celsius, [tex]C[/tex], by the equation:

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

a. In the Sahara Desert, temperatures often reach 50 degrees Celsius. How many degrees Fahrenheit is this?

b. In parts of Alaska, the temperatures can reach -60 degrees Fahrenheit. How many degrees Celsius is this?

c. There is one temperature where the degrees Fahrenheit and degrees Celsius are the same, so that [tex]C = F[/tex]. Use the equation, where [tex]F[/tex] is expressed in terms of [tex]C[/tex], to solve for this temperature.

Answer :

Sure! Let's solve each part of the question step-by-step.

a. Convert 50 degrees Celsius to Fahrenheit:

We have the formula to convert Celsius to Fahrenheit, which is:

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

Plugging in the value [tex]\( C = 50 \)[/tex]:

[tex]\[ F = \frac{9}{5} \times 50 + 32 \][/tex]

[tex]\[ F = 90 + 32 \][/tex]

[tex]\[ F = 122 \][/tex]

So, 50 degrees Celsius is equal to 122 degrees Fahrenheit.

b. Convert -60 degrees Fahrenheit to Celsius:

To convert Fahrenheit to Celsius, we use the formula:

[tex]\[ C = \frac{5}{9}(F - 32) \][/tex]

Plugging in the value [tex]\( F = -60 \)[/tex]:

[tex]\[ C = \frac{5}{9}(-60 - 32) \][/tex]

[tex]\[ C = \frac{5}{9}(-92) \][/tex]

[tex]\[ C \approx -51.11 \][/tex]

So, -60 degrees Fahrenheit is approximately -51.11 degrees Celsius.

c. Find the temperature where degrees Celsius and degrees Fahrenheit are the same:

We are looking for a temperature where [tex]\( C = F \)[/tex]. Using the equation for Fahrenheit in terms of Celsius:

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

Set [tex]\( F = C \)[/tex]:

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

Rearranging:

[tex]\[ 0 = \frac{9}{5}C - C + 32 \][/tex]

[tex]\[ 0 = \left(\frac{9}{5} - 1\right)C + 32 \][/tex]

[tex]\[ 0 = \frac{4}{5}C + 32 \][/tex]

Subtract 32 from both sides:

[tex]\[ -32 = \frac{4}{5}C \][/tex]

Multiply both sides by [tex]\(\frac{5}{4}\)[/tex] to solve for [tex]\( C \)[/tex]:

[tex]\[ C = -32 \times \frac{5}{4} \][/tex]

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

Thus, the temperature where degrees Celsius and degrees Fahrenheit are the same is -40 degrees.

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