Answer :
Sure, let's go through the problem step by step.
### a. Convert 50 degrees Celsius to Fahrenheit
To convert a temperature from Celsius to Fahrenheit, we use the formula:
[tex]\[ F = \frac{9}{5}C + 32 \][/tex]
Here, [tex]\( C = 50 \)[/tex].
Substituting 50 into the formula:
[tex]\[ F = \frac{9}{5} \times 50 + 32 \][/tex]
First, multiply [tex]\( \frac{9}{5} \)[/tex] by 50:
[tex]\[ F = 90 + 32 \][/tex]
Finally, add 32:
[tex]\[ F = 122 \][/tex]
So, 50 degrees Celsius is 122 degrees Fahrenheit.
### b. Convert -60 degrees Fahrenheit to Celsius
To convert from Fahrenheit to Celsius, we use the formula:
[tex]\[ C = \frac{5}{9}(F - 32) \][/tex]
Here, [tex]\( F = -60 \)[/tex].
Substituting -60 into the formula:
[tex]\[ C = \frac{5}{9}(-60 - 32) \][/tex]
Calculate [tex]\(-60 - 32\)[/tex]:
[tex]\[ C = \frac{5}{9}(-92) \][/tex]
Finally, multiply [tex]\( \frac{5}{9} \)[/tex] by -92:
[tex]\[ C \approx -51.11 \][/tex]
So, -60 degrees Fahrenheit is approximately -51.11 degrees Celsius.
### c. Find the temperature where degrees Fahrenheit and degrees Celsius are the same
We know the equation relating Fahrenheit and Celsius is:
[tex]\[ F = \frac{9}{5}C + 32 \][/tex]
To find the temperature where they are the same, set [tex]\( F = C \)[/tex]:
[tex]\[ C = \frac{9}{5}C + 32 \][/tex]
Rearranging this:
[tex]\[ C - \frac{9}{5}C = 32 \][/tex]
Factor the left side:
[tex]\[ \left(1 - \frac{9}{5}\right)C = 32 \][/tex]
Calculate the coefficient of [tex]\( C \)[/tex]:
[tex]\[ \left(-\frac{4}{5}\right)C = 32 \][/tex]
Now solve for [tex]\( C \)[/tex]:
[tex]\[ C = \frac{32 \times 5}{-4} \][/tex]
[tex]\[ C = -40 \][/tex]
Therefore, the temperature at which Celsius and Fahrenheit are the same is -40 degrees.
### a. Convert 50 degrees Celsius to Fahrenheit
To convert a temperature from Celsius to Fahrenheit, we use the formula:
[tex]\[ F = \frac{9}{5}C + 32 \][/tex]
Here, [tex]\( C = 50 \)[/tex].
Substituting 50 into the formula:
[tex]\[ F = \frac{9}{5} \times 50 + 32 \][/tex]
First, multiply [tex]\( \frac{9}{5} \)[/tex] by 50:
[tex]\[ F = 90 + 32 \][/tex]
Finally, add 32:
[tex]\[ F = 122 \][/tex]
So, 50 degrees Celsius is 122 degrees Fahrenheit.
### b. Convert -60 degrees Fahrenheit to Celsius
To convert from Fahrenheit to Celsius, we use the formula:
[tex]\[ C = \frac{5}{9}(F - 32) \][/tex]
Here, [tex]\( F = -60 \)[/tex].
Substituting -60 into the formula:
[tex]\[ C = \frac{5}{9}(-60 - 32) \][/tex]
Calculate [tex]\(-60 - 32\)[/tex]:
[tex]\[ C = \frac{5}{9}(-92) \][/tex]
Finally, multiply [tex]\( \frac{5}{9} \)[/tex] by -92:
[tex]\[ C \approx -51.11 \][/tex]
So, -60 degrees Fahrenheit is approximately -51.11 degrees Celsius.
### c. Find the temperature where degrees Fahrenheit and degrees Celsius are the same
We know the equation relating Fahrenheit and Celsius is:
[tex]\[ F = \frac{9}{5}C + 32 \][/tex]
To find the temperature where they are the same, set [tex]\( F = C \)[/tex]:
[tex]\[ C = \frac{9}{5}C + 32 \][/tex]
Rearranging this:
[tex]\[ C - \frac{9}{5}C = 32 \][/tex]
Factor the left side:
[tex]\[ \left(1 - \frac{9}{5}\right)C = 32 \][/tex]
Calculate the coefficient of [tex]\( C \)[/tex]:
[tex]\[ \left(-\frac{4}{5}\right)C = 32 \][/tex]
Now solve for [tex]\( C \)[/tex]:
[tex]\[ C = \frac{32 \times 5}{-4} \][/tex]
[tex]\[ C = -40 \][/tex]
Therefore, the temperature at which Celsius and Fahrenheit are the same is -40 degrees.
