Answer :
Here's a detailed step-by-step solution for each part of the question:
a. Convert 50 degrees Celsius to Fahrenheit:
To convert from Celsius to Fahrenheit, we use the formula:
[tex]\[ F = \frac{9}{5} \times C + 32 \][/tex]
Given that the temperature in the Sahara desert is 50 degrees Celsius, we plug this value into the formula:
[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 from Fahrenheit to Celsius, we use the rearranged formula:
[tex]\[ C = (F - 32) \times \frac{5}{9} \][/tex]
Given that the temperature in parts of Alaska can reach -60 degrees Fahrenheit, we use this value:
[tex]\[ C = (-60 - 32) \times \frac{5}{9} \][/tex]
[tex]\[ C = (-92) \times \frac{5}{9} \][/tex]
[tex]\[ C \approx -51.11 \][/tex]
So, -60 degrees Fahrenheit is approximately -51.11 degrees Celsius.
c. Find the temperature where Celsius equals Fahrenheit (C = F):
We need to find the temperature where the Celsius and Fahrenheit scales show the same value, which means setting [tex]\( C = F \)[/tex] in the equation:
[tex]\[ F = \frac{9}{5} C + 32 \][/tex]
Substitute [tex]\( F \)[/tex] with [tex]\( C \)[/tex]:
[tex]\[ C = \frac{9}{5} C + 32 \][/tex]
To solve for [tex]\( C \)[/tex], first subtract [tex]\(\frac{9}{5} C\)[/tex] from both sides:
[tex]\[ C - \frac{9}{5} C = 32 \][/tex]
This becomes:
[tex]\[ \left(1 - \frac{9}{5}\right) C = 32 \][/tex]
[tex]\[ \left(\frac{5}{5} - \frac{9}{5}\right) C = 32 \][/tex]
[tex]\[ \left(-\frac{4}{5}\right) C = 32 \][/tex]
Multiply both sides by [tex]\(-\frac{5}{4}\)[/tex] to isolate [tex]\( C \)[/tex]:
[tex]\[ C = 32 \times \left(-\frac{5}{4}\right) \][/tex]
[tex]\[ C = -40 \][/tex]
Thus, the temperature where Celsius and Fahrenheit are the same is -40 degrees.
a. Convert 50 degrees Celsius to Fahrenheit:
To convert from Celsius to Fahrenheit, we use the formula:
[tex]\[ F = \frac{9}{5} \times C + 32 \][/tex]
Given that the temperature in the Sahara desert is 50 degrees Celsius, we plug this value into the formula:
[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 from Fahrenheit to Celsius, we use the rearranged formula:
[tex]\[ C = (F - 32) \times \frac{5}{9} \][/tex]
Given that the temperature in parts of Alaska can reach -60 degrees Fahrenheit, we use this value:
[tex]\[ C = (-60 - 32) \times \frac{5}{9} \][/tex]
[tex]\[ C = (-92) \times \frac{5}{9} \][/tex]
[tex]\[ C \approx -51.11 \][/tex]
So, -60 degrees Fahrenheit is approximately -51.11 degrees Celsius.
c. Find the temperature where Celsius equals Fahrenheit (C = F):
We need to find the temperature where the Celsius and Fahrenheit scales show the same value, which means setting [tex]\( C = F \)[/tex] in the equation:
[tex]\[ F = \frac{9}{5} C + 32 \][/tex]
Substitute [tex]\( F \)[/tex] with [tex]\( C \)[/tex]:
[tex]\[ C = \frac{9}{5} C + 32 \][/tex]
To solve for [tex]\( C \)[/tex], first subtract [tex]\(\frac{9}{5} C\)[/tex] from both sides:
[tex]\[ C - \frac{9}{5} C = 32 \][/tex]
This becomes:
[tex]\[ \left(1 - \frac{9}{5}\right) C = 32 \][/tex]
[tex]\[ \left(\frac{5}{5} - \frac{9}{5}\right) C = 32 \][/tex]
[tex]\[ \left(-\frac{4}{5}\right) C = 32 \][/tex]
Multiply both sides by [tex]\(-\frac{5}{4}\)[/tex] to isolate [tex]\( C \)[/tex]:
[tex]\[ C = 32 \times \left(-\frac{5}{4}\right) \][/tex]
[tex]\[ C = -40 \][/tex]
Thus, the temperature where Celsius and Fahrenheit are the same is -40 degrees.
