Answer :
To solve the problem regarding temperature conversions between Celsius and Fahrenheit, let's go through the steps clearly and simply:
1. Convert Celsius to Fahrenheit:
The formula to convert a temperature from Celsius (°C) to Fahrenheit (°F) is:
[tex]\[
F = C \times \frac{9}{5} + 32
\][/tex]
For a temperature of 4180 degrees Celsius, we substitute the value into the formula:
[tex]\[
F = 4180 \times \frac{9}{5} + 32
\][/tex]
This calculation gives us a result of 7556.0 degrees Fahrenheit.
2. Understanding Intervals between Celsius and Fahrenheit:
The interval from the freezing point to the boiling point of water is 100 degrees Celsius, which corresponds to 180 degrees Fahrenheit. From this, we can determine the conversion factors:
- The conversion factor for intervals, from Celsius to Fahrenheit, is:
[tex]\[
\frac{180^{\circ} F}{100^{\circ} C} = 1.8
\][/tex]
This tells us that an interval of 1 degree Celsius corresponds to 1.8 degrees Fahrenheit.
- Conversely, the conversion factor for intervals, from Fahrenheit to Celsius, is:
[tex]\[
\frac{100^{\circ} C}{180^{\circ} F} = 0.5555555555555556
\][/tex]
This means an interval of 1 degree Fahrenheit is equivalent to approximately 0.5556 degrees Celsius.
3. Verification:
Given the conversion factors:
- For every 1 degree Celsius increase, it relates to an increase of 1.8 degrees Fahrenheit, which is consistent with our calculations.
- The calculated conversion factors align well with these standard conversions.
These calculations allow us to verify the relationships between Celsius and Fahrenheit, as well as understand how temperature intervals map between these units.
1. Convert Celsius to Fahrenheit:
The formula to convert a temperature from Celsius (°C) to Fahrenheit (°F) is:
[tex]\[
F = C \times \frac{9}{5} + 32
\][/tex]
For a temperature of 4180 degrees Celsius, we substitute the value into the formula:
[tex]\[
F = 4180 \times \frac{9}{5} + 32
\][/tex]
This calculation gives us a result of 7556.0 degrees Fahrenheit.
2. Understanding Intervals between Celsius and Fahrenheit:
The interval from the freezing point to the boiling point of water is 100 degrees Celsius, which corresponds to 180 degrees Fahrenheit. From this, we can determine the conversion factors:
- The conversion factor for intervals, from Celsius to Fahrenheit, is:
[tex]\[
\frac{180^{\circ} F}{100^{\circ} C} = 1.8
\][/tex]
This tells us that an interval of 1 degree Celsius corresponds to 1.8 degrees Fahrenheit.
- Conversely, the conversion factor for intervals, from Fahrenheit to Celsius, is:
[tex]\[
\frac{100^{\circ} C}{180^{\circ} F} = 0.5555555555555556
\][/tex]
This means an interval of 1 degree Fahrenheit is equivalent to approximately 0.5556 degrees Celsius.
3. Verification:
Given the conversion factors:
- For every 1 degree Celsius increase, it relates to an increase of 1.8 degrees Fahrenheit, which is consistent with our calculations.
- The calculated conversion factors align well with these standard conversions.
These calculations allow us to verify the relationships between Celsius and Fahrenheit, as well as understand how temperature intervals map between these units.
