C=59(F−32)

The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?

A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 59 degree Celsius.
A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
A temperature increase of 59 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.

The given equation is:

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

This equation relates the temperature \( F \) in degrees Fahrenheit to the temperature \( C \) in degrees Celsius. Let's analyze the statements provided:

1. **A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of \( \frac{5}{9} \) degrees Celsius.**

   If we increase \( F \) by 1 degree Fahrenheit, let's see how it affects \( C \):

   \[
   C_1 = \frac{5}{9}(F + 1 - 32)
   \]

   Subtract the original equation \( C = \frac{5}{9}(F - 32) \):

   \[
   C_1 - C = \frac{5}{9}(F + 1 - 32) - \frac{5}{9}(F - 32) = \frac{5}{9}(1) = \frac{5}{9} \text{ degrees Celsius}
   \]

   So, a temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of \( \frac{5}{9} \) degrees Celsius, not 59 degrees Celsius.

2. **A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.**

   To find the equivalent change in Fahrenheit for a 1 degree Celsius increase, we solve for \( F \):

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

   Now, increasing \( C \) by 1 degree:

   \[
   F_1 = \frac{9}{5}(C + 1) + 32
   \]

   Subtract the original equation:

   \[
   F_1 - F = \frac{9}{5}(C + 1) + 32 - \left(\frac{9}{5}C + 32\right) = \frac{9}{5}(1) = 1.8 \text{ degrees Fahrenheit}
   \]

   So, a temperature increase of 1 degree Celsius is indeed equivalent to a temperature increase of 1.8 degrees Fahrenheit.

3. **A temperature increase of 59 degrees Fahrenheit is equivalent to a temperature increase of \( \frac{59 \times 5}{9} \) degrees Celsius.**

   From the first calculation, we know that for every 1 degree Fahrenheit increase, \( C \) increases by \( \frac{5}{9} \) degrees Celsius. So for a 59-degree Fahrenheit increase:

   \[
   \Delta C = \frac{5}{9} \times 59 \approx \frac{295}{9} \approx 32.78 \text{ degrees Celsius}
   \]

   However, the statement suggests that it is equivalent to a 1-degree Celsius increase, which is incorrect.

**Conclusion:** The correct statement is:

- **A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.**

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. What is the physical significance of the factor \( \frac{5}{9} \) in the Celsius to Fahrenheit conversion?
2. How do you derive the inverse formula to convert Celsius to Fahrenheit?
3. What is the significance of the number 32 in the Fahrenheit to Celsius conversion formula?
4. How would you convert a temperature difference of 15 degrees Celsius to Fahrenheit?
5. How does the freezing and boiling point of water compare in Celsius and Fahrenheit?

**Tip:** Remember, the Celsius and Fahrenheit scales differ not just in their zero points but also in their unit sizes; this is why a change of 1 degree in Celsius is not the same as a change of 1 degree in Fahrenheit.

Explore how temperature conversion between Celsius and Fahrenheit is calculated using the equation C = (5/9)(F - 32). Learn the relationship between Fahrenheit and Celsius temperatures and solve related problems. Suitable for advanced high school students and beyond.

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