The given equation in the image allows conversion from Fahrenheit to Celsius:

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

Part (a): Re-arrange the formula to convert from Celsius to Fahrenheit.

We need to solve for $F$ in terms of $C$. Start with the original equation:

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

1. Multiply both sides by 9 to eliminate the fraction: $9C = 5(F - 32)$

2. Divide both sides by 5: $\frac{9C}{5} = F - 32$

3. Add 32 to both sides to isolate $F$: $F = \frac{9C}{5} + 32$

This is the formula to convert Celsius to Fahrenheit: $F = \frac{9C}{5} + 32$

Part (b): Use the re-arranged equation to find the temperature in Fahrenheit if the Celsius temperature is 45°C.

Using the formula $F = \frac{9C}{5} + 32$, substitute $C = 45$:

$F = \frac{9(45)}{5} + 32$

1. Calculate $\frac{9(45)}{5} = 81$, $F = 81 + 32$

2. Add 32: $F = 113$

So, if it is 45 degrees Celsius, the temperature in Fahrenheit is 113°F.

Would you like further details or have any questions about the solution?

Here are 5 related questions to expand on this topic:

1. What is the Fahrenheit equivalent of 0°C using the rearranged formula?
2. If the temperature in Fahrenheit is 77°F, what is the corresponding temperature in Celsius?
3. How does the Celsius to Fahrenheit conversion formula change if we only focus on absolute differences in temperature?
4. Can you derive the formula for converting Kelvin to Fahrenheit based on the Celsius-Fahrenheit relationship?
5. How would you explain the concept of temperature conversions to someone unfamiliar with the formulas?

Tip: Always check your units when performing conversions. Misunderstanding Celsius and Fahrenheit could lead to significant errors in interpretation!