1. **Convert -40°C to Fahrenheit** The formula to convert Celsius to Fahrenheit is: $$F = \frac{9}{5}C + 32$$ 2. Substitute $C = -40$: $$F = \frac{9}{5} \times (-40) + 32$$ 3. Calculate the multiplication: $$F = \frac{9}{5} \times (-40) + 32 = -72 + 32$$ 4. Simplify: $$F = -40$$ **Notice:** -40°C equals -40°F, which is the unique point where Celsius and Fahrenheit scales intersect. --- 5. **Find the difference in Fahrenheit for a 15°C difference** The difference in Fahrenheit corresponding to a Celsius difference is: $$\Delta F = \frac{9}{5} \times \Delta C$$ 6. Substitute $\Delta C = 15$: $$\Delta F = \frac{9}{5} \times 15 = 27$$ --- 7. **Compare -10°C and 10°F to find which is colder** Convert -10°C to Fahrenheit: $$F = \frac{9}{5} \times (-10) + 32 = -18 + 32 = 14$$ Since 14°F (equivalent to -10°C) is warmer than 10°F, 10°F is colder. **Final answers:** -40°C = -40°F (unique intersection point) Temperature difference of 15°C = 27°F difference 10°F is colder than -10°C