Final answer:
The temperature -22°F in City X converts to -30°C, -15°C in City Y converts to 5°F, and -10°C in City Z converts to 14°F. Among all these, City X at -30°C is the coldest. Additionally, a 40.0°F decrease corresponds to a 22.2°C decrease, and the Fahrenheit and Celsius scales are the same at -40°.
Step-by-step explanation:
To solve this problem, we will use two equations for temperature conversion between degrees Fahrenheit (°F) and degrees Celsius (°C).
- For converting °F to °C, the formula is: C = (5/9) × (F - 32).
- For converting °C to °F, the formula is: F = (1.8 × C) + 32.
Let's convert the given temperatures:
- City X: -22°F to °C:
C = (5/9) × (-22 - 32) = (5/9) × (-54) = -30°C - City Y: -15°C to °F:
F = (1.8 × -15) + 32 = -27 + 32 = 5°F - City Z: -10°C to °F:
F = (1.8 × -10) + 32 = -18 + 32 = 14°F
Comparing the temperatures in °C, City X is the coldest because -30°C is the lowest temperature.
Now, let's address the supplementary questions regarding temperature changes and intersection points of the temperature scales:
- (a) A decrease of 40.0°F in temperature is equivalent to a decrease in Celsius which is calculated as:
C = (5/9) × 40.0 ≈ 22.2°C - (b) Any change in temperature in degrees Fahrenheit is nine-fifths of the change in degrees Celsius because of the (9/5) factor in the conversion formula from Celsius to Fahrenheit.
The temperature at which the Fahrenheit and Celsius scales have the same numerical value is -40°, as this value doesn't change when using the conversion formulas. The Fahrenheit and Kelvin scales never have the same numerical value because they use different starting points (absolute zero).