Question

The function C(f)=(5)/(9)(f-32) converts a temperature, f degrees Fahrenheit, to C degrees Celsius. (b) when C(f)=-10, f

Answer 1

A 40.0°F decrease in Fahrenheit temperature equates to a 4.44°C decrease in Celsius. The change in temperature in Fahrenheit degrees is always nine-fifths the change in Celsius degrees, according to the conversion formula ΔF = ΔC x (9/5).

Step-by-step explanation:

To determine how many degrees Celsius the temperature decreases when there is a 40.0°F decrease in temperature, we can use the conversion formula °C = 0.555 x (°F - 32). If the Fahrenheit temperature decreases by 40.0°F, we can calculate the Celsius change by:

• Subtracting 32 from the decrease in Fahrenheit: 40.0 - 32 = 8.0
• Multiplying the result by 5/9 (or 0.555): 8.0 x 0.555 = 4.44

Therefore, the temperature decreases by 4.44 degrees Celsius.

To show that any change in temperature in Fahrenheit degrees is nine-fifths the change in Celsius degrees:

1. Let ΔF represent the change in Fahrenheit and ΔC represent the change in Celsius.
2. The conversion formula between Fahrenheit and Celsius is ΔF = ΔC x (9/5).
3. Therefore, for any change in Celsius (ΔC), the change in Fahrenheit is nine-fifths of that.