Question

Convert the compound inequality into Fahrenheit for the temperature of your boots:

-40 ≤ 5/9 . (F - 32) ≤ 15
a) -40 ≤ 5/9 . (F - 32) ≤ 15
b) -15 ≤ 9/5 . (F - 32) ≤ 40
c) -40 ≤ 5/9 . (F - 32) ≤ 40
d) -15 ≤ 5/9 . (F - 32) ≤ 40

Answer 1

A decrease of 40.0°F in temperature is equivalent to a decrease of approximately 4.44°C. Furthermore, any change in temperature in Fahrenheit degrees is nine-fifths the change in Celsius degrees, due to the conversion rate between the two scales.

Step-by-step explanation:

The conversion of temperature from Fahrenheit to Celsius can be done using the formula C = 5/9 × (F - 32). If we have a decrease of 40.0°F in temperature, we want to find the equivalent decrease in Celsius. Applying the aforementioned formula:

• First, substitute 40 for F: C = 5/9 × (40 - 32)
• Simplify inside the parentheses: C = 5/9 × 8
• Multiply by the fraction: C = 5/9 × 8 = 40/9
• Divide to find the change in Celsius: C ≈ 4.44°C

Therefore, a decrease of 40.0°F in temperature translates to a decrease of approximately 4.44°C.

For part (b), we demonstrate that a change in Fahrenheit is nine-fifths of a change in Celsius by taking an arbitrary change in Celsius, say ΔC, and calculating the corresponding change in Fahrenheit using the formula ΔF = 9/5 × ΔC. This shows that the change in Fahrenheit is indeed nine-fifths of the change in Celsius, aligning with the temperature conversion rate between the two scales.