Question

In the equation c = 9/5(f - 32), which variable is considered the independent one? a) c

b) f
c) 9
d) 5

Answer 1

The independent variable in the equation c = 9/5(f - 32) is f, representing degrees Fahrenheit.

Step-by-step explanation:

In the equation c = 9/5(f - 32), the independent variable is f, which represents the temperature in degrees Fahrenheit. The temperature in degrees Celsius (c) is dependent on the value of f.

To address the problem presented:

1. (a) To find out how many degrees Celsius the temperature decreases when there is a 40.0°F decrease in temperature, we first need to understand that the conversion factor between Celsius and Fahrenheit is such that a change in 1°F corresponds to a change of 5/9°C. Therefore, a 40.0°F decrease in temperature would also correspond to a 40.0 × 5/9°C decrease, which calculates to approximately 22.22°C.
2. (b) To show that any change in temperature in Fahrenheit degrees is nine-fifths the change in Celsius degrees, we can take the original formula and manipulate it to reflect a change (Δ) in temperature: Δc = 9/5(Δf). This implies that for every 1°C change, there is a corresponding 9/5°F change.