Question

for a fixed amount of a gas at a constant temperature, the volume of the gas is inversely proportional to its pressure. at a pressure of 30 pounds per square inch (psi), a gas has a volume of 600 in.³. which function can be used to model the volume of the gas y, in cubic inches, when the pressure is x psi? y = 20x y = 18,000x y =20/x y =18,000/x

Explanation:

Step1: Recall inverse variation formula

Inverse variation is modeled by \( y=\frac{k}{x} \) (here \( y \) is volume, \( x \) is pressure, so \( y = \frac{k}{z} \) where \( z \) is pressure).

Step2: Find the constant \( k \)

Given \( y = 600 \) when \( z = 30 \). Substitute into \( y=\frac{k}{z} \): \( 600=\frac{k}{30} \). Solve for \( k \): \( k = 600\times30=18000 \).

Step3: Write the function

Substitute \( k = 18000 \) into \( y=\frac{k}{z} \), we get \( y=\frac{18000}{z} \) (or \( y = \frac{18000}{x} \) with \( x \) as pressure).

Answer:

\( y=\frac{18000}{x} \) (corresponding to the option \( y = 18,000/x \))