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 = 18,000/x what would the volume of the gas be if the pressure is increased to 40 psi? in.³

Explanation:

Step1: Recall inverse proportionality

Since volume \( y \) is inversely proportional to pressure \( x \), the relationship is \( y=\frac{k}{x} \), where \( k \) is the constant of proportionality.

Step2: Find the constant \( k \)

We know when \( x = 30 \) psi, \( y = 600 \) in³. Substitute into \( y=\frac{k}{x} \): \( 600=\frac{k}{30} \). Solve for \( k \): \( k = 600\times30=18000 \). So the function is \( y=\frac{18000}{x} \).

Step3: Calculate volume at 40 psi

Now, to find the volume when \( x = 40 \) psi, substitute \( x = 40 \) into \( y=\frac{18000}{x} \): \( y=\frac{18000}{40}=450 \).

Answer:

450