for a fixed amount of a gas at a constant temperature, the volume of the gas is inversely proportional to…

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

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

Answer

Explanation:

Step1: Recall inverse - proportion formula

For two variables $y$ and $x$ that are inversely proportional, the formula is $y=\frac{k}{x}$, where $k$ is the constant of proportionality.

Step2: Find the constant of proportionality $k$

We know that when $x = 30$ psi and $y=600$ in³. Substitute these values into $y=\frac{k}{x}$, we get $600=\frac{k}{30}$. Solving for $k$ gives $k = 600\times30=18000$.

Step3: Write the function

Substitute $k = 18000$ into $y=\frac{k}{x}$, the function is $y=\frac{18000}{x}$.

Answer:

$y = 18000/x$