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?

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?

Answer

Explanation:

Step1: Recall inverse - proportion formula

The formula for inverse proportion is $y=\frac{k}{x}$, where $k$ is the constant of proportionality.

Step2: Find the value of the constant $k$

We know that when $x = 30$ psi and $y=600$ in³. Substitute these values into $y=\frac{k}{x}$: $600=\frac{k}{30}$. Solving for $k$, we multiply both sides by 30, so $k = 600\times30=18000$.

Step3: Write the function

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

Answer:

$y=\frac{18000}{x}$