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 = 18,000/x complete what would the volume of the gas be if the pressure is increased to 40 psi? 450 in.³ complete if the volume of the gas increases from 600 to 800 in.³, by how much does the pressure change? it decreases by 7.5 psi. it decreases by 22.5 psi. it increases by 7.5 psi. it increases by 22.5 psi.
Answer
Explanation:
Step1: Recall inverse - proportion formula
For inverse proportion $y=\frac{k}{x}$, where $y$ is volume, $x$ is pressure and $k$ is a constant. Given $x = 30$ psi and $y=600$ in³, we find $k$ as $k = xy$. So $k=30\times600 = 18000$.
Step2: Find volume when pressure is 40 psi
Substitute $x = 40$ into $y=\frac{18000}{x}$. Then $y=\frac{18000}{40}=450$ in³.
Step3: Find pressure when volume is 800 in³
Substitute $y = 800$ into $y=\frac{18000}{x}$, we get $800=\frac{18000}{x}$, then $x=\frac{18000}{800}=22.5$ psi.
Step4: Calculate pressure change
Initial pressure is 30 psi. New pressure is 22.5 psi. The change in pressure is $30 - 22.5=7.5$ psi, and it decreases.
Answer:
It decreases by 7.5 psi.