Question

When a tire is inflated, the air pressure is inversely proportional to the volume of the air. If the pressure of a certain tire is 27 psi when the volume is 120 cu in., what is the pressure when the volume is 130 cu in.?When the volume is 130 cu in., the pressure is__(Round to the nearest tenth as needed.)

Answer 1

When the volume is 130 cu​ in., the pressure is 24.9 psi.

Explanation:

Given that the air pressure (p) is inversely proportional to the volume(v) of the air.

The equation of proportionalty is :

`\begin{gathered} p=(k)/(v) \\ k=constant\;of\;proportionality \end{gathered}`

When p=27 psi, v=120 cu​ in.

`\begin{gathered} 27=(k)/(120) \\ k=27*120 \\ k=3240 \end{gathered}`

The equation connecting p and v is:

`p=(3240)/(v)`

When the volume, v = 130 cu​ in.

`\begin{gathered} p=(3240)/(130) \\ =24.9231 \\ \approx24.9\;psi \end{gathered}`

When the volume is 130 cu​ in., the pressure is approximately 24.9 psi (rounded to the nearest tenth).