Respuesta :
If two quentities (V, P) are very inversely, so
[tex]\begin{gathered} V=\frac{k}{P} \\ OR \\ \frac{V_1}{V_2}=\frac{P_2}{P_1} \end{gathered}[/tex]Where k is the constant of variation, we can get it by using the initial values of V and P
Let us use the second rule
Since V is 248 cubic inches when P is 5 pounds per square inch, then
[tex]\begin{gathered} V_1=248 \\ P_1=5 \end{gathered}[/tex]We need to find V when P = 7 pounds per square inch
[tex]\begin{gathered} V_2=? \\ P_2=7 \end{gathered}[/tex]Let us substitute these values in the second rule
[tex]\frac{248}{V_2}=\frac{7}{5}[/tex]By using cross multiplication
[tex]\begin{gathered} V_2\times7=248\times5 \\ 7V_2=1240 \end{gathered}[/tex]Divide both sides by 7
[tex]\begin{gathered} \frac{V_2}{7}=\frac{1240}{7} \\ V_2=177.142857 \end{gathered}[/tex]Round it to the nearest integer
[tex]V_2=177in^3[/tex]The volume of the gas is 177 cubic inches
