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Sagot :
Here, the pressure the gas exerts varies inversely with the volume.
Where the constant, k = temperature of the gas
Let p represent the pressure the gas exerts
Let v represent the volume.
Since the relationship here is an inverse variation, we have the formula:
[tex]p=\frac{k}{v}[/tex]Given:
v = 76
p = 16
Let's solve for k:
[tex]\begin{gathered} 16=\frac{k}{76} \\ \\ 76\times16=k \\ \\ k=76\times16 \\ \\ k=1216 \end{gathered}[/tex]Now, let's find the volume when the pressure is 64.
Substitute 1216 for k and 64 for p, to find the volume:
[tex]\begin{gathered} p=\frac{k}{v} \\ \\ 64=\frac{1216}{v} \\ \\ v=\frac{1216}{64} \\ \\ v=19in^3 \end{gathered}[/tex]Therefore, when the pressure is 64 pounds per square inch, the volume will be 19 in. cubed.
ANSWER:
[tex]C.19in^3[/tex]
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