Write an equation that expresses the relationship. Use k as the constant of variation.
-When the temperature stays the same, the volume of a gas is inversely proportional to the pressure of the gas. If a balloon is filled with 60 cubic inches of a gas at a pressure of 14 pounds per square inch, find the new pressure of the gas if the volume is decreased to 12 cubic inches.
A) 70 pounds per square inch
B) $\frac { 6 } { 7 }$ pounds per square inch
C) 56 pounds per square inch
D) 65 pounds per square inch

Question

Write an equation that expresses the relationship. Use k as the constant of variation.
-When the temperature stays the same, the volume of a gas is inversely proportional to the pressure of the gas. If a balloon is filled with 60 cubic inches of a gas at a pressure of 14 pounds per square inch, find the new pressure of the gas if the volume is decreased to 12 cubic inches. 
A) 70 pounds per square inch
B) $\frac { 6 } { 7 }$ pounds per square inch
C) 56 pounds per square inch
D) 65 pounds per square inch

Quizplus · Accepted Answer

The relationship between volume and pressure in this scenario is given by the equation $V = \frac{k}{P}$, where $V$ is the volume of the gas, $P$ is the pressure, and $k$ is the constant of variation. Given $V = 60$ cubic inches and $P = 14$ pounds per square inch, we can find $k = 60 \times 14 = 840$. When the volume is decreased to 12 cubic inches, the new pressure $P'$ can be found using the equation $12 = \frac{840}{P'}$, solving for $P'$ gives $P' = 70$ pounds per square inch.

Write an Equation That Expresses the Relationship 67\frac { 6 } { 7 }76​

Write an Equation That Expresses the Relationship $\frac { 6 } { 7 }$