Question

at a set temperature, the volume, v, of a gas varies inversely as the pressure, p, exerted on the gas. if the volume is 1,075 cubic centimeters when the pressure is 55 pascals, find the constant of proportionality. using the numerical constant of proportionality, write the inverse - variation equation represented by this situation. find the pressure if the volume is 1,150 cubic centimeters. provide an answer accurate to the nearest hundredth.

Explanation:

Step1: Recall inverse - variation formula

For inverse variation, $V=\frac{k}{P}$, where $k$ is the constant of proportionality. We can rewrite it as $k = V\times P$.

Step2: Calculate the constant of proportionality

Given $V = 1075$ cubic - centimeters and $P = 55$ pascals. Substitute into $k=V\times P$. So, $k=1075\times55 = 59125$.

Step3: Write the inverse - variation equation

Substitute $k = 59125$ into $V=\frac{k}{P}$, the equation is $V=\frac{59125}{P}$.

Step4: Find the pressure when $V = 1150$

Substitute $V = 1150$ into $V=\frac{59125}{P}$, we get $1150=\frac{59125}{P}$. Cross - multiply: $1150P=59125$. Then $P=\frac{59125}{1150}=51.413\approx51.41$ pascals.

Answer:

Constant of proportionality: $59125$
Inverse - variation equation: $V=\frac{59125}{P}$
Pressure when $V = 1150$: $51.41$ pascals