Answer:
Inverse Variation states that a relationship between two variables x and y, represent an inverse variation if it can be expressed in the form of:
i.e [tex]y \propto \frac{1}{x}[/tex] or [tex]y = \frac{k}{x}[/tex] ; where k is the constant of variation.
In the given problem :
[tex]P=\frac{8.31}{v}[/tex] where v is the volume(liters) and P is the pressure.
We have the value of the constant K
i.e K = 8.31
so, Pv = 8.31 ......[1]
From the given table;
if v = 83.1 liters and P= a ;
Substitute in [1] to solve for a;
[tex]83.1a = 8.31[/tex]
Simplify:
a = 0.1 kilopascals
Similarly,
if v = b liters and P = 0.4 kilopascals
Substitute in [1] to solve for b;
[tex]0.4b = 8.31[/tex]
Simplify:
b = 20.775 liters
and
if v = 415.5 liters and P =c ;
Substitute in [1] to solve for c;
[tex]415.5c = 8.31[/tex]
Simplify:
c = 0.02 kilopascals .
Therefore, value of:
a = 0.1
b = 20.775
c = 0.02
