Answer:
Joint variation says that:
If x varies jointly with y and z i.e,
[tex]x \propto yz[/tex] then the equation is in the form of
[tex]x = k (yz)[/tex], where, k is the constant of variation.
As per the statement:
if e varies jointly with f and g
then by definition we have;
[tex]e = k \cdot fg[/tex] ......[1]
To solve for k:
When e = 4, f = 2 and g = 8
Substitute these in [1] we have;
[tex]4 = k \cdot 2 \cdot 8[/tex]
⇒[tex]4 = 16k[/tex]
Divide both sides by 16 we have;
[tex]\frac{1}{4} = k[/tex]
or
[tex]k = \frac{1}{4}[/tex]=0.25
Therefore, the constant of variation is, [tex]\frac{1}{4}[/tex] or 0.25.
