Answer:
Constant of variation is, [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Joint Variation states that it is jointly proportional to a set of variables i.e, it means that z is directly proportional to each variable taken one at a time.
Given the statement: The quantity n varies jointly with the product of z and the square of the sum of x and y.
"The square of sum of x and y" means [tex](x+y)^2[/tex]
"Product of z and the square of the sum of x and z" means [tex]z \times (x+y)^2[/tex]
then; by definition we have;
[tex]n \propto z \times (x+y)^2[/tex]
our equation will be of the form of:
[tex]n = k \cdot z(x+y)^2[/tex] ......[1] ; where k is constant of Variation.
Given: n =18 , x =2 , y= 1 and z = 3
Solve for k;
Substitute these given values in [1] we have;
[tex]18= k \cdot 3(2+1)^2[/tex]
Simplify:
[tex]18= k \cdot 27[/tex]
Divide both sides by 27 we get;
[tex]k = \frac{18}{27} = \frac{2}{3}[/tex]
therefore, the constant of variation is, [tex]\frac{2}{3}[/tex]
