Answer:
Constant of variation is, \(\frac{2}{3}\)
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 \((x+y)^2\)
"Product of z and the square of the sum of x and z" means \(z \times (x+y)^2\)
then; by definition we have;
\(n \propto z \times (x+y)^2\)
our equation will be of the form of:
\(n = k \cdot z(x+y)^2\) ......[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;
\(18= k \cdot 3(2+1)^2\)
Simplify:
\(18= k \cdot 27\)
Divide both sides by 27 we get;
\(k = \frac{18}{27} = \frac{2}{3}\)
therefore, the constant of variation is, \(\frac{2}{3}\)
