Explanation:
To find the constant of variation in this problem, we can set up an equation using the given information.
The problem states that the quantity n varies jointly with the product of z and the square of the sum of x and y. Mathematically, we can express this relationship as:
n = k * z * (x + y)^2
where k is the constant of variation that we need to find.
Given the specific values of x = 2, y = 1, z = 3, and n = 18, we can substitute these values into the equation and solve for k.
18 = k * 3 * (2 + 1)^2
Simplifying further:
18 = k * 3 * 3^2
18 = 9k * 3
18 = 27k
To find k, divide both sides of the equation by 27:
k = 18 / 27
k = 2/3
Therefore, the constant of variation is 2/3.