Answer:
The constant of variation is [tex]\frac{2}{3}[/tex].
Step-by-step explanation:
Given : The quantity n varies jointly with the product of z and the square of the sum of x and y When n is 18, x = 2, y = 1, and z = 3.
To find : What is the constant of variation?
Solution :
The quantity n varies jointly with the product of z and the square of the sum of x and y,
i.e. [tex]n\propto z(x+y)^2[/tex]
[tex]n=k\times z(x+y)^2[/tex]
Where, k is the constant of variation.
Substitute n=18, x = 2, y = 1, and z = 3,
[tex]18=k\times 3(2+1)^2\\\\18=k\times 3(3)^2\\\\18=k\times 3\times 9\\\\18=27k\\\\k=\frac{18}{27}\\\\k=\frac{2}{3}[/tex]
Therefore, the constant of variation is [tex]\frac{2}{3}[/tex].
