Respuesta :
The constant of variation is, [tex]\frac{2}{3}[/tex].
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;
n ∝ [tex]z \times (x+y)^{2}[/tex]
our equation will be of the form of:
n = k. z × [tex](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.3(2+1)^{2}[/tex]
Simplify:
18 = k. (27)
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].
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