Respuesta :
Answer:
Joint variation states:
if y varies jointly with x and z
then the equation we get;
[tex]y = k \cdot xz[/tex]
where, k is the constant of variation.
As per the statement:
If y varies jointly with x and z
Using above definition we have;
⇒[tex]y = k \cdot xz[/tex] ....[1]
y = 200 when x = 8 and z = 10
Substitute these value in [1] to solve for k;
[tex]200 = k \cdot 8 \cdot 10[/tex]
⇒[tex]200 = 80k[/tex]
Divide both sides by 80 we have;
2.5 = k
or
k = 2.5
then we get an equation:
[tex]y=2.5 \cdot xz[/tex]
We have to find x when y = 165 and z = 11.
then;
[tex]165 = 2.5 \cdot x \cdot 11[/tex]
⇒[tex]165 = 27.5x[/tex]
Divide both sides by 27.5 we have;
6 = x
or
x = 6
Therefore, the value of k = 2.5 and value of x is 6 when y = 165 and z = 11.
