Answer:
z=12
Step-by-step explanation:
It is given that x varies jointly as y and z, it means
[tex]x\propto yz[/tex]
[tex]x=kyz[/tex]
[tex]x(y,z)=kyz[/tex]
where, k is the constant of proportionality.
It is given that x=8 when y=4 and z=9
[tex](8)=k(4)(9)[/tex]
[tex]8=36k[/tex]
Divide both sides by 36.
[tex]\frac{8}{36}=k[/tex]
[tex]\frac{2}{9}=k[/tex]
The value of k is 2/9.
[tex]x=\frac{2}{9}yz[/tex]
We need to find the value of z when x=16 and y=6.
Substitute x=16 and y=6 in the above equation.
[tex]16=\frac{2}{9}(6)z[/tex]
[tex]16=\frac{4}{3}z[/tex]
Multiply both sides by 3.
[tex]48=4z[/tex]
Divide both sides by 4.
[tex]12=z[/tex]
Therefore, the value of z is 12.
