Answer:
Step-by-step explanation:
According to the question,
[tex]x[/tex]∝[tex]y^3[/tex] .......(1)
[tex]y[/tex]∝[tex]\sqrt{z}[/tex] .......(2)
From equation 1,2 let constant of proportionality be [tex]k1,k2[/tex] respectively.
⇒[tex]x=k1(y^3)[/tex] .......(3)
⇒[tex]y=k2(\sqrt{z} )[/tex] .......(4)
From the above equations putting 4 into 3,
[tex]x=k1((k2\sqrt{z})^3) =k1.k2^3.(\sqrt{z})^3[/tex]
Let the new constant to the above equation be [tex]k3[/tex],
[tex]x=k3(\sqrt{z})^3[/tex]
Given,if x=1, when z=4
[tex]1=k3(\sqrt{4} )^3=k3(8)[/tex]
⇒[tex]k3=\frac{1}{8}[/tex]
Now if x=27, then z=?
[tex]27=\frac{1}{8} (\sqrt{z} )^3[/tex]
⇒[tex](\sqrt{z} )^3=27(8)[/tex]
⇒[tex]\sqrt{z}=3(2)=6[/tex]
[tex]z=36[/tex]
