Answer: [tex]y=15.75[/tex]
Step-by-step explanation:
If y varies is jointly with [tex]x^{2}[/tex] and inversely as [tex]\sqrt[3]{z}[/tex], then you can write the following expression, where k is the constant of proportionality:
[tex]y=k*\frac{x^{2}}{\sqrt[3]{z}}[/tex]
If y=84, x=6 and z=27, you can find the constant of proportionality:
[tex]k=y\frac{\sqrt[3]{z}}{x^{2}}[/tex]
[tex]k=84\frac{\sqrt[3]{27}}{6^{2}}[/tex]
[tex]k=7[/tex]
Then, when x=3 and z=64 y is:
[tex]y=7(\frac{3^{2}}{\sqrt[3]{64}})[/tex]
[tex]y=\frac{63}{4}[/tex]
[tex]y=15.75[/tex]
