Question

Write an equation describing the relationship of the given variables

Answer 1

`\begin{gathered} y=k\cdot(x^2z^2)/(√(w)√(t)) \\ \text{when, x=}2\text{,z=3,w=16,t=}3\text{ the value of y is 1} \\ 1=k\cdot((2)^2(3)^2)/(√(16)√(3)) \\ 1=k\cdot((4)(9))/((4)(√(3))) \\ 1=k\cdot(9)/(√(3)) \\ \text{Solving k} \\ k=(√(3))/(9) \\ \text{Hence } \\ y=(\frac{\sqrt[]{3}}{9})\cdot\frac{x^2z^2}{\sqrt[]{w}\sqrt[]{t}} \\ y=\text{?, when x=}3\text{,z=}2\text{,w=}36\text{, t=1} \\ y=(\frac{\sqrt[]{3}}{9})\cdot(((3)^2(2)^2)/(√(36)√(1))) \\ y=(\frac{\sqrt[]{3}}{9})\cdot(\frac{(9)^{}(4)^{}}{(6)(1)}) \\ y=(\frac{\sqrt[]{3}}{9})\cdot((36)/(6)) \\ y=(\frac{\sqrt[]{3}}{9})\cdot(6) \\ y=(6√(3))/(9) \\ y=\frac{2\sqrt[]{3}}{3} \\ \text{The value of y is }\frac{2\sqrt[]{3}}{3}\approx1.1547 \end{gathered}`