Answer: The required constant of variation is 4 and the equation is [tex]y=\dfrac{4xz}{w}.[/tex]
Step-by-step explanation: We are given to find the constant of variation for the following relation and to write an equation for the statement :
y is a joint variation of x and z and varies inversely with w. When x = 3, z = 4, and w = 6, y is equal to 8.
According to the given information, we can write
[tex]y\propto x,~~y\propto z,~~y\propto\dfrac{1}{w}.[/tex]
So, we get
[tex]y\propto\dfrac{xz}{w}\\\\\\\Rightarrow y=k\times\dfrac{xz}{w},~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{where k is the constant of variation}]~~~~~~~~(i)[/tex]
Now, when x = 3, z = 4 and w = 6, then y = 8.
From equation (i), we get
[tex]y=k\times\dfrac{xz}{w}\\\\\\\Rightarrow 8=k\times\dfrac{3\times4}{6}\\\\\\\Rightarrow 8=2k\\\\\Rightarrow k=\dfrac{8}{2}\\\\\Rightarrow k=4.[/tex]
Therefore, the constant of variation is 4 and the equation for the given statement is
[tex]y=4\times\dfrac{xz}{w}\\\\\\\Rightarrow y=\dfrac{4xz}{w}.[/tex]
Thus, the required constant of variation is 4 and the equation is [tex]y=\dfrac{4xz}{w}.[/tex]
