Question

Find the constant of variation for the relation and use it 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.

Answer 1

y = kxz / w where k is constant of variation

Plugging in the given values:-

8 = k*3*4/ 6

48 = 12 k

k = 4

Answer 2

Answer: The required constant of variation is 4 and the equation is
`y=(4xz)/(w).`

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

`y\propto x,~~y\propto z,~~y\propto(1)/(w).`

So, we get

`y\propto(xz)/(w)\\\\\\\Rightarrow y=k*(xz)/(w),~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{where k is the constant of variation}]~~~~~~~~(i)`

Now, when x = 3, z = 4 and w = 6, then y = 8.

From equation (i), we get

`y=k*(xz)/(w)\\\\\\\Rightarrow 8=k*(3*4)/(6)\\\\\\\Rightarrow 8=2k\\\\\Rightarrow k=(8)/(2)\\\\\Rightarrow k=4.`

Therefore, the constant of variation is 4 and the equation for the given statement is

`y=4*(xz)/(w)\\\\\\\Rightarrow y=(4xz)/(w).`

Thus, the required constant of variation is 4 and the equation is
`y=(4xz)/(w).`