Question

Write an equation describing the relationship of the given variables. y varies jointly as x and z and inversely as w. When x=5, z=2 and w=20, then y=4. Find y when x=3, z=8 and w=48.The value for y is:Answer

Answer 1

y varies jointly as x and z and inversely as w. will be represented below as

`\begin{gathered} y\propto(xz)/(w) \\ y=(kxz)/(w) \end{gathered}`

When x=5 , z=2 and w =20 then y=4

`\begin{gathered} y=(kxz)/(w) \\ 4=(k*5*2)/(20) \\ 4=(10k)/(20) \\ \text{cross multiply, } \\ 4*20=10k \\ 10k=80 \\ \text{divide both sides by 10} \\ (10k)/(10)=(80)/(10) \\ k=8 \end{gathered}`

The equation connecting x,y,z,w i given below as

`y=(8xz)/(w)`

To figure out the value for y,when x=3,z=8 and w=48

`\begin{gathered} y=(8xz)/(w) \\ y=(8*3*8)/(48) \\ y=(192)/(48) \\ y=4 \end{gathered}`

Hence,

The value of y= 4