Question

If z varies jointly with x and y and inversely as w, and if z = 2 when...

Answer 1

• General joint variation equation:

`z=k\cdot xy`

• Inverse variation:

`z=(1)/(w)`

If we unite these expressions we can get:

`z=(k\cdot xy)/(w)`

The first data is given to calculate the constant of proportionality k, where:

• z = 2

,

• x = 6

,

• y = 6

,

• w = 9

Replacing these values in the expression formed:

`2=(k\cdot(6)\cdot(6))/(9)`

Solving for k:

`2\cdot9=k\cdot36`
`k=(2\cdot9)/(36)=(1)/(2)`

Then we can replace k in the expression:

`z=(k\cdot xy)/(w)=(1)/(2)\cdot(xy)/(w)=(xy)/(2w)`
`z=(xy)/(2w)`

Finally, we can replace the last values given to get z:

`z=(2\cdot3)/(2\cdot12)`
`z=(6)/(24)`

Simplifying:

`z=(1)/(4)`

Answer:

`z=(1)/(4)`