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:

$z=\frac{1}{w}$

If we unite these expressions we can get:

$z=\frac{k\cdot xy}{w}$

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:

$2=\frac{k\cdot(6)\cdot(6)}{9}$

Solving for k:

$2\cdot9=k\cdot36$$k=\frac{2\cdot9}{36}=\frac{1}{2}$

Then we can replace k in the expression:

$z=\frac{k\cdot xy}{w}=\frac{1}{2}\cdot\frac{xy}{w}=\frac{xy}{2w}$$z=\frac{xy}{2w}$

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

$z=\frac{2\cdot3}{2\cdot12}$$z=\frac{6}{24}$

Simplifying:

$z=\frac{1}{4}$

Answer:

$z=\frac{1}{4}$