Given:
The variable y varies directly as x and inversely as z. When x = 4 and z= 14, y=2.
To find:
The combined variation equation and find y when x = 6 and z= 3.
Solution:
The variable y varies directly as x and inversely as z.
[tex]y\propto \dfrac{x}{z}[/tex]
[tex]y=k\dfrac{x}{z}[/tex] ...(i)
Where, k is the constant of proportionality.
Putting x=4, y=2 and z=14, we get
[tex]2=k\dfrac{4}{14}[/tex]
[tex]2=k\dfrac{2}{7}[/tex]
[tex]2\times \dfrac{7}{2}=k\dfrac{2}{7}\times \dfrac{7}{2}[/tex]
[tex]7=k[/tex]
Putting k=7 in (i), we get
[tex]y=7\dfrac{x}{z}[/tex]
Putting x=6 and z=3, we get
[tex]y=7\times \dfrac{6}{3}[/tex]
[tex]y=7\times 2[/tex]
[tex]y=14[/tex]
Therefore, the required equation is [tex]y=7\dfrac{x}{z}[/tex] and the value of y is 14 when x = 6 and z= 3.
