Question

1. z varies directly with x and inversely with y. z=6 when x=9 and y=3. find z when x=2 and y=1.\

\
\\(\bigcirc\\) z = 2\
\
\\(\bigcirc\\) z = 4\
\
\\(\bigcirc\\) z = 6\
\
\\(\bigcirc\\) z = 8

Explanation:

Step1: Write combined variation formula

$z = k\frac{x}{y}$ where $k$ is the constant of variation.

Step2: Solve for $k$ using given values

Substitute $z=6$, $x=9$, $y=3$:
$6 = k\frac{9}{3}$
$6 = 3k$
$k = \frac{6}{3} = 2$

Step3: Substitute $k$, $x=2$, $y=1$

$z = 2\times\frac{2}{1}$

Answer:

B. z = 4