Question

1. z varies directly with x and inversely with y.

when x = 6 and y = 2, z = 15.
what is the value of z when x = 4 and y = 9?
○ 45
○ \\(\frac{20}{9}\\)
○ 135
○ \\(\frac{72}{5}\\)

Explanation:

Step1: Write combined variation formula

$z = k \cdot \frac{x}{y}$

Step2: Calculate constant k

$15 = k \cdot \frac{6}{2} \implies 15 = 3k \implies k = 5$

Step3: Find z with new x,y

$z = 5 \cdot \frac{4}{9} = \frac{20}{9}$

Answer:

$\frac{20}{9}$