Question

1. z varies inversely with x and directly with y. when x = 6 and y = 2, z = 5. what is the value of z when x = 4 and y = 9? options: \\(\frac{135}{4}\\), \\(\frac{5}{27}\\), 60, \\(\frac{20}{9}\\)

Explanation:

Step1: Define variation formula

$z = k\frac{y}{x}$ (k=constant)

Step2: Calculate k

$5 = k\frac{2}{6} \Rightarrow k = 5\times3 = 15$

Step3: Find z at x=4,y=9

$z = 15\times\frac{9}{4} = \frac{135}{4}$

Answer:

$\frac{135}{4}$