Question

1. z varies directly with x and inversely with ( y^2 ).

when ( x = 2 ) and ( y = 5 ), ( z = 8 ).

what is the value of ( z ) when ( x = 4 ) and ( y = 9 )?

( \bigcirc ) 80

( \bigcirc ) ( \frac{2025}{4} )

( \bigcirc ) ( \frac{400}{81} )

( \bigcirc ) ( \frac{80}{9} )

Explanation:

Step1: Write variation formula

$z = k \cdot \frac{x}{y^2}$

Step2: Calculate constant k

$8 = k \cdot \frac{2}{5^2} \implies 8 = k \cdot \frac{2}{25} \implies k = 8 \cdot \frac{25}{2} = 100$

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

$z = 100 \cdot \frac{4}{9^2} = 100 \cdot \frac{4}{81} = \frac{400}{81}$

Answer:

$\frac{400}{81}$