Question

Z varies directly as x^2 and inversely as square root of y. If z=24 when x=3 and y=4

find z if x=5 and y=9

Answer 1

Explanation:

z varies directly as x^2 means that

z= x²

and inversely as square root of y further means that

z= x² / √y

If z=24 when x=3 and y=4

z = x² / √y , we established this from the given yet we also have to consider that there will be a constant number involved since 24 ≠3²/√4

24 = some number *(3²/ √4), substitute what we know

24 = some number * 9/2 ,find the constant number that is missing

24 *2 = some number * 9, multiply both sides by 2

some number = (24*2 )/9 , divide both sides by 9

some number = 48 / 9, simplify by 3

some number = 16 / 3

So our formula will be z= (16/3) (x² / √y) = 16x²/ 3√y

find z if x=5 and y=9

z = 16x²/ 3√y

z = (16*5²) / 3√9

z= (16*25)/ 3*3

z = 400/ 9