Answer:
Step-by-step 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
