SOLUTION: Thank you in advance for your help! The question is: Suppose z varies directly as x and inversely as the square of y. If z= 1/4 when x =6 and y =8, find z when x =9 and y =2.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Thank you in advance for your help! The question is: Suppose z varies directly as x and inversely as the square of y. If z= 1/4 when x =6 and y =8, find z when x =9 and y =2.      Log On


   

Question 12122: Thank you in advance for your help! The question is: Suppose z varies directly as x and inversely as the square of y. If z= 1/4 when x =6 and y =8, find z when x =9 and y =2.
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
z is proportional to %28x%2Fy%5E2%29

so, the equivalent equation is z+=+k%28x%2Fy%5E2%29, where k is the constant of proportionality.

we need to know the value of k. To do this, we need to know x,y and z, which we do... so:

1%2F4+=+%286k%29%2F8%5E2
1%2F4+=+%286k%29%2F64
--> 6k = 64/4
--> 6k = 16
--> k = 16/6
--> k = 8/3

so, the equation is z+=+%288x%29%2F%283y%5E2%29

Right, now for the question to find z when x=9 and y=2.

z+=+%288x%29%2F%283y%5E2%29
--> z+=+%288%2A9%29%2F%283%2A2%5E2%29
--> z+=+%288%2A9%29%2F%283%2A4%29 and now simplify these fractions to give...
--> z+=+%282%2A3%29%2F%281%2A1%29
--> z = 6

jon.