SOLUTION: If y varies directly as x and inversely as z^2, and y = 3 when x = 2 and z = 4, what is the value of x when y = 9 and z = 4?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: If y varies directly as x and inversely as z^2, and y = 3 when x = 2 and z = 4, what is the value of x when y = 9 and z = 4?       Log On


   

Question 93431This question is from textbook
: If y varies directly as x and inversely as z^2, and y = 3 when x = 2
and z = 4, what is the value of x when y = 9 and z = 4? This question is from textbook

Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
'y' varies directly as 'x' and inversely as 'z^2'.
Hence, y+=+k%28x%2Fz%5E2%29 _______ (1)
Now, y = 3 when x = 2 and z = 4,
Substituting the values of 'x', 'y' and 'z' in (1)
3+=+k%282%2F4%5E2%29
3+=+k%2F8
k+=+3x8+=+24

So (1) becomes
y+=+24%28x%2Fz%5E2%29 _____ (2)

Substituting the values of 'y' and 'z' in (2)
9+=+24%28x%2F4%5E2%29
9+=+24x%2F16
3+=+x%2F2
x+=+3%2A2+=+6

The reqd. value of 'x' when y = 9 and z = 4 is 6.