Z is jointly proportional to x^2 and y^2 . If z = 48 when x= 7 and y = 3 , find z when x= 6 and y = 8

Question

What is z

Answer 1

Pretty much what Ishwar has is correct except the minor arithmetic issue there.

 

So k=16/147

 

so we get z=(16/147)(6)²(8)², So z=250.7755102040816326530612244898

Answer 2

Hello Javriel

 

Since z is jointly proportional to x² and y², you set up the equation as follows:

 

z = kx²y², "k" is a constant

 

Since z = 48, and x = 7 and y = 3, first solve for k

 

k = z / (x²y²)  =  48 / (7² x 3²) = 48 / (49 x 9) = 48 / 441 = 0.109

 

Since we now know the value of k, and x = 6, y = 8, we can solve for z

 

z = 0.109 x 6² x 8² = 0.109 x 36 x 84 = 330