The quantity z varies directly with w^2 and inversely with x and y When w=4, x=12, and y= - 2, z= - 8. What is z when w= - 4, x= - 2, and y=12.

Question

it asks about the variations of direct and inverse.  

Answer 1

z = kw²/(xy)

 

Since z = -8 when w = 4, x = 12, and y = -2

 

So, -8 = k(4)² / [(12)(-2)]

 

      - 8 = 16k / (-24)

 

       192 = 16k

 

          k = 12

 

z = 12w² / (xy)

 

When w = -4, x = -2, and y = 12, z = 12(-4)² / [(-2)(-4)]

 

                                                     = 192 / 8 = 24