SOLUTION: z varies directly as x^3 and inversely as y^3. If z = 184 when x = 10 and y = 6, find z if x = 9 and y = 3. (Round off your answer to the nearest hundredth.)

Question 1058213: z varies directly as x^3 and inversely as y^3.
If z = 184 when x = 10 and y = 6,
find z if x = 9 and y = 3.
(Round off your answer to the nearest hundredth.)
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!
z varies directly as x^3 and inversely as y^3.
If z = 184 when x = 10 and y = 6,
find z if x = 9 and y = 3.
(Round off your answer to the nearest hundredth.)




Formula:
                       
                       "directly" variable (or product of "jointly" variables)
                         (if no directly or jointly variables, write 1 here)
"Varying" quantity = k�---------------------------------------------------------
                      "inversely" variable (or product of "inversely variables")
                        (If no inversely variable(s), write 1 here)

The "varying" quantity is z.
There is one "directly" variable, x�
There is one "inversely" variable, y�

Substituting
                      x�
               z = k�----
                      y�

Substituting the complete set of data, 
where ALL the variables are given:

z=184, x=10, y=6


                      10�
             184 = k�-----
                      6�

                      1000
             184 = k�-----
                       216

Reduce 1000/216 to 125/27

                      125
             184 = k�-----
                       27

Solve for k. Multiply through by 27

                      
            4968 = k�125
                      
            4968
            ---- = k
             125 
             
                       

Now substitute k = 4968/125 into:

                      x�
               z = k�----
                      y�

which gives:

                   4968  x� 
               z = ----�----
                    125  y�
                      

Now substitute the second set of data,
and solve for the missing letter z

Substitute x=9 and y=3 into

                   4968  x� 
               z = ----�----
                    125  y�

                   4968  9� 
               z = ----�----
                    125  3�

We grab the calculator and get
                           
               z = 1073.088

Round to the nearest hundredth:

               z = 1073.09

Edwin

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