SOLUTION: suppose p varies directly as the square of z and inversely as r. if p=32/3 when z=4 and r=10, find p when z=3 and 3=32 i cannot grasp what the question is wants me to do. it i

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Question 678100: suppose p varies directly as the square of z and inversely as r. if p=32/3 when z=4 and r=10, find p when z=3 and 3=32

i cannot grasp what the question is wants me to do. it is very complicated and i am not sure where to start
Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website!
The statement "p varies directly as the square of z and inversely as r" translates into the equation:

where the "k" is what is called the constant of variation.

This problem, as many variation problems do, gives you the values for all the variables (so you can figure out the value of k. Then it gives you the values of all but one variable and asks you to find the value for the missing variable.

So we start by finding the value for k. We're told that p = 32/3 when z = 4 and r = 10. Substituting these into our equation we get:

Now we solve for k. First we simplify:

Multiplying both sides by 15 (to eliminate the fractions):

Dividing both sides by 18:

Now that we know k our equation is:

And we can use this to find p when z = 3 and (I assume) r = 32:

Simplifying...