SOLUTION: Hi! I have been stuck on a few questions. My math teacher didn't go through enough examples for me to get these type of questions. Find p when q=5.40 and r= 2.84 if p varie

Question 1205031: Hi!
I have been stuck on a few questions. My math teacher didn't go through enough examples for me to get these type of questions.
Find p when q=5.40 and r= 2.84 if p varies directly as the square of p and inversely as the cube of r and p=13.013 when q=4.30 and r=2.95.
thanks in advanced for your help.

Found 2 solutions by mananth, greenestamps:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Find p when q=5.40 and r= 2.84 if p varies directly as the square of p and inversely as the cube of r and p=13.013 when q=4.30 and r=2.95.
There appears to be a typo . error check and repost correctly (as the square of p)?
Find p when q=5.40 and r= 2.84 if p varies directly as the square of q and inversely as the cube of r and p=13.013 when q=4.30 and r=2.95.
Since you corrected the problem in your email here is the solution

First convert the variation into an equation by introducing a constant. We will put k as a constant

p=13.013 when q=4.30 and r=2.95. plug p q,r to find k
13.013 = k*( (4.3)^2/(2.95)^3)
= 18.0678
You know k

Find p when q=5.40 and r= 2.84 and k=18.0678

p= 23
which @greenstamps has already solved after editing your problem

Answer by greenestamps(13195) (Show Source): You can put this solution on YOUR website!

Obviously there is a typo -- p can't vary directly as the square of p.

Equally obviously, as the problem is presented, the intent is that p varies directly as the square of q.

Given that, here is my choice of how to solve this kind of problem.

p varies directly as the square of q. In the given scenario, q=4.30, and in the new scenario q=5.40. Since p varies as the square of q, this increase in the value of q causes the value of p to increase by a factor of (5.40/4.30)^2.

p varies inversely as the cube of r. In the given scenario, r=2.95, and in the new scenario r=2.84. Since p varies inversely as the cube of r, this decrease in the value of r causes the value of p to increase by a factor of (2.95/2.84)^3.

Find the new value of p by multiplying the value of r in the given scenario by these two factors.

which evaluates to 23, correct to 3 decimal places.

ANSWER: 23

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