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

Algebra ->  Inverses -> 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      Log On


   

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) About Me  (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

p%28alpha%29+%28q%5E2%2Fr%5E3%29
First convert the variation into an equation by introducing a constant. We will put k as a constant
p=+k%2A++%28q%5E2%2Fr%5E3%29
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)
k+=+%2813.013+%2A%282.95%29%5E3%29%2F%284.3%29%5E2= 18.0678
You know k

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

p=+k%2A++%28q%5E2%2Fr%5E3%29

p=+18.0678%2A++%285.40%5E2%2F2.84%5E3%29
p= 23
which @greenstamps has already solved after editing your problem


















Answer by greenestamps(13195) About Me  (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.

p=%2813.013%29%28%285.40%2F4.30%29%5E2%29%28%282.95%2F2.84%29%5E3%29

which evaluates to 23, correct to 3 decimal places.

ANSWER: 23