p varies partly as q and partly as the square of r. when p=6, q=8, r=4 and when p=10, q=12, r=5

Answer 1

To find the relationship between p, q, and r, we can set up two proportion equations based on the given information:

First, we know that p varies partly as q, so we can set up the proportion:

p/q = k₁

where k₁ is the constant of proportionality.

Second, we know that p varies partly as the square of r, so we can set up the proportion:

p/r² = k₂

where k₂ is the constant of proportionality.

Using the given values, we can solve for k₁ and k₂:

For the first equation, when p = 6 and q = 8:

6/8 = k₁
3/4 = k₁

For the second equation, when p = 6 and r = 4:

6/4² = k₂
6/16 = k₂
3/8 = k₂

So, we have the equations:

p/q = 3/4
p/r² = 3/8

Now, let's substitute the given values of p, q, and r into these equations to verify the relationship:

For the first given condition:
6/8 = 3/4
0.75 = 0.75 (true)

For the second given condition:
10/12 = 3/4
0.8333 = 0.75 (approx. true)

So, the relationship between p, q, and r is:

p/q = 3/4 and p/r² = 3/8