Question

p varies jointly as q and the square of r, and p = 200 when q = 2 and r = 3. Find p when q = 5 and r= 2.

Answer 1

Step-by-step explanation:

If a variables varies jointly, we can just divide it by the other variables in relation to it.

For example, since p variables jointly as q and square of r, then

$\frac{p}{q {r}^{2} } = k$

where k is a constant

First, let find k. Substitute p= 200

q= 2, and r=3.

$\frac{200}{2(3) {}^{2} } = k$

$\frac{200}{18} = k$

$\frac{100}{9} = k$

Now, since we know our constant, let find p.

$\frac{p}{q {r}^{2} } = \frac{100}{9}$

Q is 5, and r is 2.

$\frac{p}{5( {2}^{2}) } = \frac{100}{9}$

$\frac{p}{20} = \frac{100}{9}$

$p = \frac{2000}{9}$