Question

If p is inversely proportional to the square of q, and p is 30 when q is 10 determine p when q is equal to 5

Answer 1

The value of p = 120 when q = 5

Explanation:

We know that if y varies inversely with x, we get the equation

y ∝ 1/x

y = k/x

k = yx

where 'k' is called the constant of proportionality.

In our case,

If p is inversely proportional to the square of q, then

p ∝ 1/q²

p = k/q²

k = pq²

As p is 30 when q is 10, so

substituting p = 30 and q = 10

k = (30) (10)²

k = (30)(100)

k = 3000

Now,

Determining the value of p when q = 5

Using the equation

p = k/q²

now substituting k = 3000 and q = 5

p = 3000 / (5)²

p = 3000/25

p = 120

Therefore, the value of p = 120 when q = 5