Question

if p is inversely proportional to the square of q and p is 24 when q is 12 determine p when q equals to 4

Answer 1

To find p when q equals 4, first calculate the constant of proportionality using the given values (p=24, q=12). Then use this constant to calculate p when q=4, resulting in a value of 216 for p.

Step-by-step explanation:

Since p is inversely proportional to the square of q, we can express this relationship with the equation p = k/q^2, where k is the constant of proportionality. Given that p is 24 when q is 12, we first find k by substituting these values into the equation: 24 = k/12^2.

Calculating k, we get:

1. k = 24 × 12^2
2. k = 24 × 144
3. k = 3456

Now, to determine p when q is 4, substitute k and q back into the original proportionality equation:

1. p = 3456/4^2
2. p = 3456/16
3. p = 216

Therefore, when q equals 4, p equals 216.