If P varies inversely as the square root of q, where p = 3 and q = 16, find the value of q when p = 4.

Answer Details

The given relationship tells us that P is inversely proportional to the square root of q. This means that as q increases, P decreases, and vice versa. We can write this relationship as: P = k / √q where k is a constant of proportionality. We can solve for k using the initial values of P and q: 3 = k / √16 3 = k / 4 k = 12 Now that we have k, we can use it to find the value of q when P = 4: 4 = 12 / √q 4√q = 12 √q = 3 Squaring both sides, we get: q = 9 Therefore, the value of q when P = 4 is 9.