If P varies inversely as the square root of q, where p = 3 and q = 16, find the value of q when p = 4.
Question 1 Report
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.
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