Question
If p is inversely proportional to the square of q, and p is 21 when q is 12, determine p when q is equal to 6.
Answers
GPT 3.5
If p is inversely proportional to the square of q, we can write this as:
p = k/q^2
where k is a constant of proportionality.
Given that p is 21 when q is 12, we can substitute these values into the equation to solve for k:
21 = k/12^2
21 = k/144
k = 21 * 144
k = 3024
Now that we have found the value of k, we can use this to determine p when q is 6:
p = 3024 / 6^2
p = 3024 / 36
p = 84
Therefore, when q is equal to 6, p is equal to 84.
p = k/q^2
where k is a constant of proportionality.
Given that p is 21 when q is 12, we can substitute these values into the equation to solve for k:
21 = k/12^2
21 = k/144
k = 21 * 144
k = 3024
Now that we have found the value of k, we can use this to determine p when q is 6:
p = 3024 / 6^2
p = 3024 / 36
p = 84
Therefore, when q is equal to 6, p is equal to 84.