Final answer:
P is inversely proportional to x, meaning the product of P and x is constant. With P = 9 when x = 4, the constant k is calculated as 36. When x = 12, P is found to be 3.
Step-by-step explanation:
When we say that P is inversely proportional to x, it means that as x increases, P decreases in such a way that the product of P and x is constant. This can be represented by the formula P = k/x, where k is the constant of proportionality. From the information given, P = 9 when x = 4, so we can find the constant k by multiplying these values together: k = P × x = 9 × 4 = 36.
Now, to find P when x = 12, we use the constant k we found: P = k / x = 36 / 12 = 3. Therefore, when x = 12, P equals 3.