Answer:
To solve this problem, we can use the concept of direct proportionality and set up a proportion.
Given that q is directly proportional to (p-1)^2, we can write the equation as:
q = k(p-1)^2
where k is the constant of proportionality.
We are given that q is 20 when p is 3. Plugging these values into the equation, we get:
20 = k(3-1)^2
20 = k(2)^2
20 = 4k
Dividing both sides of the equation by 4, we find:
k = 5
Now we can use this value of k to solve for p when q is 80.
80 = 5(p-1)^2
Dividing both sides of the equation by 5, we get:
16 = (p-1)^2
Taking the square root of both sides, we have:
4 = p-1 or -4 = p-1
Adding 1 to both sides, we find two possible values for p:
p = 5 or p = -3
Therefore, when q is 80, the values of p can be either 5 or -3.
Explanation: