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If q is directly proportional to (p-1)2 and q is 20, p is 3 find values of p when q is 80.

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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:

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