Question

p is directly proportional to the square of q. it is known that p=12 for a certain value of q. find the value of p when q is doubled ​

Answer 1

Answer: p = 48

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Step-by-step explanation:

We're told that "p is directly proportional to the square of q", which means that we have the equation

p = k*q^2

for some constant k

Replace p with 12 because we're also told that p = 12.

So we now have this equation

12 = k*q^2

which is the same as

kq^2 = 12

We'll use this later.

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Let's go back to the original equation. We'll replace q with 2q to represent the value of q doubling

p = k*q^2

p = k*(2q)^2 ... replace q with 2q

p = k*4q^2

p = 4k*q^2

p = 4*(kq^2)

p = 4(12) ...... replace kq^2 with 12

p = 48

Therefore, if q is doubled, then p = 12 quadruples to p = 48.