Question

if p is inversely proportional to the square of q, and p is 9 when q is 5, determine p when q is equal to 3

Answer 1

p is inversely proportional to the square of q. The value of p when q is 3 is 25.

Step-by-step explanation:

When two variables are inversely proportional, their product is constant.

In this case, p is inversely proportional to the square of q. So we can write the equation as: p = k/q², where k is the constant of proportionality.

We are given that when q is 5, p is 9. So we can substitute these values into the equation to find the value of k: 9 = k/5². Solving for k, we get k = 225.

Now we can use this value of k to find p when q is equal to 3: p = 225/3². Simplifying, we get p = 225/9 = 25.

Therefore, when q is equal to 3, p is 25.

Answer 2

Answer: tell me if i am wrong

p = 304

Step-by-step explanation:

Given p is inversely proportional to q² then the equation relating them is

p =
`(k)/(q^(2) )` ← k is the constant of proportion

To find k use the condition p = 19 when q is 8, then

19 =
`(k)/(8^(2) )` =
`(k)/(64)` ( multiply both sides by 64 )

k = 1216

p =
`(1216)/(q^(2) )` ← equation of proportion

When q = 2, then

p =
`(1216)/(2^(2) )`=
`(1216)/(4)`=304