SOLUTION: P varies jointly as T and the square of​ Q, and P=16 when T=17 and Q=4. Find P when T=2 and Q=8

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Question 1102923: P varies jointly as T and the square of​ Q, and P=16 when T=17 and Q=4. Find P when T=2 and Q=8
Answer by greenestamps(13206) About Me  (Show Source):
You can put this solution on YOUR website!


The described joint variation means
P+=+k%28T%29%28Q%5E2%29
where k is a constant of variation.

One way to find the answer to your problem is to use the given values of P, T, and Q to determine the value of k and then use that value of k with the new values of Q and T to find the new value of P:

16+=+k%2817%29%284%5E2%29
16+=+17k%2816%29
1+=+17k
k+=+1%2F17
Then
P+=+%281%2F17%29%282%29%288%5E2%29+=+128%2F17

Another way to work a problem like this, which I like to at least try to use, is to just consider how each changed "input" value changes the "output" value.

In this problem, the value of T changes from 17 to 2; since the value of P varies directly with T, the value of P gets multiplied by 2/17.
And in this problem the value of Q changes from 4 to 8, so it is doubled. Since P varies directly as the square of Q, the value of P gets multiplied by 4.

All together, the original P value of 16 gets multiplied by (2/17) and by 4, giving the new P value as 16%2A%282%2F17%29%2A4+=+128%2F17.


You should try to learn both methods; for different problems, depending on the given numbers, one or the other of the two methods might be the easier one to use.