Question 1102923
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The described joint variation means
{{{P = k(T)(Q^2)}}}
where k is a constant of variation.<br>
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:<br>
{{{16 = k(17)(4^2)}}}
{{{16 = 17k(16)}}}
{{{1 = 17k}}}
{{{k = 1/17}}}
Then
{{{P = (1/17)(2)(8^2) = 128/17}}}<br>
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.<br>
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.<br>
All together, the original P value of 16 gets multiplied by (2/17) and by 4, giving the new P value as {{{16*(2/17)*4 = 128/17}}}.
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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.