If r varies jointly as p and q and inversely as t, then how do you find an equation for r if r=6 when p=8, q=−3, and t=3?

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If r varies jointly as p and q and inversely as t, then how do you find an equation for r if r=6 when p=8, q=−3, and t=3?

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Answer 1 · 2017-07-30T15:55:18

$r = - \frac{3 p q}{4 t}$ $r=-(3pq)/(4t)$

Explanation:

$the initial statement is r \propto \frac{p q}{t}$ $"the initial statement is "rprop(pq)/t$

$to convert to an equation multiply by k the constant$ $"to convert to an equation multiply by k the constant"$
$of variation$ $"of variation"$

$\Rightarrow r = \frac{k p q}{t}$ $rArrr=(kpq)/t$

$to find k use the given condition$ $"to find k use the given condition"$

$r = 6 when p = 8, q = - 3 and t = 3$ $r=6" when "p=8,q=-3" and "t=3$

$r = \frac{k p q}{t}$ $r=(kpq)/t$

$\Rightarrow k p q = r t \leftarrow cross-multiplying$ $rArrkpq=rtlarrcolor(blue)" cross-multiplying"$

$\Rightarrow k = \frac{r t}{p q} = \frac{6 \times 3}{8 \times - 3} = \frac{18}{- 24} = - \frac{3}{4}$ $rArrk=(rt)/(pq)=(6xx3)/(8xx-3)=18/(-24)=-3/4$

$rArr" equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(r=-(3pq)/(4t)color(white)(2/2)|)))$

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If r varies jointly as p and q and inversely as t, then how do you find an equation for r if r=6 when p=8, q=−3, and t=3?

1 Answer

Explanation:

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