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P varies directly with Q and inversely with R. P=9, when Q=3 and R=4. How do you find Q when P=1 and R=1/2?

1 Answer

Jan 7, 2018

$Q = \frac{1}{24}$ $Q=1/24$

Explanation:

If $P$ $P$ varies directly with $Q$ $Q$ and inversely with $R$ $R$ then
$XXX \frac{P \cdot R}{Q} = k$ $color(white)("XXX")(P * R)/Q=k$ for some constant $k$ $k$

If $P = 9, Q = 3, and R = 4$ $P=9, Q=3, and R=4$ then
$XXX \frac{9 \cdot 4}{3} = k xx \to xx k = 12$ $color(white)("XXX")(9 * 4)/3=kcolor(white)("xx")rarrcolor(white)("xx")k=12$

So when $P = 1$ $P=1$ and $R = \frac{1}{2}$ $R=1/2$
$XXX \frac{1 \cdot \frac{1}{2}}{Q} = 12$ $color(white)("XXX")(1 * 1/2)/Q=12$

$XXX \frac{1}{2} = 12 Q$ $color(white)("XXX")1/2=12Q$

$XXX Q = \frac{1}{24}$ $color(white)("XXX")Q=1/24$

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