Suppose that z varies jointly as u and v and inversely as w, and that z=.8 and when u=8, v=6, w=5. How do you find z when u=3, v=10 and w=5?

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Suppose that z varies jointly as u and v and inversely as w, and that z=.8 and when u=8, v=6, w=5. How do you find z when u=3, v=10 and w=5?

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Answer 1 · 2017-09-26T18:50:23

$z = \frac{4}{5}$ $z=4/5$

Explanation:

$the initial statement is z \propto \frac{u v}{w}$ $"the initial statement is "zprop(uv)/w$

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

$\Rightarrow z = \frac{k u v}{w}$ $rArrz=(kuv)/w$

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

$z = 0.8 when u = 8, v = 6, w = 5$ $z=0.8" when "u=8,v=6,w=5$

$z = \frac{k u v}{w}$ $z=(kuv)/w$

$\Rightarrow k = \frac{w z}{u v} = \frac{5 \times 0.8}{3 \times 10} = \frac{0.8}{6} = \frac{8}{60} = \frac{2}{15}$ $rArrk=(wz)/(uv)=(5xx0.8)/(3xx10)=0.8/6=8/60=2/15$

$"equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(z=(2uv)/(15w))color(white)(2/2)|)))$

$"when "u=3,v=10" and "w=5$

$rArrz=(2xx3xx10)/(15xx5)=60/75=4/5$

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Suppose that z varies jointly as u and v and inversely as w, and that z=.8 and when u=8, v=6, w=5. How do you find z when u=3, v=10 and w=5?

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Explanation:

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