Suppose that y varies directly with x and inversely with z, y=18 when x=15 and z=5. How do you write the equation that models the relationship, then find y when x=21 and z=7?

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Suppose that y varies directly with x and inversely with z, y=18 when x=15 and z=5. How do you write the equation that models the relationship, then find y when x=21 and z=7?

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Answer 1 · 2018-04-01T07:43:24

$y = 18$ $y=18$

Explanation:

$the initial statement is y \propto \frac{x}{z}$ $"the initial statement is "ypropx/z$

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

$\Rightarrow y = k \times \frac{x}{z} = \frac{k x}{z}$ $rArry=kxx x/z=(kx)/z$

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

$y = 18 when x = 15 and z = 5$ $y=18" when "x=15" and "z=5$

$y = \frac{k x}{z} \Rightarrow k = \frac{y z}{x} = \frac{18 \times 5}{15} = 6$ $y=(kx)/zrArrk=(yz)/x=(18xx5)/15=6$

$"equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(y=(6x)/z)color(white)(2/2)|)))$

$"when "x=21" and "z=7" then"$

$y=(6xx21)/7=18$

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Suppose that y varies directly with x and inversely with z, y=18 when x=15 and z=5. How do you write the equation that models the relationship, then find y when x=21 and z=7?

1 Answer

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