If $x$ $x$ varies directly as $y$ $y$ and inversely as $z$ $z$ and when $y = 7$ $y=7$ and $z = 2$ $z=2$ , $x = 14$ $x=14$ , what is $x$ $x$ when $y = 16$ $y=16$ and $z = 4$ $z=4$ ?

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If $x$ $x$ varies directly as $y$ $y$ and inversely as $z$ $z$ and when $y = 7$ $y=7$ and $z = 2$ $z=2$ , $x = 14$ $x=14$ , what is $x$ $x$ when $y = 16$ $y=16$ and $z = 4$ $z=4$ ?

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Answer 1 · 2017-06-14T07:06:44

$x = 16$ $x=16$

Explanation:

$x$ $x$ varies directly as $y$ $y$ and inversely as $z$ $z$ means $x \propto y$ $xpropy$ and $x \propto \frac{1}{z}$ $xprop1/z$ i.e.

$x \propto y \times \frac{1}{z}$ $xpropy xx1/z$

In other words $x = k \times \frac{y}{z}$ $x=kxxy/z$ where $k$ $k$ is a constant

Since when $y = 7$ $y=7$ and $z = 2$ $z=2$ , we have $x = 14$ $x=14$ , we have

$14 = k \times \frac{7}{2}$ $14=kxx7/2$ and $k = 14 \times \frac{2}{7} = 4$ $k=14xx2/7=4$

and hence $x = 4 \frac{y}{z}$ $x=4y/z$

and when $y = 16$ $y=16$ and $z = 4$ $z=4$

$z = 4 \times \frac{16}{4} = 16$ $z=4xx16/4=16$

Answer 2 · 2017-06-14T07:25:39

$x = 16$ $x=16$

Explanation:

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

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

$\Rightarrow x = k \times \frac{y}{z} = \frac{k y}{z}$ $rArrx=kxxy/z=(ky)/z$

$to find k use the condition given for x,y and z$ $"to find k use the condition given for x,y and z"$

$x = 14, y = 7, z = 2$ $x=14,y=7,z=2$

$x = \frac{k y}{z} \Rightarrow k = \frac{x z}{y} = \frac{14 \times 2}{7} = 4$ $x=(ky)/zrArrk=(xz)/y=(14xx2)/7=4$

$rArr"equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(x=(4y)/z)color(white)(2/2)|)))$

$"when " y=16" and " z=4$

$rArrx=(4xx16)/4=16$

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If $x$ $x$ varies directly as $y$ $y$ and inversely as $z$ $z$ and when $y = 7$ $y=7$ and $z = 2$ $z=2$ , $x = 14$ $x=14$ , what is $x$ $x$ when $y = 16$ $y=16$ and $z = 4$ $z=4$ ?

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Explanation:

Explanation:

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If xxx varies directly as yyy and inversely as zzz and when y=7y=7y=7 and z=2z=2z=2, x=14x=14x=14, what is xxx when y=16y=16y=16 and z=4z=4z=4?

2 Answers

Explanation:

Explanation:

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If $x$ $x$ varies directly as $y$ $y$ and inversely as $z$ $z$ and when $y = 7$ $y=7$ and $z = 2$ $z=2$ , $x = 14$ $x=14$ , what is $x$ $x$ when $y = 16$ $y=16$ and $z = 4$ $z=4$ ?