Y is inversely proportional to √x . When x = 9, y = c, where c is a constant. When x=25, y = c-16. Show that when x=36, y = 20?

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Y is inversely proportional to √x . When x = 9, y = c, where c is a constant. When x=25, y = c-16. Show that when x=36, y = 20?

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Answer 1 · 2017-12-03T16:14:00

$see explanation$ $"see explanation"$

Explanation:

$the initial statement is y \propto \frac{1}{\sqrt{x}}$ $"the initial statement is "yprop1/sqrtx$

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

$\Rightarrow y = \frac{k}{\sqrt{x}}$ $rArry=k/sqrtx$

$when x = 9, y = c$ $"when "x=9,y=c$

$\Rightarrow k = 3 c$ $rArrk=3c$

$\Rightarrow y = \frac{3 c}{\sqrt{x}} \leftarrow equation of variation$ $rArry=(3c)/sqrtxlarrcolor(blue)"equation of variation"$

$when x = 25, y = c - 16$ $"when "x=25,y=c-16$

$\Rightarrow c - 16 = \frac{3 c}{5}$ $rArrc-16=(3c)/5$

$multiply through by 5$ $"multiply through by 5"$

$\Rightarrow 5 c - 80 = 3 c$ $rArr5c-80=3c$

$\Rightarrow 5 c - 3 c = 80$ $rArr5c-3c=80$

$\Rightarrow 2 c = 80 \Rightarrow c = 40$ $rArr2c=80rArrc=40$

$when x = 36$ $"when "x=36$

$y = \frac{3 \times 40}{6} = \frac{120}{6} = 20$ $y=(3xx40)/6=120/6=20$

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Y is inversely proportional to √x . When x = 9, y = c, where c is a constant. When x=25, y = c-16. Show that when x=36, y = 20?

1 Answer

Explanation:

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