y is varies directly as the square of x and inversely as z. if x is inceased by 10% and z is decreased by 20%, find the percentage change in y.


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Question Number 57284 by Jmasanja last updated on 01/Apr/19

$y i s v a r i e s d i r e c t l y a s t h e s q u a r e o f x a n d$ $i n v e r s e l y a s z .$ $i f x i s i n c e a s e d b y 10 % a n d z i s$ $d e c r e a s e d b y 20 %, f i n d t h e p e r c e n t a g e$ $c h a n g e i n y .$
Commented by mr W last updated on 01/Apr/19

$x_{2} = 1.1 x_{1}$ $z_{2} = 0.8 z_{1}$ $\frac{y_{2}}{y_{1}} = {(\frac{x_{2}}{x_{1}})}^{2} (\frac{z_{1}}{z_{2}}) = 1 . 1^{2} \times \frac{1}{0.8} = 1.5125$ $\Rightarrow y i s i n c r e a s e d b y 51 . 25 % .$
	Answered by tanmay.chaudhury50@gmail.com last updated on 01/Apr/19

	$y \propto x^{2}$ $y \propto \frac{1}{z}$ $c o m b i n i n g$ $y \propto \frac{x^{2}}{z} \to y = k \times \frac{x^{2}}{z}$ $l e t x c h a n g e s f r o m 100 \to 110$ $z c h a n g e s f r o m 100 \to 80$ $y_{1} = \frac{{k x}^{2}}{z}$ $y_{1} = \frac{k \times 100^{2}}{100} s o y_{1} = 100 k$ $n o w y_{2} = \frac{k \times 110^{2}}{80}$ $y_{2} = \frac{k \times 1210}{8}$ $△ y = y_{2} - y_{1} = \frac{1210 k}{8} - \frac{100 k}{1} = \frac{1210 k - 800 k}{8}$ $△ y = \frac{410 k}{8}$ $% i n c r e a s e o f y i s \frac{△ y}{y_{1}} \times 100$ $= \frac{410 k}{8 \times 100 k} \times 100$ $= \frac{410}{8} = 51 . 25 % i n c r e a s e$
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