Question

x ∝ 1/√y and when x = 40 then y = 16. If x = 10, find y.

Answer 1

Hi,

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Answer: y = 256
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Solution:

$x \: \: \alpha \: \frac{1}{ \sqrt{y} } \\ \\ x = \frac{c}{ \sqrt{y} } \\ \\ c = x \sqrt{y} \\ \\ c = 40 \sqrt{16} \\ \\ c = 40 \times 4 \\ \\ c = 160$

Now , x = 10

since the value of proportionality constant will

be fixed,so c = 140

y = ?
$\sqrt{y} = \frac{c}{x} \\ \\ \sqrt{y} = \frac{160}{10} \\ \\ \sqrt{y} = 16 \\ \\ y = {(16)}^{2} \\ \\ y = 256$
hope it helps you.

Answer 2

It is given that ,

x directly proportional to 1/√y

=> x√y = c [ constant ] -----( 1 )

i ) if x = 40 , y = 16 ,

c = 40× √16

=> c = 40× 4

c = 160 -------------( 2 )

ii ) If x = 10 , y = ?

c = x√y [ from ( 1 ) ]

160 = 10 × √y

=> 160/10 = √y

=> √y = 16

square on both sides of the equation,

( √y )² = 16²

y = 256

Therefore ,

x = 10 , y = 256

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