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The values of $x$ and $y$ are always positive, and $x^2$ and $y^2$ vary inversely. If $y$ is 10 when $x$ is 2, then find $x$ when $y$ is 4000.

 Feb 20, 2021
 #1
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y^2   =  k  / x^2

 

10^2  = k / 2^2

 

100  =  k   / 4

 

4 * 100   = k =  400  = the proportionality constant

 

So

 

(4000)^2 =   400  /  x^2       rearrange  as

 

x^2  =  400  / ( 4000)^2             take  the  sqrt  of  each side

 

x =    sqrt (400)  /sqrt (4000^2)

 

x =   20  /  4000

 

x  = 2/400

 

x  =  1  / 200

 

 

cool cool cool

 Feb 20, 2021

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