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12 votes
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Given that y is inversely proportional to the square of (x+1),

(a) Express y in terms of x and k, where k is a constant.
(b) Given that x=4 when y=2, find an equation connecting y to x.
(c) Hence, find the value of x when y = 4.​

User Fwg
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1 Answer

9 votes
9 votes


\\ \sf\longmapsto y\propto (1)/((x+1)^2)


\\ \sf\longmapsto y=(k)/((x+1)^2)


\\ \sf\longmapsto y=(k)/(x^2+2x+1)

#2

Put x=4


\\ \sf\longmapsto 2=(k)/(x^2+2x+1)


\\ \sf\longmapsto 2x^2+4x+2=k


\\ \sf\longmapsto 2(x^2+2x+1)=k


\\ \sf\longmapsto x^2+2x+1=k

  • Put x=4


\\ \sf\longmapsto 16+8+1=k


\\ \sf\longmapsto k=25

  • Put in equation


\\ \sf\longmapsto y=(25)/(x^2+2x+1)

#3

y=4


\\ \sf\longmapsto x^2+2x+1=(25)/(4)


\\ \sf\longmapsto x^2+2x+1=25/4-1=21/4


\\ \sf\longmapsto x(x+2)=21/4


\\ \sf\longmapsto x=21/4\:or 13/4

User Livia
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