Melody08
contestada

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.​

Respuesta :

[tex]\\ \sf\longmapsto y\propto \dfrac{1}{(x+1)^2}[/tex]

[tex]\\ \sf\longmapsto y=\dfrac{k}{(x+1)^2}[/tex]

[tex]\\ \sf\longmapsto y=\dfrac{k}{x^2+2x+1}[/tex]

#2

Put x=4

[tex]\\ \sf\longmapsto 2=\dfrac{k}{x^2+2x+1}[/tex]

[tex]\\ \sf\longmapsto 2x^2+4x+2=k[/tex]

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

[tex]\\ \sf\longmapsto x^2+2x+1=k[/tex]

  • Put x=4

[tex]\\ \sf\longmapsto 16+8+1=k[/tex]

[tex]\\ \sf\longmapsto k=25[/tex]

  • Put in equation

[tex]\\ \sf\longmapsto y=\dfrac{25}{x^2+2x+1}[/tex]

#3

y=4

[tex]\\ \sf\longmapsto x^2+2x+1=\dfrac{25}{4}[/tex]

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

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

[tex]\\ \sf\longmapsto x=21/4\:or 13/4[/tex]

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