Respuesta :

Hrishii

Answer:

6.708

Step-by-step explanation:

  • Y varies directly as the square of x (Given)

  • [tex]\implies y\:\alpha \:x^2[/tex]......(1)

  • Y varies inversely as the square root of z (Given)
  • [tex]\implies y\:\alpha\: \frac{1}{\sqrt z}[/tex]......(2)

  • Combining (1) & (2), we find:

  • [tex]y\:\alpha \:\frac{x^2}{\sqrt z}[/tex]

  • [tex]\implies y=\frac{kx^2}{\sqrt z}[/tex] (Where k is constant of proportionality).....(3)

  • Now, when y = 2, x = 3 and z = 4, we find the value of k i.e. constant.

  • [tex]2=\frac{k(3)^2}{\sqrt 4}[/tex]

  • [tex]\implies 2=\frac{k(9)}{2}[/tex]

  • [tex]\implies k =\frac{4}{9}[/tex]

  • Plugging the value of k in (3), we find:

  • [tex]y=\frac{4x^2}{9\sqrt z}[/tex] ....(4)

  • Next, in equation (4), plug y = 5, x = n and z = 16 and obtain the value of n by solving it.

  • [tex]5=\frac{4(n)^2}{9\sqrt {16}}[/tex]

  • [tex]\implies 5=\frac{4(n)^2}{9(4)}[/tex]

  • [tex]\implies 5=\frac{(n)^2}{9}[/tex]

  • [tex]\implies 5(9)=(n)^2[/tex]

  • [tex]\implies 45=(n)^2[/tex]

  • [tex]\implies n=\sqrt{45}[/tex]

  • [tex]\implies n=6.70820393 [/tex]

  • [tex]\implies n\approx 6.708 [/tex]

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