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Find the value of n, correct to 4 significant figures.​

Find the value of n, correct to 4 significant figures.​-example-1
User Hpaulj
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1 Answer

3 votes

Answer:

6.708

Explanation:

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


  • \implies y\:\alpha \:x^2......(1)

  • Y varies inversely as the square root of z (Given)

  • \implies y\:\alpha\: (1)/(\sqrt z)......(2)

  • Combining (1) & (2), we find:


  • y\:\alpha \:(x^2)/(\sqrt z)


  • \implies y=(kx^2)/(\sqrt z) (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.


  • 2=(k(3)^2)/(\sqrt 4)


  • \implies 2=(k(9))/(2)


  • \implies k =(4)/(9)

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


  • y=(4x^2)/(9\sqrt z) ....(4)

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


  • 5=\frac{4(n)^2}{9\sqrt {16}}


  • \implies 5=(4(n)^2)/(9(4))


  • \implies 5=((n)^2)/(9)


  • \implies 5(9)=(n)^2


  • \implies 45=(n)^2


  • \implies n=√(45)


  • \implies n=6.70820393


  • \implies n\approx 6.708
User Cody Gray
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