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frosja888 [35]
1 year ago
9

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

Mathematics
1 answer:
Law Incorporation [45]1 year ago
7 0

Answer:

6.708

Step-by-step 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\: \frac{1}{\sqrt z}......(2)

  • Combining (1) & (2), we find:

  • y\:\alpha \:\frac{x^2}{\sqrt z}

  • \implies y=\frac{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=\frac{k(3)^2}{\sqrt 4}

  • \implies 2=\frac{k(9)}{2}

  • \implies k =\frac{4}{9}

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

  • y=\frac{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=\frac{4(n)^2}{9(4)}

  • \implies 5=\frac{(n)^2}{9}

  • \implies 5(9)=(n)^2

  • \implies 45=(n)^2

  • \implies n=\sqrt{45}

  • \implies n=6.70820393

  • \implies n\approx 6.708
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