Question

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

Answer 1

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`