Question

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

Answer 1

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.

• $5=\frac{4(n)^2}{9\sqrt {16}}$

• $\implies 5=\frac{4(n)^2}{9(4)}$

• $\implies 5=\frac{(n)^2}{9}$

• $\implies 5(9)=(n)^2$

• $\implies 45=(n)^2$

• $\implies n=\sqrt{45}$

• $\implies n=6.70820393$

• $\implies n\approx 6.708$