**Question 5**:

It is given that

*R*varies directly as the square root of

*S*and inversely as the square of

*T*. Find the relation between

*R*,

*S*and

*T*.

*Solution:*$$R\text{}\alpha \text{}\frac{\sqrt{S}}{{T}^{2}}$$

**Question 6**:

It is given that

*P*varies directly as the square of*Q*and inversely as the square root of*R*. Given that the constant is*k*, find the relation between*P*,*Q*and*R*.

*Solution:*$$\begin{array}{l}P\text{}\alpha \text{}\frac{{Q}^{2}}{\sqrt{R}}\\ P=\frac{k{Q}^{2}}{\sqrt{R}}\end{array}$$

**Question 7**:

Given that

*P*varies inversely as the cube root of

*Q*. The relationship between

*P*and

*Q*is

*Solution:*$$\begin{array}{l}P\text{}\alpha \text{}\frac{1}{\sqrt[3]{Q}}\\ P\text{}\alpha \text{}\frac{1}{{Q}^{\frac{1}{3}}}\end{array}$$

**Question 8**:

Given that

*y*varies inversely as the cube of

*x*and

*y*= 16 when

*x*= ½. Express

*y*in terms of

*x*.

*Solution:*$$\begin{array}{l}y\text{}\alpha \text{}\frac{1}{{x}^{3}}\\ y=\frac{k}{{x}^{3}}\\ \text{When}y=16,\text{}x=\frac{1}{2}\\ 16=\frac{k}{{\left(\frac{1}{2}\right)}^{3}}\\ 16=\frac{k}{\frac{1}{8}}\\ k=2\\ y=\frac{2}{{x}^{3}}\end{array}$$

**Question 9**:

*W*varies directly with

*X*and inversely with the square root of

*Y*. Given that

*k*is a constant, find the relation between

*W*,

*X*and

*Y*.

*Solution:*$$\begin{array}{l}W\text{}\alpha \text{}\frac{X}{\sqrt{Y}}\\ W\text{=}\frac{kX}{\sqrt{Y}}\\ W\text{=}\frac{kX}{{Y}^{{}^{\frac{1}{2}}}}\end{array}$$