Question

Please assist me in understanding how to solve number 4

Answer 1

Given that;

y varies directly with the square of x

`y\propto x^2`

This expression above becomes

`\begin{gathered} y=kx^2 \\ Where\text{ k is the constant} \end{gathered}`

When

`y=10\text{ and x}=5`

Substitute the values for x and y into the expression above to find k

`\begin{gathered} y=kx^2 \\ 10=k(5)^2 \\ 10=k(25) \\ 10=25k \\ Divide\text{ both sides 25} \\ (25k)/(25)=(10)/(25) \\ k=(2)/(5) \end{gathered}`

The expression becomes

`\begin{gathered} y=kx^2 \\ y=(2)/(5)x^2 \end{gathered}`

a) The value of y when x = 20

`\begin{gathered} y=(2)/(5)x^2 \\ y=(2)/(5)(20)^2 \\ y=(2)/(5)(400) \\ y=160 \end{gathered}`

Hence, the value of y is 160

b) The value of x when y = 40

`\begin{gathered} y=(2)/(5)x^2 \\ 40=(2)/(5)x^2 \\ Crossmultiply \\ 40(5)=2x^2 \\ 200=2x^2 \\ Divide\text{ both sides by 2} \\ (200)/(2)=(2x^2)/(2) \\ 100=x^2 \\ x^2=100 \\ Square\text{ root of both sides} \\ √(x^2)=√(100) \\ x=10 \end{gathered}`

Hence, the value of x is 10