Question

Yis inversely proportional to the square of x.

A table of values for x and y is shown.

a) Express y in terms of x.
b) Work out the positive value of x when y = 25

Answer 1

(a)
`y = (4)/(x^2)`

(b)
`x = (2)/(5)`

Explanation:

Given

Variation: Inverse proportional.

This is represented as:

`y\ \alpha\ (1)/(x^2)`

See attachment for table

Solving (a):

First convert variation to equation

`y = k(1)/(x^2)`

From the table:

`(x,y) = (1,4)`

So, we have:

`4 = k * (1)/(1^2)`

`4 = k * (1)/(1)`

`4 = k * 1`

`4 = k`

`k = 4`

Substitute 4 for k in
`y = k(1)/(x^2)`

`y = 4 * (1)/(x^2)`

`y = (4)/(x^2)`

Solving (b): x when y = 25.

Substitute 25 for y in
`y = (4)/(x^2)`

`25 = (4)/(x^2)`

Cross Multiply

`25 * x^2 = 4`

Divide through by 25

`x^2 = (4)/(25)`

Take positive square roots of both sides

`x = \sqrt{(4)/(25)`

`x = (2)/(5)`