Question

The table shows a set of values for x and y

y is inversely proportional to the square x.
a) Find an equation for y in terms of x. (2)
b) Find the positive value of x when y = 25 (2)

Answer 1

see explanation

Explanation:

(a)

given y is inversely proportional to x² then the equation relating them is

y =
`(k)/(x^2)` ← k is the constant of variation

to find k use any ordered pair from the table

using (2, 4 ) , then

4 =
`(k)/(2^2)` =
`(k)/(4)` ( multiply both sides by 4 )

16 = k

y =
`(16)/(x^2)` ← equation of variation

(b)

when y = 25 , that is

25 =
`(16)/(x^2)` ( multiply both sides by x² )

25x² = 16 ( divide both sides by 25 )

x² =
`(16)/(25)` ( take square root of both sides )

x = ±
`\sqrt{(16)/(25) }` = ±
`(4)/(5)`

the positive value of x is then
`(4)/(5)`