Question

If Y varies inversely as twice x. When x = 3, y = 6 what is the value of y when x = 9?

Answer 1

`y=2`

Explanation:

If `y` is inversely proportional to `2x`, therefore `2x*y=k` for some constant `k`

When, `x=3`, `y=6`, `:. k=36`

`:. 2xy=36`

When `x=9`, `y=36/(2x)=36/18=2`

`:. y=2` when `x=9`

Answer 2

`y=2`

Explanation:

`"the initial statement is "yprop1/(2x)`

`"to convert to an equation multiply by k the "`
`"constant of variation"`

`rArry=kxx1/(2x)=k/(2x)`

`"to find k use the given condition"`

`"when "x=3, y=6`

`y=k/(2x)rArrk=2xy=2xx3xx6=36`

`"equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(y=36/(2x)=18/x)color(white)(2/2)|)))`

`"when "x=9`

`rArry=18/9=2`