Question

Y varies inversely with the square of x, Given that y= 1/3 when x= -2, how do you express y in terms of x?

Answer 1

`y=4/(3x^2)`

Explanation:

Since `y` varies inversely with the square of `x`, `y prop 1/x^2`, or `y=k/x^2` where `k` is a constant.

Since `y=1/3ifx=-2`, `1/3=k/(-2)^2`. Solving for `k` gives `4/3`.

Thus, we can express `y` in terms of `x` as `y=4/(3x^2)`.

Answer 2

`y=4/(3x^2)`

Explanation:

Inverse means `1/"variable"`

The square of x is expressed as `x^2`

`"Initially " yprop1/x^2`

`rArry=kxx1/x^2=k/x^2` where k is the constant of variation.

To find k use the given condition `y=1/3" when " x=-2`

`y=k/x^2rArrk=yx^2=1/3xx(-2)^2=4/3`

`rArr color(red)(bar(ul(|color(white)(2/2)color(black)(y=4/(3x^2))color(white)(2/2)|)))larr" is the equation"`

Answer 3

`Y = 4/(3 x^2)`

Explanation:

Y varies inversely with square of x means

`Y = k (1/x^2)` where `k` is a constant

plug in `Y = 1/3` and `x = -2` in the above equation.

`1/3 = k (1/(-2)^2)`

`1/3 = k (1/4)`

multiply with `4` to both sides.

`4/3 = k`

therefore,
`Y = 4/3 (1/x^2) = 4/(3 x^2)`