Question

Question #92b07

Answer 1

The required equation that describes the inverse variation is given by: `y = 1.6/x`

Explanation:

It is given that y varies inversely with x .

We are also given that: y equals 0.2 when x = 8.

We must remember that for two quantities with inverse variation, as one quantity increases, the other quantity decreases.

We must determine the equation for the inverse variation .

An inverse variation can be represented by the equation `color(green)(y = k/x)`.

That is, y varies inversely as x if there is some nonzero constant k such that, `x xx y=k or y=k/x` where `x!=0,y!=0`

We can solve Inverse variation problems using the equation `color(green)(y = k/x)`.

We use the information given in the problem to find the value of k .

In our problem, we need to find k when x = 8 and y = 0.2.

`rArr 0.2 = k/8`

We will rewrite the above equation as `rArr 0.2/1 = k/8` to help us with simplification.

When we cross-multiply, we get `k = 8 xx 0.2 = 1.6`

Hence, the required equation that describes the inverse variation is given by:

`color(red)(y = 1.6/x)`

I believe this problem solving process is helpful.

Answer 2

`y=1.6/x`

Explanation:

`"the initial statement is "yprop1/x`

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

`rArry=kxx1/x=k/x`

`"to find k use the given condition"`

`y=0.2" when "x=8`

`y=k/xrArrk=yx=0.2xx8=1.6`

`"equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(y=1.6/x)color(white)(2/2)|)))`