Question

Y varies inversely with x. When y = 0.7, x = 1.8. What is the value of k, the constant of inverse variation? Round to the nearest hundredth, if necessary.

Answer 1

`k=1.26` (nearest to 100th).

Explanation:

Direct proportion is given by: `y prop x`
Inverse proportion is given by `y prop 1/x`

So here we have inverse proportion:

`y= prop 1/x`

`0.7 prop 1/1.8`

Removing the `prop` sign and we get the constant `k`.

`0.7 prop 1/1.8`

`0.7 = k.(1/1.8)`

`0.7 = k/1.8`

`0.7 xx 1.8 = k`

`1.26 = k`

Therefore `k=1.26` (nearest to 100th).

Answer 2

`1.26`

Explanation:

If `y` is inversely proportional to `x`, then we have:

`yprop1/x`

or

`y*x=k`

`=>xy=k`

We got: `x=1.8,y=0.7`

`:.k=1.8*0.7`

`=1.26`