Question

How do you write a general formula to describe each variation if y varies inversely with `sqrt x`; y =4 when x=9?

Answer 1

`color(blue)(y = 12/sqrtx)`

Explanation:

In an inverse variation, as one quantity increases, the other decreases: It is shown as `y prop1/x`

However, in this case the inverse variation is with `sqrtx`

`y prop1/sqrtx`

All variations (also called proportions) are connected by a constant,`k`

`:. color(blue)(y = k/sqrtx)" larr` we need to find the value of `k`

`k = yxx sqrtx" "larr` isolate `k` by cross- multiplying

Use the given values for `x and y`

`k= 4 xx sqrt9= 4xx 3 = 12" "` we now know `k`

Replace `k` by `12`

`:. color(blue)(y = 12/sqrtx)`