Please help! Suppose that \alpha is inversely proportional to \beta. If \alpha=4 when \beta=9, find \alpha when \beta=-72

Question

Please help!

Suppose that
`\alpha` is inversely proportional to
`\beta`. If
`\alpha=4` when
`\beta=9`, find
`\alpha` when
`\beta=-72`

Answer 1

The answer is

`\alpha = - (1)/(2)`

Explanation:

From the question

`\alpha` is inversely proportional to
`\beta` is written as

`\alpha = (k)/( \beta )`

where k is the constant of proportionality

When

`\alpha` = 4

`\beta` = 9

Substituting the values into the formula

we have

`4 = (k)/(9)`

cross multiply

k = 4 × 9

k = 36

So the formula for the variation is

`\alpha = (36)/( \beta ) [/tex</strong>]</p><p></p><p>when </p><p></p><p><strong>[tex]\beta` = - 72

That's

`\alpha = (36)/( - 72)`

Simplify

We have the final answer as

`\alpha = - ( 1)/(2)`

Hope this helps you