Question

Question #91fad

Answer 1

`y≈2.9" to 1 decimal place"`

Explanation:

When dealing with `color(blue)"inverse proportion"` we know that the relationship involves `color(blue)(1/("quantity"))`

`"the square of x means "x^2`

`rArryprop1/(x^2)`

To convert into an equation, we require to introduce k ,
`color(blue)"the constant of proportion"`

`rArry=kxx1/x^2`

`rArry=k/x^2to(1)`

To find k, use the given values of x and y.

`"That is "y=7.5" when "x=2.6`

`"From "(1):k=yx^2larr" cross-multiplying"`

`rArrk=7.5xx(2.6)^2=50.7`

`"We can now express "(1)" as "y=50.7/x^2`

`x=4.2toy=50.7/(4.2)^2`

`rArry=2.9" to 1 decimal place"`