Question

Assume varies inversely with . Find the constant of proportionality and the function.

1. = 8 when = 5
2. = 3 when = 11
3. = 50 when = 100

Answer 1

`k = 40` and
`y = (40)/(x)`

`k = 33` and
`y = (33)/(x)`

`k = 5000` and
`y = (5000)/(x)`

Explanation:

Given

y varies inversely with x.

This is represented as:

`y =(k)/(x)`

Where k is the constant of proportionality.

(a):
`y = 8\ when\ x= 5`

This gives:

`8 =(k)/(5)`

`k = 8 * 5`

`k = 40` -- the constant of proportionality.

To calculate the function, substitute 40 for k in
`y =(k)/(x)`

`y = (40)/(x)`

`(b): y= 3\ when\ x = 11`

This gives:

`3 =(k)/(11)`

`k = 3 * 11`

`k = 33` -- the constant of proportionality.

To calculate the function, substitute 33 for k in
`y =(k)/(x)`

`y = (33)/(x)`

`(c): y= 50\ when\ x = 100`

This gives:

`50 =(k)/(100)`

`k = 50 * 100`

`k = 5000` -- the constant of proportionality.

To calculate the function, substitute 5000 for k in
`y =(k)/(x)`

`y = (5000)/(x)`