Question

y is directly proportional to x^3. it is known that =5 for a particular value of x. find the value of y when this value of y when this value of x is multplied by 1/2.​

Answer 1

The value of
`y` when the value of
`x` is multiplied by
`(1)/(2)` is
`(5)/(8)`.

Explanation:

According to the statement, we have the following relationship:

`y = k\cdot x^(3)` (1)

Where:

`x` - Independent variable.

`y` - Dependent variable.

`k` - Proportionality constant.

We can eliminate the proportionality constant by constructing the following relationship:

`(y_(2))/(y_(1)) = \left((x_(2))/(x_(1)) \right)^(3)`

If we know that
`y_(1) = y`,
`y_(2) = 5`,
`x_(2) = x_(o)` and
`x_(1) = (1)/(2)\cdot x_(o)`, then the value of
`y` when the value of
`x` is multiplied by
`(1)/(2)` is:

`(5)/(y) = \left((x_(o))/((1)/(2)\cdot x_(o) ) \right)^(3)`

`(5)/(y) = 8`

`y = (5)/(8)`

The value of
`y` when the value of
`x` is multiplied by
`(1)/(2)` is
`(5)/(8)`.