Question

It is given that p is inversely proportional to 4/4r ​ and p=8 when r=1296. what is the value of p when r=4096?

Answer 1

When
`\( r = 4096 \),` the value of
`\( p \)` is approximately
`\( 25.28 \)`, derived from the inverse proportionality
`\( p \)` inversely proportional to
`\( (4)/(4r) \)`, given
`\( p = 8 \)` when
`\( r = 1296 \)`.

Given
`\( p \)` is inversely proportional to
`\( (4)/(4r) \)` and when
`\( p = 8 \)` when
`\( r = 1296 \)`:

Let's find the constant of proportionality:

When
`\( p = 8 \)` and
`\( r = 1296 \)`:

`\( p * (4)/(4r) = k \)`

`\( 8 * (4)/(4 * 1296) = k \)`

`\( (32)/(5184) = k \)`

`\( k = (1)/(162) \)`

Now that we have the constant of proportionality
`\( k \)`, we can use it to find the value of
`\( p \)` when
`\( r = 4096 \):`

When
`\( r = 4096 \)`:

`\( p * (4)/(4r) = (1)/(162) \)`

`\( p * (4)/(4 * 4096) = (1)/(162) \)`

`\( p * (1)/(4096) = (1)/(162) \)`

`\( p = (1)/(162) * 4096 \)`

`\( p = 25.28 \)`

Therefore, when
`\( r = 4096 \),` the value of
`\( p \)` is approximately
`\( 25.28 \)`.