Question

If p varies inversely as q^2, and p=4 when q=1/2, find p when q=3/2.

Answer 1

if p varies Inversely as q.2, AND P=4 WHEN q=1\2, find p when q=3\2.

Answer 2

p =
`(4)/(9)`

Explanation:

Given p varies inversely as q² then the equation relating them is

p =
`(k)/(q^2)` ← k is the constant of variation

To find k use the condition p = 4 when q =
`(1)/(2)` , that is

4 =
`(1)/(((1)/(2)) ^(2) )` =
`(1)/((1)/(4) )` ( multiply both sides by
`(1)/(4)` )

1 = k

p =
`(1)/(q^2)` ← equation of variation

When q =
`(3)/(2)` , then

p =
`(1)/(((3)/(2))^2 )` =
`(1)/((9)/(4) )` =
`(4)/(9)`