Question

p= kq^3. when p= 9 , q= 3 a) calculate the value of k b) calculate p when q= 6 c) calculate p when q= 1 d) calculate q when p= 576

Answer 1

see explanation

Explanation:

Given

p = kq³

(a)

To find k use the condition when p = 9, q = 3, that is

9 = k × 3³ = 27k ( divide both sides by 27 )

k =
`(9)/(27)` =
`(1)/(3)`

p =
`(1)/(3)` q³ ← equation of variation

(b)

When q = 6, then

p =
`(1)/(3)` × 6³ =
`(1)/(3)` × 216 = 72

(c)

When q = 1, then

p =
`(1)/(3)` × 1³ =
`(1)/(3)`

(d)

When p = 576 , then

576 =
`(1)/(3)` q³ ( multiply both sides by 3 )

1728 = q³ ( take the cube root of both sides )

q =
`\sqrt[3]{1728}` = 12