Question

Can someone please help answer the questions attached - it's on inverse proportion? :)

Answer 1

see explanation

Explanation:

(a)

given y is inversely proportional to x³ then the equation relating them is

y =
`(k)/(x^3)` ← k is the constant of proportion

to find k use any of the ordered pairs from the table

using (1, 8 ) , then

8 =
`(k)/(1^3)` =
`(k)/(1)` ⇒ k = 8

y =
`(8)/(x^3)` ← equation of proportion

(b)

when y = 64 , then

64 =
`(8)/(x^3)` ( multiply both sides by x³ )

64x³ = 8 ( divide both sides by 64 )

x³ =
`(8)/(64)` =
`(1)/(8)` ( take cube root of both sides )

x =
`\sqrt[3]{(1)/(8) }` =
`(1)/(2)`