Question

Y is inversely proportional to the cube of x. If Y = 5 when x = 2, then k = 20.

Answer 1

False

Step-by-step explanation:

Y is inversely proportional to the cube of x. Mathematically, this means

`y\propto(1)/(x^3)`

If we now introduce a proportionality constant k, then we get

`y=(k)/(x^3)`

Now if y = 5 when x = 2, then

`5=(k)/(2^3)`
`5=(k)/(8)`

Multiplying both sides by 8 gives

`5*8=k`
`\boxed{k=40.}`

Hence, the value of k is NOT 20.

Therefore, the statement that "If Y = 5 when x = 2, then k = 20." is false.