Question

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

Answer 1

Answer:

False

Explanation:

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

$y\propto\frac{1}{x^3}$

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

$y=\frac{k}{x^3}$

Now if y = 5 when x = 2, then

$5=\frac{k}{2^3}$$5=\frac{k}{8}$

Multiplying both sides by 8 gives

$5\times8=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.