IsaianO507532 IsaianO507532
  • 03-11-2022
  • Mathematics
contestada

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

Respuesta :

ZaleahB734043 ZaleahB734043
  • 03-11-2022

Answer:

False

Explanation:

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

[tex]y\propto\frac{1}{x^3}[/tex]

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

[tex]y=\frac{k}{x^3}[/tex]

Now if y = 5 when x = 2, then

[tex]5=\frac{k}{2^3}[/tex][tex]5=\frac{k}{8}[/tex]

Multiplying both sides by 8 gives

[tex]5\times8=k[/tex][tex]\boxed{k=40.}[/tex]

Hence, the value of k is NOT 20.

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

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