Question

If y varies inversely as a cube of x and y=4 when x=3, what is y when x=2 ?

Answer 1

When you say, «y varies inversely as a cube of x», what does that mean?

At first if you said: «y varies as a cube of x»
then, you would get the following variation equation.

\(\large\color{#996633}{\displaystyle y= k\cdot x^3 }\)


But, when you say: «y varies inversely as a cube of x»
then, you get:

\(\large\color{#996633}{\displaystyle y= \frac{k}{x^3} }\)

Answer 2

Now, you now your equation:

\(\large\color{darkgoldenrod}{\displaystyle y= \frac{k}{x^3} }\)

And you are given that y=4, when x=3.
Plug that in:

\(\large\color{darkgoldenrod}{\displaystyle 4= \frac{k}{3^3} }\)

and solve for k.

Answer 3

@SolomonZelman +1 for latex!

Answer 4

[1]

Then, after you have found what \(\large\color{black}{k }\) is equal to,
you need to re-write your \(\large\color{black}{\displaystyle y= k/x^3 }\)
equation, BUT now instead of writing \(\large\color{black}{\displaystyle k }\), put in
the value for \(\large\color{black}{\displaystyle k }\) that you have found.

(BASICALLY, PLUG THE SOLUTION FOR K INTO THE VARIATION)


[2]

Then, you need to do the last thing:
Find the value of y, when x=2.
Plug in x=2, (the value of k you already have substituted),
and solve for y.

Answer 5

G☼☼d luck!

Answer 6

You are amazing thank you so much for breaking it down so well!!!