anonymous
  • anonymous
If y varies inversely as a cube of x and y=4 when x=3, what is y when x=2 ?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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SolomonZelman
  • SolomonZelman
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: \(\large\color{#996633}{\displaystyle y= \frac{k}{x^3} }\)
SolomonZelman
  • SolomonZelman
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.
lochana
  • lochana
@SolomonZelman +1 for latex!

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SolomonZelman
  • SolomonZelman
[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.
SolomonZelman
  • SolomonZelman
G☼☼d luck!
anonymous
  • anonymous
You are amazing thank you so much for breaking it down so well!!!

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