Question 9 of 14 , Step 1 of 1 $7 / 14$ Correct If $y$ varies inversely as $x^{3}$ and $y=12$ when $x=4$, find $y$ if $x=6$. (Round off your answer to the nearest hundredth.) Answer How to enter your answer (opens in new window) Keyboard S \[ y= \]

Step 1 ：The problem is asking for the value of y when x=6, given that y varies inversely as x^3 and y=12 when x=4.

Step 2 ：The formula for inverse variation is \(y = k/x^n\), where k is the constant of variation and n is the power of x.

Step 3 ：First, we need to find the value of k when y=12 and x=4. Substituting these values into the formula, we get \(12 = k/4^3\). Solving for k, we find that k = 768.

Step 4 ：Then, we can substitute x=6 into the equation to find the new value of y. Using the formula \(y = k/x^3\) and substituting the values we have, we get \(y = 768/6^3\).

Step 5 ：Solving this equation, we find that y is approximately 3.56.

Step 6 ：Final Answer: The value of \(y\) when \(x=6\) is approximately \(\boxed{3.56}\).