Use the given information to find the unknown value.
$y$ varies directly as the cube of $x$. When $x=4$, then $y=5$. Find $y$ when $x=5$
Enter the exact answer.

Answer

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Answer

$\boxed{y = 9.765625}$

Steps

Step 1 ：Given that $y$ varies directly as the cube of $x$, we can write the equation as $y = kx^3$

Step 2 ：Using the given values, when $x=4$, $y=5$, we can find the constant $k$

Step 3 ：Substitute the values into the equation: $5 = k(4^3)$

Step 4 ：Solve for $k$: $k = \frac{5}{4^3} = \frac{5}{64} = 0.078125$

Step 5 ：Now, we need to find the value of $y$ when $x=5$

Step 6 ：Substitute the values of $k$ and $x$ into the equation: $y = 0.078125(5^3)$

Step 7 ：Calculate the value of $y$: $y = 0.078125(125) = 9.765625$

Step 8 ：$\boxed{y = 9.765625}$