The problem in the image states:

• $y$ varies directly as the cube of $x$, meaning $y = kx^3$, where $k$ is a constant.
• Given: $y = 17$ when $x = 2$.
• We need to find $y$ when $x = 10$.

Step 1: Find the constant of variation $k$

Using the given values $y = 17$ and $x = 2$:

$y = kx^3$ $17 = k(2^3)$ $17 = k(8)$ $k = \frac{17}{8} = 2.125$

Step 2: Use $k$ to find $y$ when $x = 10$

Now that we know $k = 2.125$, we can find $y$ when $x = 10$:

$y = 2.125 \times (10^3)$ $y = 2.125 \times 1000$ $y = 2125$

Thus, $y = 2125$ when $x = 10$.

Would you like further details or explanations?

Here are some related questions you might explore:

1. What is the formula for direct variation?
2. How is the cube function $x^3$ different from the square function $x^2$?
3. What happens to $y$ if $x$ is doubled in this problem?
4. How does the constant of variation $k$ affect the relationship between $x$ and $y$?
5. Can direct variation also involve fractional powers of $x$?

Tip: When solving direct variation problems, always start by determining the constant of variation $k$ using the initial conditions provided.