if y is directly proportional to X cubed and Y equals 36 when X equals eight find Y if x equals seven

Since \( y \) is directly proportional to \( x^3 \), we can express this relationship as:

\[
y = kx^3
\]

where \( k \) is the constant of proportionality. 

### Step 1: Find the constant \( k \)
We are given that \( y = 36 \) when \( x = 8 \). Substitute these values into the equation:

\[
36 = k(8^3)
\]
\[
36 = k(512)
\]
\[
k = \frac{36}{512}
\]
\[
k = \frac{9}{128}
\]

### Step 2: Use the constant to find \( y \) when \( x = 7 \)
Now, substitute \( x = 7 \) and \( k = \frac{9}{128} \) into the equation \( y = kx^3 \):

\[
y = \frac{9}{128}(7^3)
\]
\[
y = \frac{9}{128}(343)
\]
\[
y = \frac{9 \times 343}{128}
\]
\[
y = \frac{3087}{128}
\]
\[
y \approx 24.12
\]

Thus, when \( x = 7 \), \( y \approx 24.12 \).

Would you like more details on any step, or do you have any questions?

Here are five related questions:
1. How would you solve if \( y \) were inversely proportional to \( x^3 \)?
2. What is the difference between direct and inverse proportionality?
3. How can we verify if a proportional relationship holds between two variables?
4. What happens to \( y \) as \( x \) increases in a direct proportionality to \( x^3 \)?
5. Can proportional relationships be nonlinear?

**Tip**: Always substitute known values into a proportionality equation first to find the constant.

If y is directly proportional to X cubed and Y equals 36 when X equals eight, find Y if X equals seven.

Learn how to solve a problem involving direct proportionality where Y is directly proportional to X cubed. Given Y = 36 when X = 8, find Y when X = 7. This problem is ideal for students in Grades 9-10, covering concepts such as algebra, cubic functions, and direct proportionality.

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