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The problem states that \( y \) is inversely proportional to the square of \( (x + 1) \), and you're given that \( y = 0.875 \) when \( x = 1 \). You are asked to find \( y \) when \( x = 4 \).

### Step 1: Express the relationship
Since \( y \) is inversely proportional to \( (x + 1)^2 \), we can express this relationship as:
\[
y = \frac{k}{(x + 1)^2}
\]
where \( k \) is a constant.

### Step 2: Find the constant \( k \)
You're given that \( y = 0.875 \) when \( x = 1 \). Substituting these values into the equation:
\[
0.875 = \frac{k}{(1 + 1)^2}
\]
\[
0.875 = \frac{k}{4}
\]
Solving for \( k \):
\[
k = 0.875 \times 4 = 3.5
\]

### Step 3: Use \( k \) to find \( y \) when \( x = 4 \)
Now, substitute \( k = 3.5 \) and \( x = 4 \) into the equation:
\[
y = \frac{3.5}{(4 + 1)^2} = \frac{3.5}{5^2} = \frac{3.5}{25}
\]
\[
y = 0.14
\]

Thus, when \( x = 4 \), \( y = 0.14 \).

Would you like further clarification on any of these steps?

Here are 5 related questions for practice:
1. What happens to \( y \) as \( x \) approaches infinity?
2. How would the relationship change if \( y \) were directly proportional to \( (x + 1)^2 \)?
3. What is the value of \( y \) when \( x = 0 \)?
4. If \( y \) is inversely proportional to \( (x + 1)^3 \), how does the equation change?
5. What is the interpretation of the constant \( k \) in this context?

**Tip:** In inverse proportionality problems, as the input (e.g., \( x \)) increases, the output (e.g., \( y \)) decreases at a faster rate if the exponent in the denominator is larger.

y is inversely proportional to the square of (x + 1). y = 0.875 when x = 1. Find y when x = 4.

Learn how to solve the equation where y is inversely proportional to (x+1)^2. The problem involves finding the value of y when x = 4, given that y = 0.875 when x = 1. This solution explains inverse proportionality and algebraic steps in detail, suitable for students in Grades 8-10.

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