5. STORAGE The front of a storage bunker can be modeled by $$ y=-\frac{5}{216}(x-72)(x+72) $$, where $$ x $$ and $$ y $$ are measured in inches. The $$ x $$-axis represents the ground. Find the width of the bunker at ground level. (Section 7.5 )

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To determine the width of the storage bunker at ground level, we analyze the given quadratic equation that models the front of the bunker:

$$
y = -\frac{5}{216}(x - 72)(x + 72)
$$

Here, $$ y $$ represents the height above the ground, and $$ x $$ represents the horizontal position in inches.

**Step 1: Identify Ground Level**
Ground level corresponds to $$ y = 0 $$. Therefore, we set the equation to zero and solve for $$ x $$:

$$
0 = -\frac{5}{216}(x - 72)(x + 72)
$$

**Step 2: Solve for $$ x $$**
The equation will be zero if either factor is zero:

1. $$ x - 72 = 0 $$  →  $$ x = 72 $$ inches
2. $$ x + 72 = 0 $$  →  $$ x = -72 $$ inches

These solutions represent the points where the bunker meets the ground on either side.

**Step 3: Calculate the Width**
The width of the bunker at ground level is the distance between $$ x = -72 $$ inches and $$ x = 72 $$ inches:

$$
\text{Width} = 72 - (-72) = 144 \text{ inches}
$$

**Conclusion:**
The width of the storage bunker at ground level is **144 inches**.
The width of the bunker at ground level is 144 inches.

STORAGE The front of a storage bunker can
be modeled by ,
where and are measured in inches.
The -axis represents the ground. Find
the width of the bunker at ground level.
(Section 7.5 )

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STORAGE The front of a storage bunker can be modeled by , where and are measured in inches. The -axis represents the ground. Find the width of the bunker at ground level. (Section 7.5 )