Question

modeling real life the entrance of a tunnel can be modeled by $y = -\frac{11}{50}(x - 4)(x - 24)$, where $x$ and $y$ are measured in feet. the $x$-axis represents the ground. find the width of the tunnel at ground level.

Explanation:

Step1: Find x-intercepts (y=0)

Set \( y = 0 \), so \( 0 = -\frac{11}{50}(x - 4)(x - 24) \).
Since the product is zero, \( x - 4 = 0 \) or \( x - 24 = 0 \).
Thus, \( x = 4 \) or \( x = 24 \).

Step2: Calculate width (difference of x-intercepts)

Width = \( 24 - 4 = 20 \).

Answer:

20