# 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.

Question
Modeling data distributions
The entrance of a tunnel can be modeled by $$\displaystyle{y}=-{\frac{{{11}}}{{{50}}}}{\left({x}-{4}\right)}{\left({x}-{24}\right)}$$ where x and y are measured in feet. The x-axis represents the ground. Find the width of the tunnel at ground level.

2021-01-29
Calculation:
The given equation $$\displaystyle{y}={\frac{{-{11}}}{{{50}}}}{\left({x}-{4}\right)}{\left({x}-{24}\right)}$$ at x-axis.
$$\displaystyle{y}={0}$$
$$\displaystyle{0}={\frac{{-{11}}}{{{50}}}}{\left({x}-{4}\right)}{\left({x}-{24}\right)}$$
$$\displaystyle{0}={\left({x}-{4}\right)}{\left({x}-{24}\right)}$$
$$\displaystyle{x}-{4}={0}\ \text{of}\ {x}-{24}={0}$$
$$\displaystyle{x}={4}\ \text{or}\ {x}={24}$$
$$\displaystyle{x}={4},{24}$$
Thus, the width of tunnel is $$\displaystyle={24}-{4}={20}.$$

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