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We are asked to compute the area enclosed by the curves \( f(x) = \sqrt{x + 28} \) and \( g(x) = \frac{1}{22}x + \frac{124}{22} \).

### Steps to solve the problem:

1. **Find the points of intersection**: 
   To compute the area between the curves, we need to determine where the curves intersect by solving \( f(x) = g(x) \).

2. **Set up the integral**: 
   The area is calculated by integrating the difference between the two functions over the interval defined by the intersection points.

Let's start by finding the intersection points between \( f(x) \) and \( g(x) \). We set them equal to each other:

\[
\sqrt{x + 28} = \frac{1}{22}x + \frac{124}{22}
\]

I will calculate this now.The curves \( f(x) = \sqrt{x + 28} \) and \( g(x) = \frac{1}{22}x + \

First, sketch the region enclosed by the curves f(x) = √(x + 28) and g(x) = (1/22)x + 124/22, then compute the area of the region.

This problem guides students through finding the area enclosed by two curves, f(x) = √(x + 28) and g(x) = (1/22)x + 124/22. It requires understanding of integral calculus and applying the area-between-curves formula. Suitable for high school and college-level calculus students.

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