The widths (in meters) of a kidney-shaped swimming pool were measured at 5-meter intervals as indicated in the figure. Use the Midpoint Rule with n = 4 to estimate the area S of the pool if a1 = 6.2, a2 = 7.2, a3 = 6.8, a4 = 5.6, a5 = 5, a6 = 4.8, and a7 = 4.8. m2 a, a a, a a, a, а,
The widths (in meters) of a kidney-shaped swimming pool were measured at 5-meter intervals as indicated in the figure. Use the Midpoint Rule with n = 4 to estimate the area S of the pool if a1 = 6.2, a2 = 7.2, a3 = 6.8, a4 = 5.6, a5 = 5, a6 = 4.8, and a7 = 4.8. m2 a, a a, a a, a, а,
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Chapter2: Second-order Linear Odes
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![### Estimating the Area of a Kidney-Shaped Swimming Pool
**Formula for Midpoint Rule:**
\[ S \approx \Delta x \left( \frac{f(x_0) + f(x_1)}{2} + \frac{f(x_1) + f(x_2)}{2} + \cdots + \frac{f(x_{n-1}) + f(x_n)}{2} \right) \]
Here is an illustration of the kidney-shaped swimming pool:
The widths (in meters) of a kidney-shaped swimming pool were measured at 5-meter intervals as indicated in the figure. Use the Midpoint Rule with \( n = 4 \) to estimate the area \( S \) of the pool if \( a_1 = 6.2 \), \( a_2 = 7.2 \), \( a_3 = 6.8 \), \( a_4 = 5.6 \), \( a_5 = 5 \), \( a_6 = 4.8 \), and \( a_7 = 4.8 \).
### Explanation of the Diagram:
In the provided diagram, a kidney-shaped swimming pool is shown with vertical measurements taken at 5-meter intervals. The measurements, denoted as \( a_1, a_2, \ldots, a_7 \), are given:
- \( a_1 = 6.2 \)
- \( a_2 = 7.2 \)
- \( a_3 = 6.8 \)
- \( a_4 = 5.6 \)
- \( a_5 = 5 \)
- \( a_6 = 4.8 \)
- \( a_7 = 4.8 \)
To estimate the area \( S \) of the pool, we use the Midpoint Rule with \( n = 4 \).
1. Divide the length of the pool into \( n \) intervals of equal width (in this case, \( \Delta x = 10 \) meters since there are 4 intervals).
2. Use the given widths at these intervals to approximate the area.
### Calculation Using Midpoint Rule:
- Midpoints for width calculation:
- Midpoint between \( a_1 \) and \( a_2 \): \( \frac{6.2 +](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6653f5ea-9ae4-4965-89e5-4546e31fc625%2Fdd435eab-ffba-42ad-815b-ce3bdf5fbf8c%2Ft8ibrnv.png&w=3840&q=75)
Transcribed Image Text:### Estimating the Area of a Kidney-Shaped Swimming Pool
**Formula for Midpoint Rule:**
\[ S \approx \Delta x \left( \frac{f(x_0) + f(x_1)}{2} + \frac{f(x_1) + f(x_2)}{2} + \cdots + \frac{f(x_{n-1}) + f(x_n)}{2} \right) \]
Here is an illustration of the kidney-shaped swimming pool:
The widths (in meters) of a kidney-shaped swimming pool were measured at 5-meter intervals as indicated in the figure. Use the Midpoint Rule with \( n = 4 \) to estimate the area \( S \) of the pool if \( a_1 = 6.2 \), \( a_2 = 7.2 \), \( a_3 = 6.8 \), \( a_4 = 5.6 \), \( a_5 = 5 \), \( a_6 = 4.8 \), and \( a_7 = 4.8 \).
### Explanation of the Diagram:
In the provided diagram, a kidney-shaped swimming pool is shown with vertical measurements taken at 5-meter intervals. The measurements, denoted as \( a_1, a_2, \ldots, a_7 \), are given:
- \( a_1 = 6.2 \)
- \( a_2 = 7.2 \)
- \( a_3 = 6.8 \)
- \( a_4 = 5.6 \)
- \( a_5 = 5 \)
- \( a_6 = 4.8 \)
- \( a_7 = 4.8 \)
To estimate the area \( S \) of the pool, we use the Midpoint Rule with \( n = 4 \).
1. Divide the length of the pool into \( n \) intervals of equal width (in this case, \( \Delta x = 10 \) meters since there are 4 intervals).
2. Use the given widths at these intervals to approximate the area.
### Calculation Using Midpoint Rule:
- Midpoints for width calculation:
- Midpoint between \( a_1 \) and \( a_2 \): \( \frac{6.2 +
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