15. [0/0.43 Points] DETAILS PREVIOUS ANSWERS LARPCALCCC3 4.1.502.XP. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A sprinkler on a golf green is set to spray water over a distance of 20 meters and to rotate through an angle of 160°. Draw a diagram that shows the region that can be irrigated with the sprinkler. Find the area of the region. (Round your answer to two decimal places.) x m? 558.73
Optimization
Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.
Integration
Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.
Application of Integration
In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.
Volume
In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).
Area
Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.
![**Problem Statement:**
A sprinkler on a golf green is set to spray water over a distance of 20 meters and to rotate through an angle of 160°. Draw a diagram that shows the region that can be irrigated with the sprinkler. Find the area of the region. (Round your answer to two decimal places.)
**Details:**
- Distance: 20 meters
- Angle: 160°
**Solution:**
1. **Concept:**
The sprinkler's area of irrigation is a sector of a circle with a radius of 20 meters and a central angle of 160°.
2. **Calculation:**
The formula for the area \( A \) of a sector with radius \( r \) and angle \( \theta \) in degrees is:
\[
A = \frac{\theta}{360} \times \pi r^2
\]
3. **Substitute the values:**
\[
A = \frac{160}{360} \times \pi \times 20^2
\]
\[
A = \frac{4}{9} \times \pi \times 400
\]
\[
A \approx 558.83 \, \text{m}^2
\]
The answer provided in the image incorrectly shows 558.73 m², marked with an error. The correct rounded area to two decimal places is 558.83 m².
**Visual Representation:**
- The diagram would generally show a circle with radius 20 meters, with a shaded sector representing the 160° angle.
- The center of the circle is the location of the sprinkler, and the radius lines mark the boundary of the irrigated region.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F397ac19d-419d-47a7-b806-aa011335da74%2F38cac4a8-4da0-4e61-8cbc-d91c6c10b1ea%2Fki49rqq_processed.jpeg&w=3840&q=75)
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