Question 7. On a scale 1 centimeter = 10 kilometers (km) what distance on a map represent 20,000 meters (m) of terrain? Step 1: Convert 10 km into m. 10 km = 10,00&m. Thus 1 cm on the map = 10,000 m of terrain. Step 2: Using ratio 1 cm 10,000 m we can calculate that 20,000 m will be represented by: 20,000 / 10,000 = cm
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.
![**Question 7.** On a scale 1 centimeter = 10 kilometers (km) what distance on a map represents 20,000 meters (m) of terrain?
**Step 1:** Convert 10 km into m. 10 km = 10,000 m. Thus 1 cm on the map = 10,000 m of terrain.
**Step 2:** Using ratio 1 cm = 10,000 m, we can calculate that 20,000 m will be represented by:
\[ \text{20,000 / 10,000 = ______ cm} \]
**Base your answers to the following questions on the topographic map in Figure 17 below. Points A, B, C, D, and X represent locations on the map. Elevations are measured in feet.**
**Figure 17:**
The diagram is a topographic map showing contour lines indicating elevation. Key features include:
- A "Lake" indicated in the northern part of the map.
- A "Fish Creek" flowing eastward.
- Contour lines with values like "800" indicating elevation.
- A labeled area "Rock Mountain" centrally positioned with an "X" marking a specific point.
- Various points labeled A, B, C, D, representing different elevations and locations on the map.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F38bfdb53-f21a-47c3-b185-9f74cf226bef%2Fe90e699a-ab59-4f85-8ef3-905363e0aa4d%2Fnemiej_processed.jpeg&w=3840&q=75)
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