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- Horizontal distance = 12.5 km = 12,500 meters.
- Percent grade = (rise ÷ run) × 100 = (1,300 ÷ 12,500) × 100 = <<1300/12500*100=10.4>>10.4%.
- A cartographer is projecting a cylindrical map of longitude and latitude using the Mercator projection. If the true width of a region between 0° and 6° east longitude is 420 kilometers, and the map scale at the equator is 1:10,000,000, what is the width of this region on the map in centimeters?
- Scale: 1 cm = 10,000 meters, so map width = 420,000 ÷ 10,000 = <<420000/10000=42>>42 cm.
- A cartographer is calculating the area of a lake using pixel counting from a satellite image with 0.2-meter resolution. The lake covers 25,000 pixels. What is the area of the lake in square kilometers?
- Each pixel is 0.2 meters, so area per pixel = 0.2 × 0.2 = <<0.2*0.2=0.04>>0.04 m².
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