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Home » Average speed: \(\frac2507 \approx 35.71\) mph - Silent Sales Machine

Average speed: \(\frac2507 \approx 35.71\) mph - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 A cartographer is calculating the gradient of a mountain trail that rises from 850 meters to 2,150 meters over a horizontal distance of 12.5 kilometers. What is the percent grade of the trail?

📌 Elevation gain = 2,150 − 850 = <<2150-850=1300>>1,300 meters.

📌 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?

📌 Actual distance = 420 km = 420,000 meters.

📌 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?

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