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29 January, 23:12

West of a city, a certain eastbound route is straight and makes a steep descent toward the city. The highway has a 14% grade, which means that its slope is - 14 100. Driving on this road, you notice from elevation signs that you have descended a distance of 1000 ft. What is the change in your horizontal distance in miles

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  1. 29 January, 23:29
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    1.35 miles

    Explanation:

    Since the slope is 14% grade = - 14/100. This is a negative slope.

    The distance of 1000 ft descended is a vertical descent, so assuming our initial position is 0, and Δx is the change in horizontal distance.

    tanθ = - 14/100 = (0 - 1000) / Δx = - 1000) / Δx

    -14/100 = - 1000) / Δx

    Δx = - 1000 * - 100/14 = 7142.86 ft

    5280 ft = 1 mile

    7142.86 ft = 7142.86/5280 miles = 1.353 miles ≅ 1.35 miles
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