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Marathon |
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The slope of a line gives a measure of its steepness. The steepness of a road or highway is determined by finding its gradient, or grade. We use the same ratio, rise/run, to find the slope and the gradient. But slopes are usually given as a fraction or a decimal, while gradients are expressed as percentages. Also, gradients are often given as nonnegative numbers and described as “uphill” or “downhill” rather than as a signed (positive or negative) number.
A highway climbs from 3000 feet in elevation to 5000 feet in elevation over 10 miles. What is the slope of the highway? What is its gradient? To find the slope, first find the rise and run. The run is 10 miles. The rise is 5000 feet – 3000 feet = 2000 feet. Now, check that the rise and run have the same units. Notice that the run is given in miles but the rise is given in feet. To convert 10 miles to feet, multiply by 5280. The run is (10 miles)5280 feet/mile = 52,800 feet. Use the ratio rise/run to find the slope. The slope is 2000/52,800 = 5/132. To find the gradient, convert this fraction to a percent. 5/132 = 0.038 or 3.8%.
Be careful in the problems below to make sure that both numerator and denominator are in the same units — feet, meters, etc., depending on the problem. |
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Internet Activity |
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Activity 3.4
Click this link to view your assignment for this activity.
http://go.hrw.com/resources/go_mt/e1/c3/EMARA.PDF |
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Adobe Acrobat Reader
You will need Adobe Acrobat Reader to open and print the activity. To download the reader, click "Adobe Acrobat Reader" above.
http://www.adobe.com/products/acrobat/readstep.html |
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Exploration |
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The Boston Marathon
This site provides information about the Boston Marathon, an example of athletic courage and physical endurance.
http://www.baa.org/BostonMarathon/Default.asp |
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The Boston Marathon – Interactive Map
If you have time and your system has the necessary plug-in feature, use this interactive map to read the brief descriptions of the course.
http://www.townonline.com/marathon/flash/index.html |
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Bike Grades in the Bay Area
This site for bicyclists in the San Francisco Bay Area lists several dozen popular bicycling routes. Gradiometer graphs supplement the data.
http://www-graphics.stanford.edu/~lucasp/bike-grade.html |
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