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Math in the News: 5/15/11


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In this issue of Math in the News we look at the flooding along the Mississippi River. In particular, we look at the flooding in Memphis.

We explore concepts from 3D geometry and algebra.

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Math in the News: 5/15/11

  1. 1. 5/16/11<br />
  2. 2. Flooding<br />3D Geometry<br />Memphis is located right by a bend in the Mississippi River.<br />This satellite photo from Google Maps shows the Mississippi prior to the floods.<br />
  3. 3. Flooding<br />3D Geometry<br />This image shows the extensive flooding that has occurred.<br />Given the two images, how can we estimate the amount of water that makes up this flood?<br />
  4. 4. Flooding<br />3D Geometry<br />In this illustration we see the portion of the Mississippi River that flows past Memphis.<br />
  5. 5. Flooding<br />3D Geometry<br />Think of this portion of the river as a curved rectangular prism, as shown.<br />
  6. 6. Flooding<br />3D Geometry<br />If we “straighten out” this rectangular prism, we get a standard-looking rectangular prism.<br />The volume of a rectangular prism is length • width • height<br />
  7. 7. Flooding<br />3D Geometry<br />But this volume only provides the amount of water when the river isn’t flooding. <br />What we’re interested in is a second rectangular prism that makes up the excess water.<br />
  8. 8. Flooding<br />3D Geometry<br />We can use this diagram to find the volume of flooding for different amounts of water.<br />The Volume is a linear function for different values of x, the height of the flooding, in inches.<br />
  9. 9. Flooding<br />3D Geometry<br />In this graph, the x-values are the inches of flooding occurring, and the y-values are volume of flood water.<br />
  10. 10. Flooding<br />3D Geometry<br />But remember that the river is also flowing at an average speed of 2 mph.<br />This means that every hour another rectangular prism’s worth of water flows through, increasing the amount of flooding.<br />
  11. 11. Flooding<br />A Family of Linear Functions<br />Because a can vary, we get a family of linear functions. In each case the y-value represents the accumulated volume of flooding for the specific number of days. 2335680000000.<br />
  12. 12. Flooding<br />3D Geometry<br />To see how massive the flooding can be. Take V = 24•f1(2)x and evaluate it for x = 20.<br />This would be a situation where 2 inches of flooding occurs for 20 days.<br />Equivalent to the water from 10 New Orleans Super Domes!<br />