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# Optimization Problem

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### Optimization Problem

1. 1. Steph Garver Taylor Joyce Madison Klinghoffer Gabe Long Lena Sabih Megan Watson Optimization Problem
2. 2. Problem to Solve <ul><li>Little Tommy Chaney is standing at point (7,0) away from a curving river. The river curves at the rate of y=0.5x ². What is the closest point on the river from where Tommy is standing? </li></ul>
3. 3. 1. Equation <ul><li>y=0.5x ² </li></ul>
4. 4. 2. Graph the Equation Window= [-1,10] by [-1,10]
5. 5. 3. Put Point and Tommy on Graph Window= [-1,10] by [-1,10] Anywhere on line Tommy is at (7,0)
6. 6. 4. Put Triangle on Graph Window= [-1,10] by [-1,10]
7. 7. 5. Label Sides of Triangle Window= [-1,10] by [-1,10] y x 7-x D
8. 8. 6. Solve for D Window= [-1,10] by [-1,10] y x 7-x D Using Pythagorean Theorem… D= y ²+(7-x) ²
9. 9. 7. Put 0.5x ² in for y Window= [-1,10] by [-1,10] y x 7-x D Using Pythagorean Theorem… D= y ²+(7-x) ² D= (0.5x²)²+(7-x)²
10. 10. 8. Put D= (0.5x²)²+(7-x)² in Calculator
11. 11. 9. Find Minimum (2.13,5.37)
12. 12. 10. Go back to original equation to find y <ul><li>Minimum- (2.13,5.37) </li></ul><ul><li>x= 2.13 </li></ul><ul><li>Original Equation- y=0.5 x²… </li></ul><ul><li>y= 0.5(2.13)² </li></ul><ul><li>y= 2.27 </li></ul><ul><li>(2.13, 2.27) </li></ul>
13. 13. 11. State the Final Answer <ul><li>The closest point on the river from where Tommy is standing is (2.13, 2.27) </li></ul>
14. 14. Music from Title Page <ul><li>Teenage Wasteland by the Who </li></ul>