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Wartime Battle

Wartime Battle. Solving Equations by Graphing. You’re in the Navy NOW. Identify where to place mines to sink enemy ships Know path of our vessel Know path of enemy vessels Determine graphically then mathematically optimal mine locations

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Wartime Battle

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  1. Wartime Battle Solving Equations by Graphing

  2. You’re in the Navy NOW • Identify where to place mines to sink enemy ships • Know path of our vessel • Know path of enemy vessels • Determine graphically then mathematically optimal mine locations • Note: you are not the captain of the vessel and cannot change your course

  3. Review Graphing Lines • 3x + 2y = 12 • Graph using intercepts • X intercept, y=0 • 3x +2(0) = 12 • 3x = 12 • x = 4 • Y intercept, x=0 • 3(0) +2y = 12 • 2y = 12 • y = 6

  4. Review Graphing Lines • 3x + 2y = 12 • Graph using y=mx+b • 3x + 2y = 12 • -3x • 2y = -3x + 12 • Divide by 2 • y= -3/2x + 6 • Y intercept = 6 • Slope = -3/2

  5. Get Started • Graph Battleship Course • Ask for check • Graph Enemy Courses • Calculate point to place mines • Might need to Estimate

  6. Paths Enemy Path 2 Mine # 1,( -7.5, 2.5) Enemy Path 3 Enemy Path 1 Mine # 2,( 0.5, -5.5) Mine # 3,( 4,-9)

  7. Verify Mathematically Battleship Path Enemy Path 3 • x + y = -5 • y = -x – 5 • Estimated point (4, -9) • -9=-(4) – 5 • -9 = -9 • 2x + y = -1 • y = -2x – 1 • Estimated point (4, -9) • -9 = -2(4) – 1 • -9= -8 -1 • -9 = -9

  8. Solve Mathematically Battleship Path Enemy Path 3 • x + y = -5 • y = -x – 5 • 2x + y = -1 • y = -2x – 1 Estimated point (4, -9) • -x – 5 = -2x – 1 • +1 +x • -4 = -x • 4 = x • y = -x – 5 • y = -(4) – 5 • y = -9

  9. Verify Mathematically Battleship Path Enemy Path 1 • x + y = -5 • y = -x – 5 • Estimated point (-7.5, 2.5) • 2.5=-(-7.5) – 5 • 2.5 = 7.5-5 • 2.5=2.5 • x – 3y = -15 • y = 1/3x +5 • Estimated point (-7.5, 2.5) • 2.5 = 1/3(-7.5) +5 • 2.5= -2.5+5 • 2.5=2.5

  10. Solve Mathematically Battleship Path Enemy Path 1 • x + y = -5 • y = -x – 5 • x – 3y = -15 • y = 1/3x +5 Estimated point (-7.5, 2.5) • -x – 5 = 1/3x +5 • -5 +x • -10 = 4/3x • -10(3/4) = x • -7.5 = x • y = -x – 5 • y = -(-7.5) – 5 • y = 7.5-5 • y=2.5

  11. Solve Mathematically Battleship Path Enemy Path 2 • x + y = -5 • y = -x – 5 • 4x – y = 7 • y = 4x – 7 • -x – 5 = 4x – 7 • +7 +x • 2 = 5x • 2/5 = x • 0.4 • y = -(0.4) – 5 • y = -.4 – 5 • y = -5.4 Estimated point (0.4, -5.4)

  12. Verify Mathematically Battleship Path Enemy Path 2 • x + y = -5 • y = -x – 5 • Estimated point (0.4, -5.4) • -5.4 =-(0.4, ) – 5 • -5.4 = -5.4 • 4x – y = 7 • y = 4x – 7 • Estimated point (0.4, -5.4) • -5.4= 4(0.4) – 7 • -5.4 = 1.6 -7 • -5.4 = -5.4

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