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Strategic Mine Placement: Solving Graphical Equations for Naval Warfare

Dive into a tactical exercise where you will graphically determine and mathematically verify optimal mine placements to sink enemy ships while keeping track of friendly vessel routes. You'll explore linear equations, specifically graphing lines using intercepts and the slope-intercept form. Engage with enemy paths, obeying course restrictions, and solve equations to find the perfect coordinates for mine deployment. Enhance your strategic skills while immersed in a naval warfare scenario!

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Strategic Mine Placement: Solving Graphical Equations for Naval Warfare

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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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