The Quadratic Pirates

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           History of Cannons
-One of the oldest pieces of modern
 technology that is still in use
-Made from various materials such as iron, brass, bronze
 and steel
-Formed as a strong metal tube with a plug at one end and a
 hole at the other




 -Gunpowder along with a cannonball (a round solid missile of
  stone or iron made to be fired from a cannon) are put into the
  cannon
 -An explosion, caused by a lighted fuse, shoots the cannonball
  away from the cannon at high speeds
            History of Pirates
• Piracy dates back to more than 3000 years
• The word “pirate” was first used in about 140 BC
  by the Roman historian Polybius
• The Greek historian Plutarch described pirates as
  “those who attack without legal authority not only
  ships, but also maritime cities.”
• Some other common names for pirates are:
  “Vikings,” “Sea Thieves,” and “Outlaws.”
       History of the Quadratic
• Over 3700 years ago, in Mesopotamia, math exercises
  using quadratic equations were written on cuneiform
  tablets
• The Babylonians (about 400 BC) developed an
  algorithmic approach to solving problems which gave
  rise to a quadratic equation
• 300 BC Euclid developed a geometrical approach that
  later mathematicians used to solve quadratic equations
• Hindu mathematicians took the Babylonian methods
  further and in 598-665 AD, Brahmagupta gave a modern
  method which shows negative quantities
• Today there are many modern applications of quadratic
  equations
       How does the Quadratic relate to
                  real life?
    • Every quadratic function has a U-shaped graph
      called a parabola
    • When an object has little air resistance, its path
      through the air can be approximated by a
      parabola
    • Some real life examples:
        – The path of a homerun baseball
        – The path of cannonball
        – The path above the water of a
          jumping dolphin

                                           camosun.bc.ca/~jbritton/ paraporpoise_lg.GIF

almu.astronet.pl/wiedza/ komety.shtml
    Ways to Solve a Quadratic
            Equation
1. Graphing – solutions are found at the x-
   intercepts (where the graph crosses the x-axis)




               www.colbycc.org/www/math/ algebra/parabola.gif
       Ways to Solve a Quadratic
           Equation (cont)
2. Using the quadratic formula:
   for ax2 + bx + c = 0, solutions are found
   by the formula:

               b  b  4ac        2
            x
                    2a
Try this website where it does the work for you:
          http://www.murderousmaths.co.uk/books/quadcal.htm
Quadratic Pirates Problem

The Quadratic Pirates are at it again!! They have
  tracked down King Pythagoras’ ship with
  intentions of steeling his notes on a possible
  short-cut in finding the length of the sides of a
  right triangle.
       Shipmate Scrim (short for Discriminant) was
          put in charge of setting up the angle of the
          cannon so the cannonball will be a direct
          hit on Pythagorean’s ship. Scrim set’s the
          cannon at 45° giving the path of the
          cannonball a quadratic equation of:
                       y = x2 - 200x
       If Pythagorean’s ship is 100 feet away from
          the Quadratic Pirates, will Shipmate
          Scrim’s calculations ensure a direct hit?

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                 Solution
Using the quadratic formula we find:
 a = 1, b = -200, and c = 0
By plugging these in we get:
        (200)  (200)  4(1)(0)
                           2
     x
                   2(1)
By simplifying we get:
          200  200         200  200
       x           ,    x
              2                 2
              Conclusion
• This leaves us with the roots:
          x = 200 and x = 0
• Since the Quadratic Pirates ship is
  considered to be the 0 feet mark, we
  conclude that the cannon- ball traveled
  200 feet!!!!
• Shipmate Scrim overshot the target by 100
  feet!!
• King Pythagoras makes
  it away safely from those
  Quadratic thieves!!

• Captain Quad became so
  angry about Shipmate Scrim’s
  miscalculations that he forced him to
  walk the plank!!



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                      Works Cited
• Larson, Boswell, Kanold, Stiff, R. (2001). Mcdougal littell algebra 1.
  Evanston, IL: McDougal Littell Inc..
• Wilczyñski, K. History of Piracy. Retrieved Sept. 16, 2003,
  www.piratesinfo.com/
• Piarates of the Caribbean. Retrieved Sept. 16, 2003,
  http://www.ecani.com/vi/pirates.htm
• (2003). Blast From The Past, An American Legend. Retrieved Sept.
  18, 2003, from Conestoga: http://www.bigbangcannons.com/his.htm
• Brain, M. How Flintlock Guns Work. Retrieved Sept. 18, 2003,
  http://science.howstuffworks.com/flintlock1.htm
• The Qudratic Solver. Retrieved Sept. 19, 2003, from Java Script
  Source: The Qudratic Solver
• Cannon Proof. Retrieved Sept. 19 02, 2003,
  http://dictionary.reference.com/search?q=cannon%20proof

				
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