The DW Math Thread

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  • Sirrobert - Dreamweaver
    Sirrobert - Dreamweaver Posts: 3,395 Arc User
    edited October 2012
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    Yea, but I suck at refining.
    I'm VERY happy if I get stuf to +5 already
    9 out of 10 voices in my head say I'm not crazy... the 10th is singing the music of tetris
  • truekossy
    truekossy Posts: 7,021 Arc User
    edited October 2012
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    S> Refining luck. PM offers.
  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited October 2012
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    Sirrobert - Dreamweaver wrote: »
    Yea, but I suck at refining.
    I'm VERY happy if I get stuf to +5 already
    truekossy wrote: »
    S> Refining luck. PM offers.

    Guys, don't spam in my thread. I don't give a **** if the stupid QQ thread gets closed, but this one is quite dear to me.

    Thanks b:cute
    Proving that not only archers do math since 2009. b:victory
    Current math challenge: pwi-forum.perfectworld.com/showthread.php?t=1029711&page=45
    [SIGPIC][/SIGPIC]
    "Any skills that can be used to kill you will interrupt BB when successful." -truekossy | "...Sage archers are kind of like Mac owners. They are proud of the weirdest and most unnecessary things." -Aesthor | "We ALL know Jesus doesn't play PWI. He may have suffered a lot for humanity, but he'd NEVER punish himself this way." -Abstractive | "I approve of bananas." -SashaGray
  • truekossy
    truekossy Posts: 7,021 Arc User
    edited October 2012
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    Only for you.


    You should totally get a problem that's overly complex and full of useless information that has a solution so blindingly simple most wouldn't even consider it sometime. It'd be pretty amusing.
  • Mooooooooo - Lost City
    Mooooooooo - Lost City Posts: 377 Arc User
    edited October 2012
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    truekossy wrote: »
    Only for you.


    You should totally get a problem that's overly complex and full of useless information that has a solution so blindingly simple most wouldn't even consider it sometime. It'd be pretty amusing.

    what is a cow + a duck?
    youtube channel: youtube.com/user/chezedude
  • FayHumming - Dreamweaver
    FayHumming - Dreamweaver Posts: 325 Arc User
    edited October 2012
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    Mooooooooo - Lost City wrote: »
    what is a cow + a duck?

    b:chuckle pillow
    the survival of the fittest

    -Thx all suport sell me SoW for 5M b:thanks tome/ring
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  • truekossy
    truekossy Posts: 7,021 Arc User
    edited October 2012
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    Mooooooooo - Lost City wrote: »
    what is a cow + a duck?

    Dinner. b:chuckle
  • Mooooooooo - Lost City
    Mooooooooo - Lost City Posts: 377 Arc User
    edited October 2012
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    more meth.
    youtube channel: youtube.com/user/chezedude
  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited October 2012
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    Mooooooooo - Lost City wrote: »
    more meth.

    >.>

    I should make these harder.



    一

    Given that cos 36 = (1/4) + (1/4) * sqrt(5), show that (tan^2 18)(tan^2 54) is rational. (EDIT: Forgot to mention that, even though it's sort of obvious, this is all in degrees.)

    二

    A particle moves in a vertical plane from rest under the influence of gravity and a force perpendicular to and proportional to its velocity. Obtain the equation of the trajectory, and identify the curve.

    三

    The shorter leg of an integer-sided right triangle has length 2001. How short can the other leg be?
    Proving that not only archers do math since 2009. b:victory
    Current math challenge: pwi-forum.perfectworld.com/showthread.php?t=1029711&page=45
    [SIGPIC][/SIGPIC]
    "Any skills that can be used to kill you will interrupt BB when successful." -truekossy | "...Sage archers are kind of like Mac owners. They are proud of the weirdest and most unnecessary things." -Aesthor | "We ALL know Jesus doesn't play PWI. He may have suffered a lot for humanity, but he'd NEVER punish himself this way." -Abstractive | "I approve of bananas." -SashaGray
  • Mooooooooo - Lost City
    Mooooooooo - Lost City Posts: 377 Arc User
    edited October 2012
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    Decus - Dreamweaver wrote: »
    三

    The shorter leg of an integer-sided right triangle has length 2001. How short can the other leg be?

    thez harder b:shocked

    maybe 468.

    on

    二. what do you mean moving in a vertical plane. liek gravity is only vertical?
    youtube channel: youtube.com/user/chezedude
  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited November 2012
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    Mooooooooo - Lost City wrote: »
    what do you mean moving in a vertical plane. liek gravity is only vertical?

    Ah sorry I didn't get to this sooner. You are correct. The vector for gravity is only along the yz or xz planes.
    Proving that not only archers do math since 2009. b:victory
    Current math challenge: pwi-forum.perfectworld.com/showthread.php?t=1029711&page=45
    [SIGPIC][/SIGPIC]
    "Any skills that can be used to kill you will interrupt BB when successful." -truekossy | "...Sage archers are kind of like Mac owners. They are proud of the weirdest and most unnecessary things." -Aesthor | "We ALL know Jesus doesn't play PWI. He may have suffered a lot for humanity, but he'd NEVER punish himself this way." -Abstractive | "I approve of bananas." -SashaGray
  • Xenesis - Lost City
    Xenesis - Lost City Posts: 84 Arc User
    edited November 2012
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    Anyone can help me with this , f polinomial function in two variable X,Y , deg f =3 , from r^2 -->r , show that E:= [ (x,y) : F(x,y) is not 0 , so (x,y) is not a root , is not a conected space ] i think it has to do with the analytical propieties , and continues of polinomails in X,Y

    Sorry for my english , i study in italian xD and tried to translate as i can
  • deadwieght
    deadwieght Posts: 69 Arc User
    edited November 2012
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    Decus - Dreamweaver wrote: »
    Ah sorry I didn't get to this sooner. You are correct. The vector for gravity is only along the yz or xz planes.

    theoretical phsyics...how cute. gravity is never along a straight plane, never will be, never has been and cant be. gravity, in fact, is the most misunderstood force we think we understand. using our current and accepted formulas gravity is always a curve and a never a constant because depending on where in you are it changes ;)
  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited November 2012
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    deadwieght wrote: »
    theoretical phsyics...how cute. gravity is never along a straight plane, never will be, never has been and cant be. gravity, in fact, is the most misunderstood force we think we understand. using our current and accepted formulas gravity is always a curve and a never a constant because depending on where in you are it changes ;)

    And zombies don't exist either, but I am guessing you didn't read that since you didn't seem to get the point of the thread. If you aren't going to contribute, then feel free to use the door. b:bye
    Proving that not only archers do math since 2009. b:victory
    Current math challenge: pwi-forum.perfectworld.com/showthread.php?t=1029711&page=45
    [SIGPIC][/SIGPIC]
    "Any skills that can be used to kill you will interrupt BB when successful." -truekossy | "...Sage archers are kind of like Mac owners. They are proud of the weirdest and most unnecessary things." -Aesthor | "We ALL know Jesus doesn't play PWI. He may have suffered a lot for humanity, but he'd NEVER punish himself this way." -Abstractive | "I approve of bananas." -SashaGray
  • ovenusarmanio
    ovenusarmanio Posts: 6,695 Community Moderator
    edited November 2012
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    truekossy wrote: »
    This necro is totally legit and should not be closed.

    Stickies can't be necroed. b:cute

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  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited November 2012
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    oVenusArmanio wrote: »
    Stickies can't be necroed. b:cute

    Oh gosh! Thanks Venus, I am so flattered!! What a lovely holiday gift b:cute
    Proving that not only archers do math since 2009. b:victory
    Current math challenge: pwi-forum.perfectworld.com/showthread.php?t=1029711&page=45
    [SIGPIC][/SIGPIC]
    "Any skills that can be used to kill you will interrupt BB when successful." -truekossy | "...Sage archers are kind of like Mac owners. They are proud of the weirdest and most unnecessary things." -Aesthor | "We ALL know Jesus doesn't play PWI. He may have suffered a lot for humanity, but he'd NEVER punish himself this way." -Abstractive | "I approve of bananas." -SashaGray
  • Q____Q - Dreamweaver
    Q____Q - Dreamweaver Posts: 812 Arc User
    edited November 2012
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    Decus - Dreamweaver wrote: »
    Oh gosh! Thanks Venus, I am so flattered!! What a lovely holiday gift b:cute

    grats dec \o/ :(















    christmas isn't for another month D:
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  • Darkette - Sanctuary
    Darkette - Sanctuary Posts: 148 Arc User
    edited December 2012
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    Decus - Dreamweaver wrote: »

    The shorter leg of an integer-sided right triangle has length 2001. How short can the other leg be?

    2668 (unknown leg) and 3335 (hypotenuse)


    Let integer sides = a, b, and h; let a = 2001; therefore, 2001 = a < b < h

    Assumption: Pythagorean Triple (3,4,5); so a^2 + b^2 = h^2

    Thus, using Euclid's Algorythm [gcd(a, b) = gcd(a, b - a) where b > a]; gcd = 667

    More simply: 2001/3 = 667; 667 x 4 = 2668; and 667 x 5 = 3335

    Therefore: b = 2668 and h = 3335

    Test: 2001, 2668, 3335 is right-angled and is Pythagorean = 667 x [3, 4, 5]


    I apologize for the clipped notation; I did this on an Excel spreadsheet; and, alas, I was but a poor History major. To be honest, I have a proclivity to view strings of numbers within the context of Fibonacci sequences (1,1,2,3,5,8 etc), or primes, and I write Haiku; so, my first instinct was to view 2001 and look for prime divisors. Three (3) became immediately apparent, and that caused me to think of the Pythagorean triplet -- 3,4,5. In essence, I solved the problem in under 30 seconds. The real problem was proving it; which, for an arithmatically handicapped being like me, was the real challenge.

    Coincidentally, the relationship between Fibonacci numbers, right triangles, and Pythagorean triplets is also fascinating, but it was ultimately beyond my limited capacity to prove my results using Fibonacci, though I still think this is likely the most elegant solution to your problem.
    [SIGPIC][/SIGPIC]
  • Darkette - Sanctuary
    Darkette - Sanctuary Posts: 148 Arc User
    edited December 2012
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    Decus - Dreamweaver wrote: »

    A particle moves in a vertical plane from rest under the influence of gravity and a force perpendicular to and proportional to its velocity. Obtain the equation of the trajectory, and identify the curve.

    Well, this one stumped me ... I certainly couldn't work it out on a spreadsheet LOL

    However, I have done some reading on the Coriolis effect (mostly history of research leading thereto) and I THINK I've been able to deduce the curve is a cycloid (radius g/w^2). Beyond that, I'm lost in the weeds. I'll keep nibbling at it as time permits, but I don't see a solution to this one until I've done a bit more reading. Damned, I hate admitting defeat.
    [SIGPIC][/SIGPIC]
  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited December 2012
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    Darkette - Sanctuary wrote: »
    2668 (unknown leg) and 3335 (hypotenuse)

    Excellently done! You're right in that identifying it as a 3-4-5 (*667) triangle doesn't prove anything definitive about the shortest possible side. I am not really interested in elegant solutions, as you can tell if you read farther back in the thread. I've accepted some thoroughly inelegant solutions (particularly the brute force ones, but I blame my poor selections for that)! Still, you did a nice job and I am quite happy at a new active member in the thread. Should give cheze and fiz a run for their money.
    Darkette - Sanctuary wrote: »
    ...the curve is a cycloid (radius g/w^2)...

    I don't want to say if it's right or wrong, because I don't like being given an answer right away when I am working on a problem... :3 But, I will say this! It would help to think in terms of time derivatives and to see if you can put together a set of differential equations.




    As an unrelated aside: I get complaints about the ease of problems so I provide harder ones, and then no one does them! Also, I make it a point to provide at least one 'easy' problem for a reason! ;-;

    Also, Yorkin, way to not take advantage of the physics problem I provided just for you!!! >:(
    Proving that not only archers do math since 2009. b:victory
    Current math challenge: pwi-forum.perfectworld.com/showthread.php?t=1029711&page=45
    [SIGPIC][/SIGPIC]
    "Any skills that can be used to kill you will interrupt BB when successful." -truekossy | "...Sage archers are kind of like Mac owners. They are proud of the weirdest and most unnecessary things." -Aesthor | "We ALL know Jesus doesn't play PWI. He may have suffered a lot for humanity, but he'd NEVER punish himself this way." -Abstractive | "I approve of bananas." -SashaGray
  • truekossy
    truekossy Posts: 7,021 Arc User
    edited December 2012
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    You could always ask 5th grade math questions for everyone who vanishes when it's difficult! b:cute

    Congrats on the sticky!
  • Darkette - Sanctuary
    Darkette - Sanctuary Posts: 148 Arc User
    edited December 2012
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    Decus - Dreamweaver wrote: »
    I am not really interested in elegant solutions, ...(

    Had you seen my initial response, before I edited it several times, you would have seen a most inelegant solution. In high school I was selected as a semi finalist in a national math competition. My Trig teacher disqualified me because my solutions were completely unorthodox AND brutish. That accomplished two things: (1) a lifelong fear of math, and (2) a continual pursuit of the elegant solution.

    During college I took a basic Art course, and when it came to perspective and distance, I found it a good deal simpler to convert by way of percentages, as opposed to the common practice of drawing endless horizon lines. My professor, who'd taught the course forever, had never seen such a thing.

    When I still could, I used to sew occasionally and often found various equations handy, for instance, turning to Pythagoras when calculating needed yard goods. Also, I used to enjoy orienteering very much and Pythagoras became a constant friend when calculating distances on gridded maps.

    Still fearful of mathmatics, but I do try to overcome it by way of everyday applications. Thank you for providing these problems.

    I'm afraid I have to disqualify myself from the particle-vector problem. In researching, I stumbled across the source of your question and saw the equations you are seeking. b:cry
    [SIGPIC][/SIGPIC]
  • FayHumming - Dreamweaver
    FayHumming - Dreamweaver Posts: 325 Arc User
    edited December 2012
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    b:chuckle 1 + 1 =
    the survival of the fittest

    -Thx all suport sell me SoW for 5M b:thanks tome/ring
    !!!SUPPORT OUR TROOPS!!!
  • Mooooooooo - Lost City
    Mooooooooo - Lost City Posts: 377 Arc User
    edited December 2012
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    FayHumming - Dreamweaver wrote: »
    b:chuckle 1 + 1 =

    potato
    youtube channel: youtube.com/user/chezedude
  • FayHumming - Dreamweaver
    FayHumming - Dreamweaver Posts: 325 Arc User
    edited December 2012
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    Mooooooooo - Lost City wrote: »
    potato

    tomato
    the survival of the fittest

    -Thx all suport sell me SoW for 5M b:thanks tome/ring
    !!!SUPPORT OUR TROOPS!!!
  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited December 2012
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    Oops. Mis-posted.
    Proving that not only archers do math since 2009. b:victory
    Current math challenge: pwi-forum.perfectworld.com/showthread.php?t=1029711&page=45
    [SIGPIC][/SIGPIC]
    "Any skills that can be used to kill you will interrupt BB when successful." -truekossy | "...Sage archers are kind of like Mac owners. They are proud of the weirdest and most unnecessary things." -Aesthor | "We ALL know Jesus doesn't play PWI. He may have suffered a lot for humanity, but he'd NEVER punish himself this way." -Abstractive | "I approve of bananas." -SashaGray
  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited December 2012
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    Bah I have a weird character somewhere that the forum keeps eating...
    Proving that not only archers do math since 2009. b:victory
    Current math challenge: pwi-forum.perfectworld.com/showthread.php?t=1029711&page=45
    [SIGPIC][/SIGPIC]
    "Any skills that can be used to kill you will interrupt BB when successful." -truekossy | "...Sage archers are kind of like Mac owners. They are proud of the weirdest and most unnecessary things." -Aesthor | "We ALL know Jesus doesn't play PWI. He may have suffered a lot for humanity, but he'd NEVER punish himself this way." -Abstractive | "I approve of bananas." -SashaGray
  • Nariin - Dreamweaver
    Nariin - Dreamweaver Posts: 890 Arc User
    edited December 2012
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    *pokes*
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  • _Moua_ - Dreamweaver
    _Moua_ - Dreamweaver Posts: 1 Arc User
    edited December 2012
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    More math /o\
  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited December 2012
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    Alright, since Kossy asked for it, 5th grade math it is! I added an extra coz these are simple. Please don't do all of them, let others have a chance.

    Enjoy:


    I.

    A skilled factory worker can put together a single toy in 20 seconds. A new factory
    worker takes 45 seconds to put together the same toy. After 3 minutes, how many more
    toys does the experienced worker have than the new worker?

    II.

    A group of 48 employees is taking 11 cars to the annual company picnic. If each car
    has either 4 or 5 employees, what is the number of cars carrying 5 employees?

    III.

    1 + 3 = 4
    1 + 3 + 5 = 9
    1 + 3 + 5 + 7 = 16
    1 + 3 + 5 + 7 + 9 = 25

    According to this pattern, how many consecutive odd integers are required to make a sum of 169?

    IV.

    A right triangle has two legs, one measuring 9 inches and one measuring 12 inches. What is the triangle's perimeter?
    Proving that not only archers do math since 2009. b:victory
    Current math challenge: pwi-forum.perfectworld.com/showthread.php?t=1029711&page=45
    [SIGPIC][/SIGPIC]
    "Any skills that can be used to kill you will interrupt BB when successful." -truekossy | "...Sage archers are kind of like Mac owners. They are proud of the weirdest and most unnecessary things." -Aesthor | "We ALL know Jesus doesn't play PWI. He may have suffered a lot for humanity, but he'd NEVER punish himself this way." -Abstractive | "I approve of bananas." -SashaGray
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