Monday, November 5, 2012

Fox 353


Tony García‏ from Dominican Republic submitted this one.  It looks like it requires brute force.  Better than being idle I guess!  So enjoy...



The answer is not confirmed yet.

29 comments:

  1. agreed... requires brute force at some point.

    For those interested, exact value for sin(AEF) is ((261 - 19*sqrt(161))*sqrt((
    179745369 + 14093001*sqrt(161))/737237))/1500

    which approximately equals 0.292829, hence answer B.

    A "less brutal" question could have been: what is the value of Determinant(EF,EA)?

    bleaug

    ReplyDelete
    Replies
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      This is a very happy day of my life with the help Dr Larry has rendered to me by helping me to get my divorce husband back with his magic power and love spell. i was married for 8 years and it was so terrible because my husband was really cheating on me, and was seeking for a divorce but when i came across Dr Larry email on the internet on how he help so many people to get their ex back and help fixing relationship and make people to be happy in their relationship. i explained my situation to him and then seek his help but to my greatest surprise he told me that he will help me with my case and here i am now celebrating because my Husband has change totally for good he started begging me to forgive him that he is very sorry for everything, i was really surprised and was also happy, so that was how i forgive him and now we are living together happily than ever before and He always want to be by me and can not do anything without my present. i am really happy with my marriage, what a great celebration. thank you to Dr Larry who helped me a lot, if you need his help you can contact him through email assurancesolutionhome@gmail com Website http://assurancesolutionhome.website2.me/ call or WhatsApp +2348102316854

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    2. for the past two months my wife have been disturbing me with divorce for no reason , she keeps talking about divorcing me i thought it was all a joke until recently she served me a divorce papers it was then i cried out to my friend who refers me to Dr Noble  that the Dr has solutions to every issues relating to divorce and i quickly contacted him and told him what i was passing through , he told me he needed to consult the oracle to know what"s the cause of it which he did and it was revealed that my wife's best friend Anita was responsible as she have been crushing on me for long but i have refused to give her attention so she did a spell on my wife to  hate me and divorce me so she can have me , i begged Dr noble to help me out and he did helped me by reversing the spell placed on wife by her wicked friend and she confess and die with the powerful black magic of Dr noble and my wife became normal and she later withdraw the divorce case and now we are happy together in  love and harmony . thanks Dr noble .you can contact him today for any spell or any solutions via +2349059610643 or email him on peterwiseherbalcenter@gmail.com





















































































































































































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  2. Please, show where the question require "brute force". Sorry, my mother language is Spanish: what do you mean by "brute force"?

    ReplyDelete
  3. use of less and less geometric arguments or abstract algebraic properties, more and more of cartesian coordinates or trigonometric formulae, and even, as a last resort, approx numerical equation solving.

    don't worry, we all like brute force once in a while.

    in this case, it starts once you've established that FB=... (I leave the exercise to the reader ;-).

    bleaug

    ReplyDelete
  4. Yes, this is true. "Brute force" means complete enumeration in combinatorial, or computing science. It may also be called as "exhaustive search" in different context. Here what we mean by it is: the solution require rigorous computations - as bleaug pointed out - solving high degree polynomials, quadratics, trigonometric, and numerical approximations... And ending up with long expressions.

    Let me make it more difficult to understand:
    See, there is a beauty if a solution says: x+sin(x)=1. It is a closed form formula but simple and aesthetic. We'd love it! We'll keep that way, don't even ask what x is.

    But when we say x=sqrt(12625-sqrt(98756-sqrt(3)))/1797. Then a certain level of nicety might have gone.

    Or am I wrong? That tedious expression might have its own merits and beauty? And may be not?!

    End of message... and confusion...

    8foxes

    ReplyDelete
  5. more and more of cartesian coordinates???? I have other approaches and I haven´t seen Cartesian coordinates..hehe

    ReplyDelete
  6. here is a solution using svg + mathml. It was designed with firefox, which supports both nicely. Chrome and Opera do well with svg but have problems with mathml. Not tested with ie.

    http://bleaug.free.fr/8foxes/fox353bis.html
    (use arrows, page up/down or mouse wheel)

    bleaug

    ReplyDelete
  7. Verified that 0.2928 is the answer.

    ReplyDelete
  8. I am getting two possible positions of E ,thus there may be two solutions: 0.2928 and 0.375

    ReplyDelete
  9. I have been tiny bit familiar of this your broadcast provided bright clear concept...



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  12. Let's define as follows:

    * b = height of the rectangle = CD
    * a = width of the rectangle = BC
    * c = BD = sqrt(CD^2 + BC^2)

    By using the inscribed circle:
    sqrt(1600/b^2 + b^2) = ((40/b) - (b-10))
    This leads to: b^2 - b - 40 = 0

    By taking the positive solution: b = 6.844

    Then:
    * a = 5.845
    * c = 9.000

    AE = sqrt(b^2 + (5.845)^2) = 7.442
    EF = sqrt((a*(1-5/c)-a/2)^2 +(b*(1-5/c))^2)) = 3.06
    AF = sqrt((a*(1-5/c))^2 + (b*(5/c))^2) = 4.605

    (1) Get the area of AEF by Heron's formula:

    s = (7.442 + 3.06 + 4.606) / 2 = 7.554
    S = sqrt(7.554*(7.554-7.442)*(7.554-3.06)*(7.554-4.606))
     = 3.348

    sin(AEF) = (3.348 * 2) / (7.442 * 3.06)
     = 0.294

    (2) Use the cosine formula to first get cos:

    cos(∠AEF) = (7.442^2 + 3.06^2 - 4.606^2)/
     (2 * 7.442 * 3.06)
     = 0.9558

    sin(∠AEF) = sqrt(1 - 0.9558^2)
     = 0.294

    (1) and (2) both well match.

    ReplyDelete
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