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Math Help - Swedish Math problem i got. Seems to be easy. but not quite....?

  1. #16
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    Re: Swedish Math problem i got. Seems to be easy. but not quite....?

    Quote Originally Posted by Cyrus1 View Post
    Thanks a lot for everything! The last thing i was wondering is how the method holds for when the X line is under 2 meters. I mean how do you split the angle Z in that case? Will you write
    Hej,

    I split the angle z into \alpha and \beta. If y < 2 then \tan(\beta) = \frac{y-2}x <0~\implies~\beta < 0

    That means this case is taken into consideration automatically. Compare the attached drawing which is done by my geometry program.
    Attached Thumbnails Attached Thumbnails Swedish Math problem i got. Seems to be easy. but not quite....?-swedkinonegativ.png  
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  2. #17
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    Re: Swedish Math problem i got. Seems to be easy. but not quite....?

    Quote Originally Posted by earboth View Post
    Hej,

    I've modified your sketch a little bit and here is what I've calculated:

    1. The straight line representing the place where your head could be has the equation y = x \cdot \tan(22^\circ) - 3 \cdot \tan(22^\circ)  +1

    z = \alpha+\beta

    2. \tan(\alpha)=\frac{10-y}{x} and \tan(\beta) = \frac{y-2}x

    3. From \tan(z)=\tan(\alpha + \beta)=\frac{\tan(\alpha) + \tan(\beta)}{1-\tan(\alpha) \cdot \tan(\beta)} I get:

    \tan(z)=\frac{\frac{10-y}{x} + \frac{y-2}x}{1 - \frac{10-y}{x} \cdot \frac{y-2}x}

    4. Since z has it's maximum if \tan(z) is at it's maximum I solved for x:  \frac{d(\tan(z))}{dx} = 0

    I've got x \approx 4.406798787. That means your head is at (4.406798787, 1.568383604)

    5. ... but honestly I would refuse to take this seat
    A long time has passed and i thank you for this! However, i was wondering how you calculated the maximum, by paper or by some digital tool? We are allowed to use Wolframalpha and i have inserted all of it in there but i do not recieve the same results as you do!!!
    d((10-tan??(22)x-3 tan?(22) ?)/x +(tan??(22)x-3 tan?(22) ?-2)/x)/(1-((10-tan??(22)x-3 tan?(22) ?)/x)( (tan??(22)x-3 tan?(22) ?-2)/x))/dx=0 - Wolfram|Alpha
    Please take a look at the link.
    Best regards
    Cyrus1
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  3. #18
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    Re: Swedish Math problem i got. Seems to be easy. but not quite....?

    Quote Originally Posted by Cyrus1 View Post
    A long time has passed and i thank you for this! However, i was wondering how you calculated the maximum, by paper or by some digital tool? We are allowed to use Wolframalpha and i have inserted all of it in there but i do not recieve the same results as you do!!!
    d((10-tan??(22)x-3 tan?(22) ?)/x +(tan??(22)x-3 tan?(22) ?-2)/x)/(1-((10-tan??(22)x-3 tan?(22) ?)/x)( (tan??(22)x-3 tan?(22) ?-2)/x))/dx=0 - Wolfram|Alpha
    Please take a look at the link.
    Best regards
    Cyrus1
    Good evening and happy Easter,

    as far as I can see your input-line is incorrect: You must put the term into parantheses representing y.
    y consists of 3 summands but you have suppressed the +1 .
    I don't understand why there are so many question marks in your input-line.

    And I'm not familiar with Wolfram Alpha
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  4. #19
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    Re: Swedish Math problem i got. Seems to be easy. but not quite....?

    Quote Originally Posted by earboth View Post
    Good evening and happy Easter,

    as far as I can see your input-line is incorrect: You must put the term into parantheses representing y.
    y consists of 3 summands but you have suppressed the +1 .
    I don't understand why there are so many question marks in your input-line.

    And I'm not familiar with Wolfram Alpha
    Happy easter!!!!!! Thanks.

    If you click on the link there should not be any question marks.

    What method did you use to solve this? Hard to do it by hand no?
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  5. #20
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    Re: Swedish Math problem i got. Seems to be easy. but not quite....?

    Quote Originally Posted by Cyrus1 View Post
    Happy easter!!!!!! Thanks.

    If you click on the link there should not be any question marks.

    What method did you use to solve this? Hard to do it by hand no?
    Hello,

    since you only can get approximate values I used approximate values from the beginning. It means that you have to type in a lot of cyphers but on the other hand it reduces processing time of the computer. And of course I do not do these calculations by hand.

    I've attached a protocol which is generated by the math program I use. Only the comments are added. Hopefully this will show you how I did your question.

    I use derive 6.0. This program is very old, there aren't any updates available but I know how to use it and it works fine for me.

    If you use the approximate values even Wolfram Alpha will do the job. Have a look here:
    https://www.wolframalpha.com/input/?i=derivative+of+%288x%29%2F%28x^2%2B%280.404x-2.212%29%280.404x-10.212%29%29

    Scroll down to ROOTS.
    Attached Thumbnails Attached Thumbnails Swedish Math problem i got. Seems to be easy. but not quite....?-swedkinoapprox.png  
    Last edited by earboth; April 22nd 2014 at 12:51 AM.
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  6. #21
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    Re: Swedish Math problem i got. Seems to be easy. but not quite....?

    Quote Originally Posted by Cyrus1 View Post
    Happy easter!!!!!! Thanks.

    If you click on the link there should not be any question marks.

    What method did you use to solve this? Hard to do it by hand no?
    2nd approach: I finally learned how to place an active link in this post.

    If you use the approximate values even Wolfram Alpha will do the job. Have a look here:

    https://www.wolframalpha.com/input/?...x-10.212%29%29

    Scroll down to ROOTS.
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  7. #22
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    Re: Swedish Math problem i got. Seems to be easy. but not quite....?

    Quote Originally Posted by earboth View Post
    2nd approach: I finally learned how to place an active link in this post.

    If you use the approximate values even Wolfram Alpha will do the job. Have a look here:

    https://www.wolframalpha.com/input/?...x-10.212%29%29

    Scroll down to ROOTS.
    Dear earboth, you are simply a saint! I wish you the best in life, i truly do. Might sound corny but from the bottom of my heart i hope karma or something pays you back tenfold! Thank you!
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