Results are out! Find what you need...fast. Get quick advice or join the chat
x

Unlock these great extras with your FREE membership

  • One-on-one advice about results day and Clearing
  • Free access to our personal statement wizard
  • Customise TSR to suit how you want to use it

Official TSR Mathematical Society

Announcements Posted on
Find your uni forum to get talking to other applicants, existing students and your future course-mates 27-07-2015
Win top prizes in our mega results day giveaway... 24-07-2015
  1. Offline

    ReputationRep:
    Hmm... I think this is one of that \displaystyle \int_0^a f(x) dx = \int_0^a f(a-x) dx jobs

    (Original post by sonofdot)
    so then I would get xcosecx which I could do by parts, but I can't be bothered to do that now :p:
    Kinda tough integral though, doesn't evaluate in elementary functions
  2. Offline

    ReputationRep:
    (Original post by SimonM)
    A little easy again

    Spoiler:
    Show

    Based on two basic theorems

    \displaystyle \sum_{k=0}^{\infty} x^k = \frac{1}{1-x}
    and
    \displaystyle \sum_{k=0}^{\infty} kx^k = \frac{x}{(1-x)^2}

    Combining these we get

    \displaystyle \frac{a}{b} + \frac{a+c}{bd} + \frac{a+2c}{bd^2} + \frac{a+3c}{bd^3} + \cdots = \frac{a}{b} \sum_{k=0}^{\infty} \left ( \frac{1}{d} \right )^k + \frac{c}{b} \sum_{k=0}^{\infty} k \left ( \frac{1}{d} \right)^k = \frac{a}{b} \frac{1}{1-\frac{1}{d}} + \frac{c}{b} \frac{\frac{1}{d}}{(1-\frac{1}{d})^2} = \boxed{ \frac{ad}{b(d-1)} + \frac{c}{b} \frac{d}{(d-1)^2}}


    Random trivia: \begin{pmatrix} a \\ b \end{pmatrix} is not the same thing as \displaystyle \left( \frac{a}{b} \right). The latter is something called the Jacobi symbol.
  3. Offline

    ReputationRep:
    (Original post by Zhen Lin)
    Random trivia: \begin{pmatrix} a \\ b \end{pmatrix} is not the same thing as \displaystyle \left( \frac{a}{b} \right).
    Doh
  4. Offline

    ReputationRep:
    (Original post by SimonM)
    Hmm... I think this is one of that \displaystyle \int_0^a f(x) dx = \int_0^a f(a-x) dx jobs



    Kinda tough integral though, doesn't evaluate in elementary functions

    Yep that's the way forward (that's how the teacher expected us to do it atleast)
  5. Offline

    ReputationRep:
    (Original post by SimonM)
    Hmm... I think this is one of that \displaystyle \int_0^a f(x) dx = \int_0^a f(a-x) dx jobs
    I must be being absolutely stupid, but isn't it:

     \displaystyle \int_0^a f(x) dx = - \int_0^a f(a-x) dx ?
  6. Offline

    ReputationRep:
    (Original post by GHOSH-5)
    I must be being absolutely stupid, but isn't it:

     \displaystyle \int_0^a f(x) dx = - \int_0^a f(a-x) dx ?
    Nope
  7. Offline

    ReputationRep:
    (Original post by GHOSH-5)
    I must be being absolutely stupid, but isn't it:

     \displaystyle \int_0^a f(x) dx = - \int_0^a f(a-x) dx ?
    Consider the substitution  y = a - x and the fact that  \int_0^a f(x) dx = - \int_a^0 f(x) dx
  8. Offline

    ReputationRep:
    (Original post by Hancock orbital)
    Consider the substitution  y = a - x and the fact that  \int_0^a f(x) dx = - \int_a^0 f(x) dx
    im an idiot. thank you.
  9. Offline

    ReputationRep:
    (Original post by Hancock orbital)
    Consider the substitution  y = a - x and the fact that  \int_0^a f(x) dx = - \int_a^0 f(x) dx
    im an idiot. thank you.
  10. Offline

    ReputationRep:
    [joke]
    if we define "one" as "two" and "two as "one" does that gives "two plus two equals one"?
    [/]

    anyway, join request on the way
  11. Offline

    ReputationRep:
    (Original post by ~|Shock|~)
    [joke]
    if we define "one" as "two" and "two as "one" does that gives "two plus two equals one"?
    [/]

    anyway, join request on the way
    NO
  12. Offline

    ReputationRep:
    (Original post by Ekpyrotic)
    Ok, I understand it's customary to post a problem. Might be a little old but it's a good 'un.

    ABC is isosceles.

    AB=BC

    AB= \sqrt 5

    AC=2

    Find a way to cut the triangle into 4 pieces so that they can be constructed to form a regular square.
    I must be some sort of idoit but can someone put a hint?


    Another problem, though not very mathys:

    A farmer has the following three fields and he has 4 sons and 4 daughters. He wants to leave them with land when he passes away and to be fair they all have to have the same size plot and same shape plot. How can this be achieved?

    Attached Thumbnails
    Click image for larger version. 

Name:	untitled.JPG 
Views:	149 
Size:	3.6 KB 
ID:	64324  
  13. Offline

    ReputationRep:
    (Original post by The Muon)
    A farmer has the following three fields and he has 4 sons and 4 daughters. He wants to leave them with land when he passes away and to be fair they all have to have the same size plot and same shape plot. How can this be achieved?
    Does the solution involve molesting his eldest daughter to acquire a ninth child? It's plausible; you know what farmers are like :jiggy:. I think. *ahem*.
  14. Offline

    ReputationRep:
    (Original post by The Muon)
    I must be some sort of idoit but can someone put a hint?


    Another problem, though not very mathys:

    A farmer has the following three fields and he has 4 sons and 4 daughters. He wants to leave them with land when he passes away and to be fair they all have to have the same size plot and same shape plot. How can this be achieved?

    How about leaving one field for animals to graze upon, and dividing the remaining two fields into equally sized squares and give them to his children?
  15. Offline

    ReputationRep:
    (Original post by Mathematician!)
    How about leaving one field for animals to graze upon, and diving the remaining two fields into equally sized squares and give them to his children?
    I do not know the answer, it's on the wall at college and I can never figure it out.
  16. Offline

    ReputationRep:
    (Original post by The Muon)
    I do not know the answer, it's on the wall at college and I can never figure it out.
    Well this is plausible, as it doesn't say you can't leave a field for animals :p:
  17. Offline

    ReputationRep:
    (Original post by DeanK22)
    Have not drawn this out just thought about in my head but;

    Spoiler:
    Show
     24 \div  3 = 8 and  24 \times 3 = 72

     72 \div 8 = 9


    Spoiler:
    Show
    Chop each square into 24 rectangles allocating 2 rectangles from the big square and 1 from the square beneath, alternating this pattern. Consider the rectangle at the left with nothing above or below. Give three rectangles to one person.


    Should do it - everbody gets  9 rectangles.
    Off topic, but did DeanK2 get a perm. ban?
  18. Offline

    ReputationRep:
    (Original post by DeanK22)
    This is the same person :rolleyes: ...
    No really? :rolleyes:

    What I meant is did your other account get a perm. ban?
  19. Offline

    ReputationRep:
    (Original post by DeanK22)
    I requested such a ban due to spending too much time on TSR - the irony.
    Lol! Why did you start a new account then? :eyeball:
    Changed your mind?
  20. Offline

    ReputationRep:
    (Original post by Mathematician!)
    Lol! Why did you start a new account then? :eyeball:
    Changed your mind?
    TSR was the cause for quite literally doing nothing in terms of school work and I thought this would have affected my exams (considering I had done no homework in any of my subjects) and I need three a for Oxford. Considering how my exams have recently gone though I found that you can quite literally learn whole modules in one or three days - subject specific - ergo TSR time.

Reply

Submit reply

Register

Thanks for posting! You just need to create an account in order to submit the post
  1. this can't be left blank
    that username has been taken, please choose another Forgotten your password?
  2. this can't be left blank
    this email is already registered. Forgotten your password?
  3. this can't be left blank

    6 characters or longer with both numbers and letters is safer

  4. this can't be left empty
    your full birthday is required
  1. By joining you agree to our Ts and Cs, privacy policy and site rules

  2. Slide to join now Processing…

Updated: February 10, 2015
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

Poll
Would you consider Clearing if you missed your offer?
Results and Clearing

Results are coming...

No sweat. Here's all you need to make sure you're ready

new on tsr

What's your life ambition?

Graduating, travelling, owning a business?

Study resources
x

Think you'll be in clearing or adjustment?

Hear direct from unis that want to talk to you

Get email alerts for university course places that match your subjects and grades. Just let us know what you're studying.

Quick reply
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.