A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

I don't know what to do with this question, please help! A piece of string 10m long is cut into pieces, so that the lengths of the pieces form an arithmetic sequence. (i) The lengths of the longest and shortes pieces are 1m and 25cm respectively; how many pieces are there? Answer:16 (ii) If the same string had been cut into 20 pieces with lengths that formed an arithmetic sequence, and if the length of the second longest had been 92.5 cm, how long would the shortest piece have been? (ii) Is the one I don't know what to do with. I have already completed (i)

  • This Question is Closed
  1. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    which one !?

  2. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I need help with the last question please.

  3. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Arithmetic Series: 2nd term = a1 + d where a = first term and d = common difference so here 92.5 = a1 + d

  4. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    the sum of 10 terms = the length of the string = 10,000 cms

  5. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Um isn't 1000cm?

  6. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Now the sum of n terms is (n/2)[2a1 + (n - 1)d] so here n = 20 and Sum = 10,000 so we have 10,000 = 10[2a1 + 19d]

  7. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    so we have the system of equations a1 + d = 92.5 20a1 + 19d = 10,000

  8. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Ok, one little question- why is it 2a1 ?

  9. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    2 * first term a1 will be the first term = shortest piece

  10. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Oh ok

  11. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    so you need to find the value of a1

  12. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I use a different form of that equation normally so was confused for a second

  13. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    if you multiply the first equation by -19 and add you can find a1

  14. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    yes a1 is usually used in the US in UK we usually use just a

  15. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    a1 + d = 92.5 sorry, could you just explain more about how you got this part? I dont really understand why the first term plus the common term equals the second last term? I know I am missing something

  16. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    oh - maybe i was wrong there sorry - -i took that to be the second term - its the 19th term

  17. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    also the total length = 1000 (wrong again!)

  18. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Haha, it happens! No worries.

  19. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    so the 2 equations are a1 + 18d = 92.5 20a1 + 19d = 1000

  20. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Ok, I am not sure I understand the concept behind that second equation

  21. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    that is the formula for the sum of n terms of an arithmetic series Sn = (n/2)[2a1 + (n - 1)d] here Sn = length of the string = 1000 cms, n = 20 (20 pieces) , a1 = first term, d = common difference

  22. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Ok. Then I am meant to simultaneously solve those two equations?

  23. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    yes

  24. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    i bit messy Have you got a graphical calculator?

  25. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    No I don't. Oh well, I will try it quickly now without one

  26. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    is our shortest piece still 25cm?

  27. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    No I don't think so. That was for the first question

  28. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    how long should shortest piece ... forgot to read thru it all the way

  29. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    hmm the results don't seem to give rational values..

  30. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yeah I am not getting anything that makes sense.

  31. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I got d=2.5 a=47.625 after rounding

  32. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    i thnk the equations are correct..

  33. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I probably just did something wrong then.

  34. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    yes the calc gives 47.631 and 2.4927

  35. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    10m long 20(2a+19d)/2 = 1000 a+18d = 92.5 a is about 2.5, and d is about 5

  36. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    yea my second equation was wrong 10(2a + 19d) = 201 + 190d

  37. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    2a+19d = 100 a+18d = 92.5 2a +19d = 100 -19/18a -19d = -19/18(92.5) a = (100-(19/18(92+1/2)))/(2-(19/18))

  38. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    2.5 for shortest length and 5 for common difference

  39. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    it was 190d not 19d

  40. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Ok..

  41. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    do you see the mistake I didnt distribute 10 over the (2a + 19) correctly

  42. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    I thought someone would spot my deliberate mistake - oh amistre did!

  43. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Oh! I see now!

  44. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    good there is another formula for sum of n terms of an arithmetic series Sn = (n/2)[ a1 + L] where L is the last term If you know the last term its a lot simpler

  45. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes, thats the form I normally use and I didn't remeber about the other one not needing the last term which is a big part of why I got stuck I think Just trying to solve those two equations myself now.

  46. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    probably best to multiply first one by -20 and add to get d first

  47. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yup! Did it and got the two right answers! Thank you so much for your help!

  48. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    yw

  49. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.