Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

jennychan12 Group Title

Integral Question. See below,

  • one year ago
  • one year ago

  • This Question is Closed
  1. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    O_o .

    • one year ago
  2. jennychan12 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    If \[\int\limits_{0}^{6} (x^2-2x+2)dx\] is approximated by 3 inscribed rectangles of equal width, then the approximation is... 1) 24 B) 26 C) 28 D)76 E) 48

    • one year ago
  3. jennychan12 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    sorry typed something wrong. and that 1 is supposed to be an A

    • one year ago
  4. jennychan12 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    so i got the integrated area to be 48, so answers either a b or c

    • one year ago
  5. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Wait.

    • one year ago
  6. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Wait, what kind of rectangles? Left, right, or midpoint?

    • one year ago
  7. jennychan12 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    the problem doesnt say. i'm assuming left

    • one year ago
  8. jennychan12 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    cuz it says inscribed

    • one year ago
  9. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Well you are right. It's either A, B or C :D . Now can you do it out? :) .

    • one year ago
  10. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\Delta(x)=\frac{ 6-0 }{ 3 }\]

    • one year ago
  11. jennychan12 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    i'm confused my friend says to use riemann sum. what's the formula for that?

    • one year ago
  12. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\Delta(x) = 2\]

    • one year ago
  13. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    In this particular example, a Riemann sum is basically the sum of the individual rectangles.

    • one year ago
  14. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    When you learn about definite intergals you will have a good idea about what they actually mean.

    • one year ago
  15. jennychan12 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    is it \[\frac{ b-a }{ n } \sum_{i = 1}^{n} f(x) \] ??

    • one year ago
  16. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    No wait, that's right.

    • one year ago
  17. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    So yeah you get the idea. It's the sum of all the rectangles multiples by the change in x,(i.e the width) .

    • one year ago
  18. jennychan12 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    that's what i did but i got 28 and the answer's 26

    • one year ago
  19. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Then you have to use diffrent kinds of rectangles because your answer is correct.

    • one year ago
  20. jennychan12 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    26 or 28 ?

    • one year ago
  21. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    It's 26.

    • one year ago
  22. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    But if you use left rectangles then it's 28.

    • one year ago
  23. jennychan12 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    why? sorry can u explain?

    • one year ago
  24. jennychan12 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    oh.

    • one year ago
  25. jennychan12 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    so right hand it's 26 or..?

    • one year ago
  26. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    So this is a very stupid question because it dosen't specify the type of rectangles.

    • one year ago
  27. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Well right hand is 76 actually.

    • one year ago
  28. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    But it dosen't specify what type of rectangle. Left, right or midpoint.

    • one year ago
  29. jennychan12 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    where'd the 26 come from? midpoint?

    • one year ago
  30. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    No, midpoint is 46.

    • one year ago
  31. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    But shall I explain left and right rectangles?

    • one year ago
  32. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    If you use left, you get 28. If you use right you get 76.

    • one year ago
  33. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Shall I explain?

    • one year ago
  34. jennychan12 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    wait so where did the 26 come from. please explain. i'm so lost. :(

    • one year ago
  35. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    26 isn't the correct answer.

    • one year ago
  36. jennychan12 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    cuz this other person used 2(f(1)+f(2)+f(4)) and got 26 but i don't understand where the f(1) came from...

    • one year ago
  37. jennychan12 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    oh.

    • one year ago
  38. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Wait hold on.

    • one year ago
  39. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Yeah, 28 should be correct. I disagree with the answer.

    • one year ago
  40. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    If you use 3 subintervals you CANNOT get 26 in anyway.

    • one year ago
  41. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    The formula would be (2)(f(0)+f(2)+f(4))

    • one year ago
  42. jennychan12 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah i did that... and got 28

    • one year ago
  43. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Which is absolutely correct.

    • one year ago
  44. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    It CANNOT be 26 if you use left rectangles.

    • one year ago
  45. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    if you use right rectangles it's (2)(f(2)+f(4)+f(6)) which is 76.

    • one year ago
  46. jennychan12 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah i got 28 and 76 but i chose 28. so my teacher is wrong. hmph.

    • one year ago
  47. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Yep, you teacher is wrong.

    • one year ago
  48. jennychan12 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    thanks for clarifying. :)

    • one year ago
  49. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    In reality the exact value of that integral is 48 but you will learn that later.

    • one year ago
  50. jennychan12 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah i know. i calculated it.

    • one year ago
  51. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Kk.

    • one year ago
  52. yun2thejae Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Good 'ol Riemann's screwing with everybody's head.

    • one year ago
  53. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I just hope I don't have to do it after my first year in uni :/ . AP calc helped so much though XD .

    • one year ago
  54. jennychan12 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ohhhhhhh i think i got it they used average value

    • one year ago
  55. yun2thejae Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    LOL

    • one year ago
  56. oldrin.bataku Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    $$A\simeq2(2^2-2(2)+2+4^2-2(4)+2+6^2-2(6)+2)\\\ \ \ =2(4-4+2+16-8+2+36-12+2)\\\ \ \ =2(38)=76$$ (using right end-points)$$A\simeq2(0^2-2(0)+2+2^2-2(2)+2+4^2-2(4)+2)=2(2+4-4+2+16-8+2)\\\ \ \ =2(14)=28$$ (using left end-points)$$A\simeq2(1^2-2(1)+2+3^2-2(3)+2+5^2-2(5)+2)\\\ \ \ =2(1-2+2+9-6+2+25-20+2)\\\ \ \ =2(13)=26$$ (using midpoints)

    • one year ago
  57. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    ^ Reason why they they should specify the question.

    • one year ago
  58. jennychan12 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    my friend just assumed that inscribed meant left end points

    • one year ago
  59. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    @oldrin.bataku : Please don't just give the answer next time. The point of this place is to help other people learn. Not give them the answer.

    • one year ago
  60. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    @jennychan12 : That's a flase assumption.

    • one year ago
  61. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    false*

    • one year ago
  62. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    @oldrin.bataku : If you use midpoints, it's 46 not 26.

    • one year ago
  63. yun2thejae Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Lol Oldrin and i have been spending plenty of time explaining problems to different users. I would give him a break xD. I was bored and decided to use this site for the first time today and, oddly enough, I can't stop attempting to solve problems. Probably because I don't want to forget my math whilst im on winter break.

    • one year ago
  64. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I know but it's just that's it's against the TOS so I try not to. I make that mistake too. It's cool ^_^ .

    • one year ago
  65. oldrin.bataku Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    @Dido525 you're right, 2(5) = 10 so it's actually 2(23) = 46 for the approximate area.

    • one year ago
  66. oldrin.bataku Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    If it requires inscribed rectangles then the approximation must use left end-point... mid- and right- will not be entirely under the parabola.

    • one year ago
  67. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    That's why we have the trapozoidal rule ;) . Ans simpsons rule :P .

    • one year ago
  68. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    and*

    • one year ago
  69. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    But yes @oldrin.bataku is correct. If they MUST be inscribed then you MUSt use left rectangles.

    • one year ago
  70. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    MUST*

    • one year ago
  71. oldrin.bataku Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    @Dido525 if you go into a Scientific Computation course you'll learn about plenty more numerical methods e.g. Runge-Kutta or Adams-Moulton :-p Euler's and Verlet are really common for physics problems.

    • one year ago
  72. yun2thejae Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Conversation is too much for this PoSci major xD.

    • one year ago
  73. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I looked at Runge-kutta but it makes no sense XD . I am going much deeper into math next year so hopefully then :) .

    • one year ago
  74. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Sorry that we turned this page into a discussion @jennychan12 .

    • one year ago
  75. jennychan12 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    it's aiight.

    • one year ago
  76. agent0smith Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Nobody drew a damn diagram :P

    • one year ago
  77. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Sigh...

    • one year ago
  78. yun2thejae Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Diagram was drawn in the other thread.

    • one year ago
  79. jennychan12 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ^ haha yes

    • one year ago
  80. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1355899568667:dw|

    • one year ago
  81. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Something like that.

    • one year ago
  82. jennychan12 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    if u wanna see http://openstudy.com/study#/updates/50d15940e4b069abbb70d3c0

    • one year ago
  83. agent0smith Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    that's the same thread as this one...

    • one year ago
  84. yun2thejae Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    LOL

    • one year ago
  85. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1355899651047:dw| That would be incorrect since it does not enclose the curve.

    • one year ago
  86. jennychan12 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah i got really confused and tried to do another one to resolve my confusion... :D cuz that other person made me confused

    • one year ago
  87. oldrin.bataku Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1355899646424:dw|

    • one year ago
  88. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1355899717852:dw|

    • one year ago
  89. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    If you use midpoints it still dosen't enclose the curve fully.

    • one year ago
  90. agent0smith Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Inscribed rectangles *should* mean rectangles within the curve, but it sounds like that didn't work, so the damn question is broken.

    • one year ago
  91. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Damn question.

    • one year ago
  92. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    It's is 28 though without a doubt.

    • one year ago
  93. oldrin.bataku Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    More than likely your teacher made an error.

    • one year ago
  94. jennychan12 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah

    • one year ago
  95. agent0smith Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    inscribed rectangles would give 26, but i feel like that was already covered in this mess somewhere

    • one year ago
  96. yun2thejae Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    You haven't done "work" problems in your calc class yet have you?

    • one year ago
  97. agent0smith Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Wait, why isnt the answer 26? 3 inscribed rectangles = area of 26.

    • one year ago
  98. jennychan12 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    what do u mean? kinetic energy? i do that in physics....

    • one year ago
  99. jennychan12 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    @agent0smith can u explain???

    • one year ago
  100. yun2thejae Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    there are "work" problems you use calculus for. Pray that you do not have to do them xD

    • one year ago
  101. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    If you use 3 inscribed rectangles it's 28 not 26.

    • one year ago
  102. yun2thejae Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    The previous thread came up with 26. this one says 28. let's meet half way and say it's 27...oh wait.

    • one year ago
  103. jennychan12 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    lol

    • one year ago
  104. agent0smith Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    The height of the first is 1, length is 2 height of the second is 2, length is 2 height of the third is 10, length is 2. 2+4+20

    • one year ago
  105. agent0smith Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    How'd you get 28, @Dido525

    • one year ago
  106. jennychan12 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    left endpoint is 28

    • one year ago
  107. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    =(2) * ( f(0) + f(2) + f(4) ) = (2) * ( 2 + 2 + 10 ) = 28

    • one year ago
  108. agent0smith Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Inscribed have to be all within the curve, no edges jutting out: it's not f(0), it's f(1), the height of the first rectangle.

    • one year ago
  109. agent0smith Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    That is not an inscribed rectangle.

    • one year ago
  110. jennychan12 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    that's what that other person did in that other thread 2(f(1)+f(2)+f(4)) = 26 but why would be f(1)??? where does the 1 even come from?

    • one year ago
  111. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    But f(0) is inscribed.

    • one year ago
  112. agent0smith Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I'll draw it jenny. One sec.

    • one year ago
  113. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I want to see this too.

    • one year ago
  114. agent0smith Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    dido, look at the graph: http://www.google.com/search?q=x%5E2-2x%2B2&aq=f&oq=x%5E2-2x%2B2&sugexp=chrome,mod=18&sourceid=chrome&ie=UTF-8 and then look where a rectangle at f(0) would fall... it's not inscribed. it goes over the curve.

    • one year ago
  115. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Isn't that the same thing as inscribed?

    • one year ago
  116. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Inscribed meaning within.

    • one year ago
  117. agent0smith Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    No, inscribed means it falls completely within the curve, no jutting out over it.

    • one year ago
  118. jennychan12 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    okay. i understand that f(1) = 1 but.... oh wait. i see where you're going with this....

    • one year ago
  119. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1355900439887:dw|

    • one year ago
  120. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    But rectangles will never cover a curve fully, it's impossible.

    • one year ago
  121. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Like, it covers it fully but it's an overestimate.

    • one year ago
  122. agent0smith Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    • one year ago
  123. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Ohh shoot! O_o .

    • one year ago
  124. agent0smith Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Those are inscribed rectangles, they underestimate the area greatly of course.

    • one year ago
  125. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Ahh, NOW this makes sense.

    • one year ago
  126. agent0smith Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    hahah :)

    • one year ago
  127. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    But if it's an underestimate, it's not inscribed is it?

    • one year ago
  128. jennychan12 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ok yeah i see it too.

    • one year ago
  129. agent0smith Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I googled inscribed rectangles just to be sure.

    • one year ago
  130. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Wait, why did you do a midpoint for the first rectangle?

    • one year ago
  131. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Instead of a left one?

    • one year ago
  132. agent0smith Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Because that's the only way to have it inscribed. http://en.wikipedia.org/wiki/Inscribed_figure

    • one year ago
  133. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    NOW this all makes sense :D .

    • one year ago
  134. agent0smith Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Inscribed rectangles can be either left or right endpoint

    • one year ago
  135. agent0smith Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    or midpoint

    • one year ago
  136. agent0smith Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    @jennychan12 you see how it's 26 now? the height of the first is f(1), next is f(2), then f(4)

    • one year ago
  137. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I would give you my medal if I could :P .

    • one year ago
  138. agent0smith Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    haha :) this whole confusion was all over the meaning of the word inscribed :D

    • one year ago
  139. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Agreed! :D . But hey, this might be n my final so it was good for me too :) .

    • one year ago
  140. agent0smith Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    haha good :) hopefully this clears things up Jenny, before you went and told your teacher he/she was wrong because a bunch of people on the internet said so! :D

    • one year ago
  141. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    She is offline :/ .

    • one year ago
  142. Dido525 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    @jada1701877 : You should have given that to agent.

    • one year ago
  143. jennychan12 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    thanks so much! and yeah, i went off at like 11 cuz i went to sleep. :)

    • one year ago
    • Attachments:

See more questions >>>

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.