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anonymous

  • 5 years ago

a professional football team has a stadium which seats 60000. it is found that x tickets can be sold at a price of p=10-(x/10000) dollars per ticket. find the value of x and p at which the total money received will be a maximum.

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  1. amistre64
    • 5 years ago
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    thats a linear equation with a positive slope....

  2. amistre64
    • 5 years ago
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    errr.. a negative slope lol;

  3. amistre64
    • 5 years ago
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    p = -(1/100000) x + 10

  4. amistre64
    • 5 years ago
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    when x = 0 you have a maximum of 10; the higher x goes, the less you make

  5. amistre64
    • 5 years ago
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    or am i missing something

  6. anonymous
    • 5 years ago
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    no

  7. anonymous
    • 5 years ago
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    I don't think so. There's logic in your answer ^_^

  8. amistre64
    • 5 years ago
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    this might be the derivative and is asking fo ryouto integrate from 0 to 60000

  9. anonymous
    • 5 years ago
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    hmmm, no wait, wouldn't that be a minimum?

  10. anonymous
    • 5 years ago
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    if 0 tickets are sold, then you gained p=10000

  11. amistre64
    • 5 years ago
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    f'(x) = 0 at 10000/10 then

  12. anonymous
    • 5 years ago
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    oh right lol, it's over (10,000) ^_^" my bad lol

  13. amistre64
    • 5 years ago
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    f'(x)= 1000; integrate from 0 to 60000?

  14. anonymous
    • 5 years ago
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    no need to integrate, from the function , you can figure out the maximum, just like you did :)

  15. anonymous
    • 5 years ago
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    x increases= less money, like you've said. so the maximum is at x = 0?

  16. amistre64
    • 5 years ago
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    well i am thinking that this is the derivative of a higher function; and its max value is at 1000 for x; so the integral would tell us the price right?

  17. anonymous
    • 5 years ago
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    but wouldn't wouldn't the price be found after plugging in x =0 in the function? :)

  18. amistre64
    • 5 years ago
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    if this was the true function then yes, but the wording has me believe that the optimazation is given by this equation; and not the true function...

  19. anonymous
    • 5 years ago
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    mmm, so we have to optimize in this case? ^_^to find the maximum

  20. amistre64
    • 5 years ago
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    i think so :) so we would integrate the given to find the true value; with x = 1000; becasue that is where p'(x) = 0

  21. anonymous
    • 5 years ago
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    Alright, now I got what you mean lol proceed ^_^

  22. amistre64
    • 5 years ago
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    the 60000 gives us an initial condition; possiply at (0,60000)

  23. anonymous
    • 5 years ago
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    so we'll integrate from 0->6000?

  24. amistre64
    • 5 years ago
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    dunno if we integrate of simply anchor it in at (0,60000) p=10-(x/10000)

  25. amistre64
    • 5 years ago
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    P(x)=10x -x^2/2(10000) + C

  26. amistre64
    • 5 years ago
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    10(1000) - (1000)(1000)/2(10000) 10000 - 500/10

  27. amistre64
    • 5 years ago
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    10000 - 50 = 9950 +C

  28. amistre64
    • 5 years ago
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    P(1000) = 60000 = 9950 + C C = 60000 - 9950 = 50050 P(x) = 10(x) - x^2/20000 + 50050 ??

  29. amistre64
    • 5 years ago
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    maybe integrate from 0 to 60000 :) ??? dunno

  30. anonymous
    • 5 years ago
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    I think we have made it look more complicated than it seems, lol?

  31. anonymous
    • 5 years ago
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    LOL!

  32. anonymous
    • 5 years ago
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    do you know what I think?

  33. amistre64
    • 5 years ago
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    broken question? lol

  34. anonymous
    • 5 years ago
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    since the maximum price of tickets is achieved when x=0, then for 60000 seats, the maximum price will be = 600,000

  35. anonymous
    • 5 years ago
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    .-. right?

  36. amistre64
    • 5 years ago
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    maximum price = 600,000? or max revenue?

  37. amistre64
    • 5 years ago
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    see the wording is off...

  38. anonymous
    • 5 years ago
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    hmm, we have :\[p(x) = 10-\frac{x}{10000}\] so if we take x = 0: \[p(0) = 10\] so we can tell that the original price of the ticket is = 10. Now for 60000 seats, we need 60000 people, so each person is going to buy a ticket. In the end, maximum price achieved = 600,000 I'm not sure, but I'm just computing what I have understood from the question ^_^" ahaha...

  39. anonymous
    • 5 years ago
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    so the maximum values for x and p : x = 0, and p = 10

  40. amistre64
    • 5 years ago
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    i agree that that is a possible interpretation of the problem :) but maximum price is not 600,000; that would be revenue. Max price if anything would be 10 lol

  41. anonymous
    • 5 years ago
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    oh, right >_< well, atleast you got what I mean =P

  42. dumbcow
    • 5 years ago
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    x=50,000 p=5 maximum money = p*x = 250,000

  43. amistre64
    • 5 years ago
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    if x = tickets sold, then how can 0 ticket sold bring in 600,000 :)

  44. anonymous
    • 5 years ago
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    where did you get the 50,000 and 5? .-.

  45. dumbcow
    • 5 years ago
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    money received is revenue which equals price*quantity quantity is num seats sold = x so the function to maximized is p*x = x(10-x/10,000)

  46. anonymous
    • 5 years ago
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    annnnnnwaaaar~ lol ^_^

  47. anonymous
    • 5 years ago
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    but the number of seats = 60,000 and not 50k lol :)

  48. anonymous
    • 5 years ago
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    I don't know where you guys have reached. But, I think the idea here is to maximize the total money received. Total money= price of one ticket * # of tickets= xp(x).

  49. dumbcow
    • 5 years ago
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    60,000 available not sold

  50. anonymous
    • 5 years ago
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    so how did you get 50k?

  51. amistre64
    • 5 years ago
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    i understand it now.... i think lol

  52. dumbcow
    • 5 years ago
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    differentiate above function set =0 solve for x

  53. anonymous
    • 5 years ago
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    p = 0 and solve for x?

  54. amistre64
    • 5 years ago
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    whoever wrote this problem could have been clearer ;)

  55. anonymous
    • 5 years ago
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    xp(x)=f(x)=10x-x^2/10,000 f'(x)=10-2x/10,000=0 implies x=50,000

  56. anonymous
    • 5 years ago
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    oh well, clear or not, my brain is shutdown and doesn't want to study. I had calculus II at 8 and was playing in the whole time, and got out not understanding what on Earth I took today.

  57. anonymous
    • 5 years ago
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    and I felt good abt it. I guess it's beacuse of the bananas I ate in the morning.

  58. anonymous
    • 5 years ago
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    oh, I got you anwar, thank you ^_^

  59. anonymous
    • 5 years ago
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    LOL!!

  60. anonymous
    • 5 years ago
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    You're welcome. Am I right there?

  61. anonymous
    • 5 years ago
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    it's TRUE! Bananas = get you excited, and I was off ~ completely OFF

  62. anonymous
    • 5 years ago
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    hoenstly, I have no idea. My brain is unable to compute or accept any info atm.

  63. anonymous
    • 5 years ago
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    but it looks right though ^_^

  64. amistre64
    • 5 years ago
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    i was watching the cheerleaders and got distracted lol

  65. anonymous
    • 5 years ago
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    LOL

  66. anonymous
    • 5 years ago
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    HAHA.

  67. dumbcow
    • 5 years ago
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    waterlily do you get it? or do you need more help

  68. anonymous
    • 5 years ago
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    my professor tried to grab my attention by trying, "TRYING" to introduce Taylor series today, but no hope, he gave up and ended the class after 1 hour =D!

  69. anonymous
    • 5 years ago
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    I was like, I don't like taylor series, I want to learn Fourier series!

  70. anonymous
    • 5 years ago
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    he was like, but it's not in the syllabus and etc etc etc

  71. anonymous
    • 5 years ago
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    i get it thanks

  72. anonymous
    • 5 years ago
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    loooooooooooong morning, it was HILARIOUS

  73. anonymous
    • 5 years ago
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    oh, sorry waterlily ^_^" aha...

  74. anonymous
    • 5 years ago
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    You have no more classes?

  75. anonymous
    • 5 years ago
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    let's see, my ESPII professor, cancelled today's class at 10, so no class til 3:30 , hallalujah~!

  76. anonymous
    • 5 years ago
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    and guess what!

  77. anonymous
    • 5 years ago
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    what?!

  78. anonymous
    • 5 years ago
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    I've got a test at that time! Heck knows what I'll during that hour. If I'm luney and off now, what will happen later on? ^_^

  79. anonymous
    • 5 years ago
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    I think I and mr. "dumbcow" had the same answer. He was first though.

  80. anonymous
    • 5 years ago
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    people usually revise, take advantage of these 4 free hours, but me? nooooooo, don't feel like it ._. I guess I need a day off.

  81. anonymous
    • 5 years ago
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    lol.....LOL!

  82. anonymous
    • 5 years ago
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    LOL

  83. anonymous
    • 5 years ago
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    why did he call himself dumbcow?! :D

  84. anonymous
    • 5 years ago
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    I find that a really funny and "creative" username :)

  85. anonymous
    • 5 years ago
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    I have no idea.

  86. anonymous
    • 5 years ago
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    cows are not dumb! they just don't get english that's all

  87. anonymous
    • 5 years ago
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    Do you stay at university or go home during this 4 hours?

  88. anonymous
    • 5 years ago
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    if cows are dumb for not understanding what we say, then we are dumb becase we don't understand what they say, right?

  89. anonymous
    • 5 years ago
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    LOL. they don't get english heh? what about arabic?

  90. anonymous
    • 5 years ago
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    I stay here, I don't want to get my mum tired.

  91. anonymous
    • 5 years ago
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    neither

  92. anonymous
    • 5 years ago
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    all they say is mooo

  93. anonymous
    • 5 years ago
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    I don't agree with your "cow" theorem btw :P

  94. anonymous
    • 5 years ago
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    with different wavelengths ~

  95. anonymous
    • 5 years ago
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    But I like it :)

  96. anonymous
    • 5 years ago
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    Hey, this is logic and I'm studying it this semester and I agree with my theorem

  97. anonymous
    • 5 years ago
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    omg..I sound drunk LOL with bananas~

  98. anonymous
    • 5 years ago
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    Nope, it's not.

  99. anonymous
    • 5 years ago
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    wait what?o_o

  100. anonymous
    • 5 years ago
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    yes it is

  101. anonymous
    • 5 years ago
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    let me read it again.

  102. anonymous
    • 5 years ago
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    how can bananas get you drunk?

  103. anonymous
    • 5 years ago
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    lol. Yes, your theorem makes sense :P

  104. anonymous
    • 5 years ago
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    there's this chemical compound in it, called tyro something something that get's you super duper powerful well, it usually gets ppl calm, but I don't know why it's the opposite effect on me? ._.

  105. anonymous
    • 5 years ago
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    see, I told you so , I told you so, I told you so~

  106. anonymous
    • 5 years ago
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    omg...please, bare with me this time and you'll never see me talk like this again >_<, I apologize guys

  107. anonymous
    • 5 years ago
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    never eat bananas in the morning = lesson of today

  108. anonymous
    • 5 years ago
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    You didn't say anything wrong!!

  109. anonymous
    • 5 years ago
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    I sound DRUNK LOL

  110. anonymous
    • 5 years ago
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    I don't eat bananas at all

  111. anonymous
    • 5 years ago
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    I don't know how "drunk people" sound. So, I don't knwo if you do sound like one :)

  112. anonymous
    • 5 years ago
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    know*

  113. anonymous
    • 5 years ago
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    I love bananas and my professor recommened us to eat a banana every morning to calm the nerves, but it's not WORKING with me, it's not CALMING my nevers, it's getting me OFF~

  114. anonymous
    • 5 years ago
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    lol

  115. anonymous
    • 5 years ago
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    I'm just having one of my childish moments right now ^_^"

  116. anonymous
    • 5 years ago
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    o_o...

  117. anonymous
    • 5 years ago
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    lol?

  118. anonymous
    • 5 years ago
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    These are the best moments. Enjoy them as much as you can

  119. anonymous
    • 5 years ago
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    and you + mr"dumbcow" are getting a medal for soling the questionariO~

  120. anonymous
    • 5 years ago
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    sigh~ I just need a break

  121. anonymous
    • 5 years ago
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    I didn't get a weekend for 2 weeks now, and I need one

  122. anonymous
    • 5 years ago
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    :(

  123. anonymous
    • 5 years ago
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    busy busy, quizzes, tests, quizzes, tests, studies, da da da ~

  124. anonymous
    • 5 years ago
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    Have a day off yo!!

  125. anonymous
    • 5 years ago
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    but you know what?

  126. anonymous
    • 5 years ago
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    exactly, that's what I was thinking. I'm going to my professor now, my lab professor and I'll tell him to excuse me from tomorrow's class. I just have one lab class tomorrow morning. I'll skip it, ofcourse after telling him that, and have FUN

  127. anonymous
    • 5 years ago
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    that's it, one day off is all I need

  128. anonymous
    • 5 years ago
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    YAAY.. I love "off" days!!

  129. anonymous
    • 5 years ago
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    The one you make by yourself are the best <3

  130. anonymous
    • 5 years ago
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    I don't lol. If I don't do something or work, I go NUTS, but for the first time, I AM HAPPY ABOUT IT! LOL

  131. anonymous
    • 5 years ago
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    I KNOW!

  132. anonymous
    • 5 years ago
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    I want to do something crazy !

  133. anonymous
    • 5 years ago
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    I'll mis-match my clothes

  134. anonymous
    • 5 years ago
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    for a start LOL

  135. anonymous
    • 5 years ago
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    LOL.. Day off does not mean you just sleep all day long. It is just "freedom". You "DO" whatever you like

  136. anonymous
    • 5 years ago
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    I don't sleep LOL! with this energy I can't! I don't even sleep during afternoons, I go play outside, paint, smash something, read, solve, ....no solving lol ummmmmmm

  137. anonymous
    • 5 years ago
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    run around the house screaming

  138. anonymous
    • 5 years ago
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    jump in mud, get paint all over my face!

  139. anonymous
    • 5 years ago
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    oh this is AWESOME~

  140. anonymous
    • 5 years ago
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    :O

  141. anonymous
    • 5 years ago
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    lol

  142. anonymous
    • 5 years ago
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    I can be pretty wild at times~

  143. anonymous
    • 5 years ago
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    even though I sound so calm and innocent LOL, I can be devilish at times~ well.

  144. anonymous
    • 5 years ago
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    depends on my mood ^_^"

  145. anonymous
    • 5 years ago
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    sigh~

  146. anonymous
    • 5 years ago
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    I feel better letting all this out, thanks for listening to all this crap lol :)

  147. anonymous
    • 5 years ago
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    hope I didn't scare you? ._.

  148. anonymous
    • 5 years ago
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    I AM SO SCARED!!

  149. anonymous
    • 5 years ago
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    x_x I'm sorry

  150. anonymous
    • 5 years ago
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    after what? :(

  151. anonymous
    • 5 years ago
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    :(

  152. anonymous
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    T~T alright, no mud

  153. anonymous
    • 5 years ago
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    I am setting at the corner covered by a blanket :(

  154. anonymous
    • 5 years ago
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    >_> there are spiders there

  155. anonymous
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    OMG

  156. anonymous
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    can't believe you got scared from a girl ._.

  157. anonymous
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    LOL, awwww

  158. anonymous
    • 5 years ago
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    LOL

  159. anonymous
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    don't worry, I'm not telling a soul ^_^

  160. anonymous
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    :) LOL!

  161. anonymous
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    girls are more Frightening than guys btw

  162. anonymous
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    well, not all girls :)

  163. anonymous
    • 5 years ago
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    and let's just hope no one opens his/her group chat box ^_^

  164. anonymous
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    Generally speaking!!

  165. anonymous
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    and not all guys , lol

  166. anonymous
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    well, I don't fear anything, but God

  167. anonymous
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    ^_^

  168. anonymous
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    mashallah :)

  169. anonymous
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    there's nothing to be afraid off as long as you know that you're protected by the almighty :)

  170. anonymous
    • 5 years ago
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    When u do differentation u get 100000 as x for max(Y). but max x is only 60000, so, by substituting u get y=4, so total amt. p*x=240000.

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spraguer (Moderator)
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