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mathcalculus Group Title

helpppp: find the critical points: s(t)= (t-1)^4 (t+5)^3

  • one year ago
  • one year ago

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  1. calmat01 Group Title
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    @mathcalculus , what have you tried?

    • one year ago
  2. mathcalculus Group Title
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    yes, i used the product rule: \[\frac{ d }{ dx } (t-1)^{4}* (t+5)^{3}= (t-1)^{4} * 3(t+5)^{2} + (t+5)^{3} * 4(t-1)^{3}\]

    • one year ago
  3. mathcalculus Group Title
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    then from there, i'm stuck.

    • one year ago
  4. calmat01 Group Title
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    ok, so far so good. Now, factor out the greatest common factor of both terms. For example, they both have a factor of (t-1)^3, but that's not all they have in common. What else?

    • one year ago
  5. mathcalculus Group Title
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    ?

    • one year ago
  6. calmat01 Group Title
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    Don't they both have a factor of t+5 to a power?

    • one year ago
  7. mathcalculus Group Title
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    oh yes, but are from opposite sides..

    • one year ago
  8. calmat01 Group Title
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    doesn't matter the order. AB+CA=A(B+C)

    • one year ago
  9. mathcalculus Group Title
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    can you explain to me. i dont really see where we are going with factoring

    • one year ago
  10. calmat01 Group Title
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    The purpose in factoring is to simplify the derivative into a product of three factors. One of the factors will be t-1 to a power, a second factor will be t+5 to a power, and then you will be left with some factor containing a t as well.

    • one year ago
  11. calmat01 Group Title
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    And then once you have your derivative in factored form, you can set each factor equal to zero to find your critical points.

    • one year ago
  12. mathcalculus Group Title
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    can you show me

    • one year ago
  13. mathcalculus Group Title
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    i understand what youre saying but not how sure how to do that.

    • one year ago
  14. calmat01 Group Title
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    Ok, lets look at the t-1 term in each expression.

    • one year ago
  15. mathcalculus Group Title
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    ok

    • one year ago
  16. calmat01 Group Title
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    What is the largest exponent they share?

    • one year ago
  17. mathcalculus Group Title
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    3

    • one year ago
  18. mathcalculus Group Title
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    now i know that i write (t-1)^3

    • one year ago
  19. mathcalculus Group Title
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    but what happens to the 4?

    • one year ago
  20. calmat01 Group Title
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    Exactly, so, we may factor out a \[\left( t-1 \right)^{3}\] from both expressions. Hang on, we will come to that.

    • one year ago
  21. mathcalculus Group Title
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    k

    • one year ago
  22. calmat01 Group Title
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    Let's take a looke at the first expression in its entirety. If all you are removing is the \[\left( t-1 \right)^{3}\] You would be left with \[4\left( t+5 \right)^{3}\]

    • one year ago
  23. calmat01 Group Title
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    Do you see that?

    • one year ago
  24. mathcalculus Group Title
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    no if i was to see the common factor.. i would get (t-1)^3+ (t+5)^2.... then what do i do with the numbers that are left...?

    • one year ago
  25. calmat01 Group Title
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    ok,, there is your mistake. It isn't a sum. It's a product.

    • one year ago
  26. mathcalculus Group Title
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    ok so i dont see how you got 4(t+5)^3

    • one year ago
  27. calmat01 Group Title
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    Hang on, I was only talking about factoring out the t-1 from the first expression,, not from the whole thing.

    • one year ago
  28. mathcalculus Group Title
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    well you showed me that

    • one year ago
  29. calmat01 Group Title
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    Hang on my pc is giving me fits.

    • one year ago
  30. mathcalculus Group Title
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    kk

    • one year ago
  31. calmat01 Group Title
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    |dw:1363286087022:dw|

    • one year ago
  32. mathcalculus Group Title
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    why 4(t+5)?????

    • one year ago
  33. calmat01 Group Title
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    On the outside is what they both have in common, on ther inside is what is left after you have factored out that common factor.

    • one year ago
  34. mathcalculus Group Title
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    i understand this part... (t-1)^3* (t+5)^2

    • one year ago
  35. calmat01 Group Title
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    Rememmber when I was saying if all we factored out was the (t-1)^2 You would have the 4(t+5)^3 left.

    • one year ago
  36. mathcalculus Group Title
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    but then i dont understand why it is 4(t+5) ... i did this..4(t-1) + 3(t+5)

    • one year ago
  37. calmat01 Group Title
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    Well, now we include a (t+5)^2 as well, so what is left from the 4(t+5)^3? Just the 4(t+5).

    • one year ago
  38. mathcalculus Group Title
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    okkk

    • one year ago
  39. mathcalculus Group Title
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    i understand...

    • one year ago
  40. mathcalculus Group Title
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    im left with 7t+17

    • one year ago
  41. mathcalculus Group Title
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    t= -17/7

    • one year ago
  42. calmat01 Group Title
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    Perfect. So, now that each expression of the derivative is writtern in factored form, we set each of them equal to zero to find your critical points.

    • one year ago
  43. calmat01 Group Title
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    That is one of your critical points. There are two others.

    • one year ago
  44. mathcalculus Group Title
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    ok so (t-1)^3 = 0

    • one year ago
  45. calmat01 Group Title
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    Good.

    • one year ago
  46. mathcalculus Group Title
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    x= 0?

    • one year ago
  47. calmat01 Group Title
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    Not quite.

    • one year ago
  48. calmat01 Group Title
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    If (t-1)^3=0 then t=1

    • one year ago
  49. calmat01 Group Title
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    Now you have one more to do.

    • one year ago
  50. mathcalculus Group Title
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    1? how?

    • one year ago
  51. calmat01 Group Title
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    Tinme for lunch, I will come back shortly to see if you have finished it.

    • one year ago
  52. mathcalculus Group Title
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    the exponent is in the way.

    • one year ago
  53. calmat01 Group Title
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    Well, raise each side to the 1/3 power. That will get rid of your exponent.

    • one year ago
  54. calmat01 Group Title
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    brb

    • one year ago
  55. mathcalculus Group Title
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    kkk but how do we find the y

    • one year ago
  56. calmat01 Group Title
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    Just go back in and substitute the critical values.

    • one year ago
  57. calmat01 Group Title
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    For t=1 and t=-5, you will get y=0. But for t=-17/7, you won't get y=0.

    • one year ago
  58. mathcalculus Group Title
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    i did....

    • one year ago
  59. mathcalculus Group Title
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    (1-1)^4 (1+5)^3

    • one year ago
  60. mathcalculus Group Title
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    =0

    • one year ago
  61. mathcalculus Group Title
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    and -17/7 i got a huge number.. doesn;t make sense.. :(

    • one year ago
  62. mathcalculus Group Title
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    i got -432/823543

    • one year ago
  63. calmat01 Group Title
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    Well, you will need to raise some fractions with a denominator of 7 to the 4th and 3rd powers, so yeah, it will get rather ugly!

    • one year ago
  64. mathcalculus Group Title
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    ??

    • one year ago
  65. mathcalculus Group Title
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    i see that but it keeps saying the critical points are wrong.

    • one year ago
  66. mathcalculus Group Title
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    =(

    • one year ago
  67. calmat01 Group Title
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    ok, I need to see the original problem. And what keeps saying your critical points are wrong?

    • one year ago
  68. calmat01 Group Title
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    Are you using an online program?

    • one year ago
  69. mathcalculus Group Title
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    webwork.

    • one year ago
  70. mathcalculus Group Title
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    yes

    • one year ago
  71. calmat01 Group Title
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    hang on.

    • one year ago
  72. mathcalculus Group Title
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    • one year ago
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  73. mathcalculus Group Title
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    i attached it.

    • one year ago
  74. calmat01 Group Title
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    Your value for t=-17/7 is incorrect

    • one year ago
  75. mathcalculus Group Title
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    why?

    • one year ago
  76. calmat01 Group Title
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    You should get a large numerator divided by a denominator of 7^7.

    • one year ago
  77. mathcalculus Group Title
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    so i dont know where i went wrong...

    • one year ago
  78. calmat01 Group Title
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    The numerator should be (-24)^4(18)^3

    • one year ago
  79. mathcalculus Group Title
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    we did this step by step... now t is wrong?? really?

    • one year ago
  80. calmat01 Group Title
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    No, t is not wrong, but your evaluation of the function for t=-17/7 is incorrect.

    • one year ago
  81. mathcalculus Group Title
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    so now how do i solve that?

    • one year ago
  82. mathcalculus Group Title
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    obviously i know its wrong.

    • one year ago
  83. mathcalculus Group Title
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    ive tried this problem out 3294810347 times.

    • one year ago
  84. mathcalculus Group Title
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    now what do i do?

    • one year ago
  85. calmat01 Group Title
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    Should have (-17/7-1)^4(-17/7+5)^3

    • one year ago
  86. mathcalculus Group Title
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    huhhh???

    • one year ago
  87. calmat01 Group Title
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    \[-\frac{ 17 }{ 7 }-1=-\frac{ 24 }{ 7 }\] and \[-\frac{ 17 }{ 7 }+5=\frac{ 18 }{ 7 }\]

    • one year ago
  88. mathcalculus Group Title
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    wow this is insane. ive spent an hour to 2 with this problem.

    • one year ago
  89. mathcalculus Group Title
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    why?? why did we ignore the exponents???

    • one year ago
  90. calmat01 Group Title
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    Now raise each of those terms to the appropriate powers.

    • one year ago
  91. mathcalculus Group Title
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    sn;t it suppose to be part of it?? the original problem we were given??

    • one year ago
  92. mathcalculus Group Title
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    i did

    • one year ago
  93. calmat01 Group Title
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    we didn't I was just showing you step by step.

    • one year ago
  94. mathcalculus Group Title
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    thats how i got the hugeeeeeeee number

    • one year ago
  95. mathcalculus Group Title
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    and so did i. i had it on paper.

    • one year ago
  96. mathcalculus Group Title
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    what i dont understand is that youre basically saying raise those to the power.. in other words, im redoing this whole crap again.

    • one year ago
  97. calmat01 Group Title
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    Well, the numerator should be larger than your denominator, and it wasn't according to your answer.

    • one year ago
  98. mathcalculus Group Title
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    which AGAIN, is leading m to the wrong huge answer i had before

    • one year ago
  99. calmat01 Group Title
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    No, you are finding the y-value that goes with the value you ccame out for t.

    • one year ago
  100. mathcalculus Group Title
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    so there are 4 crtical points now?

    • one year ago
  101. mathcalculus Group Title
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    or 3??

    • one year ago
  102. mathcalculus Group Title
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    youre saying raise hem to the power and multiple right???

    • one year ago
  103. mathcalculus Group Title
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    do you know rasing them to the power is going to GIVE ME A HUGEEEEEE NUMBER??

    • one year ago
  104. mathcalculus Group Title
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    do you not see that was what i had in the first place??

    • one year ago
  105. calmat01 Group Title
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    There are only the three values of t we came up with, but you want them as ordered pairs, yo

    • one year ago
  106. mathcalculus Group Title
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    ok good3 values done.

    • one year ago
  107. mathcalculus Group Title
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    obviously i want them in order pairs.

    • one year ago
  108. mathcalculus Group Title
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    i did EXACTLY what you just did with the -17/7 and got those numbers.

    • one year ago
  109. calmat01 Group Title
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    I see that, but your answer for t=-17/7 showed a smaller numerator than denominator and it shouldd be the other way around.

    • one year ago
  110. mathcalculus Group Title
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    then show me.

    • one year ago
  111. mathcalculus Group Title
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    whats the y value for -17/7

    • one year ago
  112. calmat01 Group Title
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    How did you do that? Each numerator is larger than each denominator and they both have total of 7th powers.

    • one year ago
  113. mathcalculus Group Title
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    ok find the answer.

    • one year ago
  114. mathcalculus Group Title
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    i need to see if it's correct

    • one year ago
  115. mathcalculus Group Title
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    i cant keep wasting 2-3 hours on one problem.

    • one year ago
  116. mathcalculus Group Title
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    @calcmat, are you stuck?

    • one year ago
  117. calmat01 Group Title
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    \[\left(- \frac{ 24 }{ 7 } \right)^{4}\times \left( \frac{ 18 }{ 7} \right)\]

    • one year ago
  118. calmat01 Group Title
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    yeah

    • one year ago
  119. mathcalculus Group Title
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    now 18/7 needs to be raised to the 3rd power.

    • one year ago
  120. mathcalculus Group Title
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    ACCORDING TO THE ORIGINAL PROBLEM

    • one year ago
  121. calmat01 Group Title
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    Should gha have a 3 on the second expression for the power.

    • one year ago
  122. mathcalculus Group Title
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    and i just proved my point. you are taking em to the wrong direction AGAIN.

    • one year ago
  123. calmat01 Group Title
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    Correct.

    • one year ago
  124. calmat01 Group Title
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    What are you talking about.

    • one year ago
  125. mathcalculus Group Title
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    I ASKED YOU ONE SIMPLE QUESTION. CAN YOU FIND THE ANSWER?

    • one year ago
  126. mathcalculus Group Title
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    I WANT TO SEE IF WHAT YOU'RE DOING IS ACTUALLY CORRECT

    • one year ago
  127. mathcalculus Group Title
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    IVE SPENT 2-3 HOURS WITH YOU IN THIS PROBLEM.

    • one year ago
  128. calmat01 Group Title
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    Hey, don't get mad at me, I am the one spending MY TIME helping YOU.

    • one year ago
  129. mathcalculus Group Title
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    YOURE STILL NOT ANSWERING MY QUESTION.

    • one year ago
  130. calmat01 Group Title
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    You can answer the question by taking (-24/7)^4(18/7)^3

    • one year ago
  131. mathcalculus Group Title
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    I DID. STILL A HUGE NUMBER

    • one year ago
  132. calmat01 Group Title
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    I got 2349.5 rounded to 1 decimal place.

    • one year ago
  133. mathcalculus Group Title
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    WRONG BUDDY.

    • one year ago
  134. dan815 Group Title
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    (-1+t)^3 (5+t)^2 (17+7 t) your 0's = 1,-5,-17/7

    • one year ago
  135. mathcalculus Group Title
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    nvm. i''ll solve it

    • one year ago
  136. mathcalculus Group Title
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    thanks everyone.

    • one year ago
  137. calmat01 Group Title
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    Those are the ones I got @dan815

    • one year ago
  138. mathcalculus Group Title
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    that part is correct.

    • one year ago
  139. mathcalculus Group Title
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    and @calmat01 don't round. thats wrong.

    • one year ago
  140. mathcalculus Group Title
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    keep the numbers just the way they are. p.s found the answer. thanks.

    • one year ago
  141. calmat01 Group Title
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    Ok, so my answer wasn't completely off?

    • one year ago
  142. dan815 Group Title
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    mathcalculus can you prove the divergence theorem for me?

    • one year ago
  143. calmat01 Group Title
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    So you are telling me that you should have left the answer as 1934917632/823543? That's insane @mathcalculus

    • one year ago
  144. dan815 Group Title
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    what are all these big numbers?

    • one year ago
  145. mathcalculus Group Title
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    yes.

    • one year ago
  146. mathcalculus Group Title
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    lol insane.

    • one year ago
  147. mathcalculus Group Title
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    your explanation was confusing. but the numbers are correct.

    • one year ago
  148. calmat01 Group Title
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    Gee, I spent all that time being patient with you, and all I get is my explanation was confusing?

    • one year ago
  149. mathcalculus Group Title
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    lol truth to be told...truth be told.

    • one year ago
  150. calmat01 Group Title
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    I see. Well, if truth be told, the reason it was confusing was because you forgot how to factor. But I am not bitter. Take care and good luck with the rest of your assignment.

    • one year ago
  151. mathcalculus Group Title
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    I did factor. I just didn't put it up because I was trying to understand you. And also, you were throwing out numbers without reason. & I'm glad you're not so bitter to take my words sensibly:) Thank you.

    • one year ago
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