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anonymous

  • 5 years ago

given y>0 and dy/dx=3x^2+4x/y. if the point (1,sqrt{10}) is on the graph relating x and y, then what is y when x=0?

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  1. TuringTest
    • 5 years ago
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    no chance that's supposed to be dy/dx=(3x^2+4x)/y is it ?

  2. myininaya
    • 5 years ago
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    it is

  3. myininaya
    • 5 years ago
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    he didn't like my answer maybe you can try turing

  4. TuringTest
    • 5 years ago
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    Ah, I see... You should trust myininaya spikey

  5. anonymous
    • 5 years ago
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    lol i didnt understand it :(

  6. myininaya
    • 5 years ago
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    but no he might understand you better

  7. myininaya
    • 5 years ago
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    http://openstudy.com/study#/updates/4f1ccb76e4b04992dd23dbf3

  8. anonymous
    • 5 years ago
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    dy/dx=(3x^2+4x)/y yes thats correct

  9. myininaya
    • 5 years ago
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    this is what i did turing if you want to look

  10. anonymous
    • 5 years ago
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    yep thats the other one :) do you wanna work off here or of the other one.

  11. TuringTest
    • 5 years ago
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    ok... this is a very basic separation of variables problem, in which we can treat dy/dx like a regular fraction... dy/dx=(3x^2+4x)/y ydy=3x^2+4xdx now integrate both sides... but according to the other post you don't seem to know how integrate yet :/

  12. TuringTest
    • 5 years ago
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    you don't know how to integrate that* correct?

  13. anonymous
    • 5 years ago
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    hmm im not sure. if you mean using anti derivaties than sort of

  14. anonymous
    • 5 years ago
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    \[\int\limits_{?}^{?}\] but i havent used this yet

  15. TuringTest
    • 5 years ago
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    yes exactly antiderivatives

  16. myininaya
    • 5 years ago
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    \[\int\limits_{}^{}x^n dx=\frac{x^{n+1}}{n+1}+C, n \neq -1\]

  17. myininaya
    • 5 years ago
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    or you could say the antiderivative of x^n = that

  18. anonymous
    • 5 years ago
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    ahh yes that sort of makes sense.

  19. anonymous
    • 5 years ago
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    i understand that c is a constant.

  20. TuringTest
    • 5 years ago
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    check that the derivative of that gives x^n

  21. myininaya
    • 5 years ago
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    right

  22. anonymous
    • 5 years ago
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    the derivative of ydy=(3x^2+4x)dx?

  23. TuringTest
    • 5 years ago
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    antiderivative of that

  24. myininaya
    • 5 years ago
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    no we want to integrate both sides or we can use the term antiderivative

  25. myininaya
    • 5 years ago
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    like turing said

  26. anonymous
    • 5 years ago
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    ahh okay.

  27. TuringTest
    • 5 years ago
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    so what is the antiderivative of ydy according to the formula myin posted?

  28. anonymous
    • 5 years ago
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    x^3

  29. anonymous
    • 5 years ago
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    for 3x^2

  30. anonymous
    • 5 years ago
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    i dont know for 4x

  31. TuringTest
    • 5 years ago
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    yes but that is not ydy... like I said, I can't use latex, myin will have to show you

  32. myininaya
    • 5 years ago
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    \[\int\limits_{}^{}y dy =\int\limits_{}^{}y^1 dy=\frac{y^{1+1}}{1+1}+c_1\]

  33. myininaya
    • 5 years ago
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    see n was 1 here

  34. anonymous
    • 5 years ago
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    okay im struggling alot right now because i havent had enough practice with this.

  35. myininaya
    • 5 years ago
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    its cool

  36. myininaya
    • 5 years ago
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    struggling happens but the main is don't give up

  37. anonymous
    • 5 years ago
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    okay so the rule is for 3x^2 x^n+1

  38. anonymous
    • 5 years ago
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    what formula for the 4x?

  39. anonymous
    • 5 years ago
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    the anti derivative of dx is x?

  40. TuringTest
    • 5 years ago
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    4x=4x^(1) so we can use the same formula integral of (x^n)dx=x^(n+1)/(n+1)

  41. myininaya
    • 5 years ago
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    \[\int\limits_{}^{}3x^2 dx=3 \int\limits_{}^{}x^2 dx=3 \cdot \frac{x^{2+1}}{2+1}+c_2\]

  42. myininaya
    • 5 years ago
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    \[\int\limits_{}^{}4x dx=4 \int\limits_{}^{}x dx=4\int\limits_{}^{}x^1 dx=4 \cdot \frac{x^{1+1}}{1+1}+c_3\]

  43. myininaya
    • 5 years ago
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    see i'm using that same formula every time

  44. anonymous
    • 5 years ago
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    oh okay so i have to do it for each.

  45. myininaya
    • 5 years ago
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    right

  46. myininaya
    • 5 years ago
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    \[\int\limits_{}^{}(f(x)+g(x))dx=\int\limits_{}^{}f(x) dx+\int\limits_{}^{}g(x)dx\]

  47. myininaya
    • 5 years ago
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    so we have \[\frac{y^2}{2}+c_1=3 \cdot \frac{x^{2+1}}{2+1}+c_2+4 \cdot \frac{x^{1+1}}{1+1}+c_3\]

  48. anonymous
    • 5 years ago
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    so for the formula ydy you used the formula.

  49. anonymous
    • 5 years ago
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    okay i understand how u got that equation.

  50. myininaya
    • 5 years ago
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    or you could write instead \[\frac{y^2}{2}=3 \cdot \frac{x^{2+1}}{2+1}+4 \cdot \frac{x^{1+1}}{1+1}+C\] since the sum of some constants is still a constant

  51. anonymous
    • 5 years ago
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    yes

  52. myininaya
    • 5 years ago
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    ok great! lets make this prettier

  53. myininaya
    • 5 years ago
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    \[\frac{y^2}{2}=x^3+2 x^2+C\]

  54. myininaya
    • 5 years ago
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    is that okay?

  55. anonymous
    • 5 years ago
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    yes my simplification came out the same

  56. myininaya
    • 5 years ago
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    ok we can also multiply two on both sides

  57. myininaya
    • 5 years ago
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    \[y^2=2x^3+4x^2+C\]

  58. myininaya
    • 5 years ago
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    2C is still constant so I left it as C

  59. anonymous
    • 5 years ago
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    yes

  60. myininaya
    • 5 years ago
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    you can write 2C if you feel more comfortable with that

  61. anonymous
    • 5 years ago
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    and now square both sides?

  62. myininaya
    • 5 years ago
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    square root of both sides

  63. myininaya
    • 5 years ago
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    we don't need to keep the negative value since your directions say y>0

  64. anonymous
    • 5 years ago
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    where do we have a negative value?

  65. myininaya
    • 5 years ago
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    take square root of both sides you get plus or minus

  66. anonymous
    • 5 years ago
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    thats right!

  67. myininaya
    • 5 years ago
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    we only need the plus since y>0

  68. myininaya
    • 5 years ago
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    so what I'm saying is that we have \[y=\sqrt{2x^3+4x^2+C}\]

  69. anonymous
    • 5 years ago
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    yes.

  70. myininaya
    • 5 years ago
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    you were given a point on this curve

  71. myininaya
    • 5 years ago
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    \[ (1,\sqrt{10} )\]

  72. myininaya
    • 5 years ago
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    x=1 and y=sqrt(10)

  73. anonymous
    • 5 years ago
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    yes i plug it in for x and y?

  74. myininaya
    • 5 years ago
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    so we can use this to find C

  75. myininaya
    • 5 years ago
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    \[\sqrt{10}=\sqrt{2 (1)^3+4(1)^2+C}\] => \[10=2(1)^3+4(1)^2+C\]

  76. myininaya
    • 5 years ago
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    \[10=2+4+C\]

  77. myininaya
    • 5 years ago
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    =>C=4

  78. myininaya
    • 5 years ago
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    so we have \[y=\sqrt{2x^3+4x^2+4} \]

  79. myininaya
    • 5 years ago
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    you wanted to know y when x=0, right?

  80. anonymous
    • 5 years ago
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    yes

  81. myininaya
    • 5 years ago
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    so how do you think we do that?

  82. myininaya
    • 5 years ago
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    i brb i think it will be pretty easy for turing to help without latex on this last part that you have to do

  83. anonymous
    • 5 years ago
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    okay turing i get now :D

  84. anonymous
    • 5 years ago
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    but i need help finishing

  85. myininaya
    • 5 years ago
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    ok i'm back

  86. myininaya
    • 5 years ago
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    i had to get my glasses

  87. myininaya
    • 5 years ago
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    so i can be fully nerd

  88. anonymous
    • 5 years ago
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    lol

  89. myininaya
    • 5 years ago
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    so we have \[y=\sqrt{2x^3+4x^2+4}\]

  90. anonymous
    • 5 years ago
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    yes

  91. myininaya
    • 5 years ago
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    it says what is y if x=0

  92. myininaya
    • 5 years ago
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    \[y=\sqrt{2(0)^3+4(0)^2+4}\]

  93. myininaya
    • 5 years ago
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    i replaced x with 0 so I can see what y is when x is 0

  94. myininaya
    • 5 years ago
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    \[y=\sqrt{0+0+4}=\sqrt{4}=2\]

  95. myininaya
    • 5 years ago
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    This says when x is 0, y is 2

  96. anonymous
    • 5 years ago
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    got it! :D thank you!!!! sorry i didnt really try hard enough before you were a great help!

  97. myininaya
    • 5 years ago
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    It is okay. I didn't think any offense to anything you did. Sometimes you may get someone who can explain it better. I know that I'm probably not the best explaining some things.

  98. myininaya
    • 5 years ago
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    Or you know like I way you prefer.

  99. anonymous
    • 5 years ago
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    lol yeah :D thanks again.

  100. myininaya
    • 5 years ago
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    np

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