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burhan101

  • 2 years ago

Solve for r

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  1. burhan101
    • 2 years ago
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    \[\large 0=\frac{ r-2700 }{ r^2 }+62 \pi r\]

  2. calculusxy
    • 2 years ago
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    You are trying to find the area of a radius?

  3. calculusxy
    • 2 years ago
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    Sorry I meant the area of a circle.

  4. burhan101
    • 2 years ago
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    No it's an optimization problem I am trying to do, I just need to solve for 'r'

  5. calculusxy
    • 2 years ago
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    Oh I thought that because the formula to finding the area of a circle,you have to first square the radius and then multiply it by pi (r^2)3.14.

  6. SmoothMath
    • 2 years ago
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    Multiply everything by r^2. Then factor out an r. From there it's a quadratic.

  7. SmoothMath
    • 2 years ago
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    Oh my bad. You actually get a cubic.

  8. burhan101
    • 2 years ago
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    top and bottom or just top?

  9. SmoothMath
    • 2 years ago
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    Multiply everything by r^2. When you multiply the fraction, multiply on top.

  10. burhan101
    • 2 years ago
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    \[r^2 or \frac{ r^2 }{ r^2 }\]

  11. SmoothMath
    • 2 years ago
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    Just r^2

  12. burhan101
    • 2 years ago
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    yeah so woulnt that cancel out with the fraction

  13. SmoothMath
    • 2 years ago
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    Yes =) That's the point. It gets r out of the denominator.

  14. burhan101
    • 2 years ago
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    ohh i thought you were also telling me to muktiply the top by r^3 so the function would be diff, i misunderstood

  15. SmoothMath
    • 2 years ago
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    \(\huge 0 = \frac{r-2700}{r^2} + 62\pi*r\) multiply everything by r^2 \(\huge (0)*r^2 = (\frac{r-2700}{r^2})*r^2 + (62\pi*r)*r^2\)

  16. SmoothMath
    • 2 years ago
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    Gives: \(\huge 0 = r-2700 + 62\pi*r^3\)

  17. SmoothMath
    • 2 years ago
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    And honestly from there your best bet is to use a cubic solver of some sort. Wolfram Alpha should do just fine.

  18. burhan101
    • 2 years ago
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    |dw:1371520632051:dw| yeah but the thing is like during an exam i cant use it :P

  19. Bad2zBone
    • 2 years ago
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    Are you sure the question is correct?

  20. burhan101
    • 2 years ago
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    @Bad2zBone yes

  21. Bad2zBone
    • 2 years ago
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    I suggest you double check, because you will not solve this without the aid of wolfaplha

  22. burhan101
    • 2 years ago
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    here is the question and my solution

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  23. Bad2zBone
    • 2 years ago
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    I suggest you take a look at this http://gbbservices.com/math/cubic.html

  24. SmoothMath
    • 2 years ago
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    Okay on the step where you take C', you make incorrect use of the quotient rule. The derivative of the top will be 0.

  25. SmoothMath
    • 2 years ago
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    The correct derivative is: \(\Large C' = \frac{-27900}{r^2} + 62\pi*r\)

  26. SmoothMath
    • 2 years ago
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    Set the derivative equal to 0 and solve: \(\Large \frac{-27900}{r^2} + 62\pi*r = 0\) \(\Large (\frac{-27900}{r^2} + 62\pi*r)*r^2 = 0*r^2\) \(\Large -27900 + 62\pi*r^3 = 0\) \(\Large 62\pi*r^3 = 27900\) You good from there?

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