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anonymous

  • one year ago

I don't know how to approach this question (help would be greatly appreciated!) Find the average rate of change of the area of the circle with respect to its radius r as r changes from: (i) 2 to 3, (ii) 2 to 2.5, (iii) 2 to 2.1

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  1. anonymous
    • one year ago
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    Oh actually I think I got it... I differentiate pi*r^2 and then plug in the two values given and then find the average , right?

  2. freckles
    • one year ago
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    \[\frac{\pi \cdot r_1^2 -\pi \cdot r_2^2}{r_1-r_2} \\ \pi \frac{r_1^2-r_2^2}{r_1-r_2} \\ \pi \frac{(r_1-r_2)(r_1+r_2)}{r_1-r_2} \\ \pi (r_1+r_2)\]

  3. anonymous
    • one year ago
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    2pi(2) + 2pi(3) ------------- is this right? 2

  4. anonymous
    • one year ago
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    for part (i)

  5. freckles
    • one year ago
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    \[\frac{\pi \cdot r_1^2 -\pi \cdot r_2^2}{r_1-r_2} \\ \pi \frac{r_1^2-r_2^2}{r_1-r_2} \\ \pi \frac{(r_1-r_2)(r_1+r_2)}{r_1-r_2} \\ \pi (r_1+r_2)\] this is the average rate of change of the area with respect to radius

  6. freckles
    • one year ago
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    all you have to do is add your r's and then multiply the result by pi

  7. anonymous
    • one year ago
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    Ahhh I see! That makes sense!

  8. freckles
    • one year ago
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    like I started with the one formula change of area divided by change or radi

  9. freckles
    • one year ago
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    \[\text{ average rate iof change of area}=\frac{A(r_1)-A(r_2)}{r_1-r_2}\]

  10. freckles
    • one year ago
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    but was able to simplify this to that really pretty formula

  11. anonymous
    • one year ago
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    Right, and that gives us the avg rate of change of area

  12. anonymous
    • one year ago
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    Oh that sure is a beautiful formula *_*

  13. freckles
    • one year ago
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    right if you wanted instantaneous rate of change at some r you would find the derivative then plug in that r

  14. anonymous
    • one year ago
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    Ohhh true!!

  15. sepeario
    • one year ago
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    how do you type text like that in the formula thing?

  16. anonymous
    • one year ago
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    @freckles thanks again!! :)

  17. anonymous
    • one year ago
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    @Sepeario click on 'equation'

  18. sepeario
    • one year ago
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    yeah but it always italicises the text

  19. freckles
    • one year ago
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    \[\frac{ \text{ kitty eats kitten food} }{\text{ how to do } 5+\frac{6}{7} \text{ in a fraction }}\]

  20. freckles
    • one year ago
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    \frac{ \text{ kitty eats kitten food} }{\text{ how to do } 5+\frac{6}{7} \text{ in a fraction }}

  21. sepeario
    • one year ago
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    how do you write normal text like that inside the equation thing?

  22. anonymous
    • one year ago
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    Ohh hmm I have no clue, @freckles should know :P

  23. freckles
    • one year ago
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    :) yes lol |dw:1433574618995:dw| put around that just wherever you want text do \text{ }

  24. anonymous
    • one year ago
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    Oooooh how did you know that?? :O

  25. sepeario
    • one year ago
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    oh thanks so much

  26. freckles
    • one year ago
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    just a little experience with LaTeX

  27. freckles
    • one year ago
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    I had to look up some things and also there is a LaTeX group if you want to get really good at it

  28. anonymous
    • one year ago
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    Awesomeness ;D

  29. anonymous
    • one year ago
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    Oh is there?

  30. freckles
    • one year ago
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    http://openstudy.com/study#/groups/LaTeX%20Practicing!%20%3A) there are some tutorials you can find somewhere in these threads they have posted

  31. anonymous
    • one year ago
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    Thats great!! Thanks for the link! It'll be useful! :D

  32. freckles
    • one year ago
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    By the way I do not claim to be a genius at it

  33. freckles
    • one year ago
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    I just know some basic things

  34. anonymous
    • one year ago
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    It's still a lot more that I know :P

  35. anonymous
    • one year ago
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    than*

  36. yrelhan4
    • one year ago
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    The "beautiful formula" thing kinda made me laugh. :P Nice explanation though. :)

  37. anonymous
    • one year ago
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    Haha @yrelhan4 yeah same here xD and yes, @freckles explains perfectly!

  38. freckles
    • one year ago
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    awww how kind

  39. anonymous
    • one year ago
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    ^_^ just being honest :D

  40. freckles
    • one year ago
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    goodnight and thanks good luck with calculus

  41. anonymous
    • one year ago
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    @freckles G'night and thank YOU for helping me out so much! Thanks! :)

  42. freckles
    • one year ago
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    It was no problem

  43. anonymous
    • one year ago
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    :) Sleep well

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