anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
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?
freckles
  • freckles
\[\frac{\pi \cdot r_1^2 -\pi \cdot r_2^2}{r_1-r_2} \\ \pi \frac{r_1^2-r_2^2}{r_1-r_2} \\ \pi \frac{(r_1-r_2)(r_1+r_2)}{r_1-r_2} \\ \pi (r_1+r_2)\]
anonymous
  • anonymous
2pi(2) + 2pi(3) ------------- is this right? 2

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anonymous
  • anonymous
for part (i)
freckles
  • freckles
\[\frac{\pi \cdot r_1^2 -\pi \cdot r_2^2}{r_1-r_2} \\ \pi \frac{r_1^2-r_2^2}{r_1-r_2} \\ \pi \frac{(r_1-r_2)(r_1+r_2)}{r_1-r_2} \\ \pi (r_1+r_2)\] this is the average rate of change of the area with respect to radius
freckles
  • freckles
all you have to do is add your r's and then multiply the result by pi
anonymous
  • anonymous
Ahhh I see! That makes sense!
freckles
  • freckles
like I started with the one formula change of area divided by change or radi
freckles
  • freckles
\[\text{ average rate iof change of area}=\frac{A(r_1)-A(r_2)}{r_1-r_2}\]
freckles
  • freckles
but was able to simplify this to that really pretty formula
anonymous
  • anonymous
Right, and that gives us the avg rate of change of area
anonymous
  • anonymous
Oh that sure is a beautiful formula *_*
freckles
  • freckles
right if you wanted instantaneous rate of change at some r you would find the derivative then plug in that r
anonymous
  • anonymous
Ohhh true!!
Sepeario
  • Sepeario
how do you type text like that in the formula thing?
anonymous
  • anonymous
@freckles thanks again!! :)
anonymous
  • anonymous
@Sepeario click on 'equation'
Sepeario
  • Sepeario
yeah but it always italicises the text
freckles
  • freckles
\[\frac{ \text{ kitty eats kitten food} }{\text{ how to do } 5+\frac{6}{7} \text{ in a fraction }}\]
freckles
  • freckles
\frac{ \text{ kitty eats kitten food} }{\text{ how to do } 5+\frac{6}{7} \text{ in a fraction }}
Sepeario
  • Sepeario
how do you write normal text like that inside the equation thing?
anonymous
  • anonymous
Ohh hmm I have no clue, @freckles should know :P
freckles
  • freckles
:) yes lol |dw:1433574618995:dw| put around that just wherever you want text do \text{ }
anonymous
  • anonymous
Oooooh how did you know that?? :O
Sepeario
  • Sepeario
oh thanks so much
freckles
  • freckles
just a little experience with LaTeX
freckles
  • freckles
I had to look up some things and also there is a LaTeX group if you want to get really good at it
anonymous
  • anonymous
Awesomeness ;D
anonymous
  • anonymous
Oh is there?
freckles
  • freckles
http://openstudy.com/study#/groups/LaTeX%20Practicing!%20%3A) there are some tutorials you can find somewhere in these threads they have posted
anonymous
  • anonymous
Thats great!! Thanks for the link! It'll be useful! :D
freckles
  • freckles
By the way I do not claim to be a genius at it
freckles
  • freckles
I just know some basic things
anonymous
  • anonymous
It's still a lot more that I know :P
anonymous
  • anonymous
than*
yrelhan4
  • yrelhan4
The "beautiful formula" thing kinda made me laugh. :P Nice explanation though. :)
anonymous
  • anonymous
Haha @yrelhan4 yeah same here xD and yes, @freckles explains perfectly!
freckles
  • freckles
awww how kind
anonymous
  • anonymous
^_^ just being honest :D
freckles
  • freckles
goodnight and thanks good luck with calculus
anonymous
  • anonymous
@freckles G'night and thank YOU for helping me out so much! Thanks! :)
freckles
  • freckles
It was no problem
anonymous
  • anonymous
:) Sleep well

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