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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
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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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh 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
 one year ago
Best ResponseYou've already chosen the best response.3\[\frac{\pi \cdot r_1^2 \pi \cdot r_2^2}{r_1r_2} \\ \pi \frac{r_1^2r_2^2}{r_1r_2} \\ \pi \frac{(r_1r_2)(r_1+r_2)}{r_1r_2} \\ \pi (r_1+r_2)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.02pi(2) + 2pi(3)  is this right? 2

freckles
 one year ago
Best ResponseYou've already chosen the best response.3\[\frac{\pi \cdot r_1^2 \pi \cdot r_2^2}{r_1r_2} \\ \pi \frac{r_1^2r_2^2}{r_1r_2} \\ \pi \frac{(r_1r_2)(r_1+r_2)}{r_1r_2} \\ \pi (r_1+r_2)\] this is the average rate of change of the area with respect to radius

freckles
 one year ago
Best ResponseYou've already chosen the best response.3all you have to do is add your r's and then multiply the result by pi

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ahhh I see! That makes sense!

freckles
 one year ago
Best ResponseYou've already chosen the best response.3like I started with the one formula change of area divided by change or radi

freckles
 one year ago
Best ResponseYou've already chosen the best response.3\[\text{ average rate iof change of area}=\frac{A(r_1)A(r_2)}{r_1r_2}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.3but was able to simplify this to that really pretty formula

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Right, and that gives us the avg rate of change of area

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh that sure is a beautiful formula *_*

freckles
 one year ago
Best ResponseYou've already chosen the best response.3right if you wanted instantaneous rate of change at some r you would find the derivative then plug in that r

sepeario
 one year ago
Best ResponseYou've already chosen the best response.0how do you type text like that in the formula thing?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@freckles thanks again!! :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@Sepeario click on 'equation'

sepeario
 one year ago
Best ResponseYou've already chosen the best response.0yeah but it always italicises the text

freckles
 one year ago
Best ResponseYou've already chosen the best response.3\[\frac{ \text{ kitty eats kitten food} }{\text{ how to do } 5+\frac{6}{7} \text{ in a fraction }}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.3\frac{ \text{ kitty eats kitten food} }{\text{ how to do } 5+\frac{6}{7} \text{ in a fraction }}

sepeario
 one year ago
Best ResponseYou've already chosen the best response.0how do you write normal text like that inside the equation thing?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ohh hmm I have no clue, @freckles should know :P

freckles
 one year ago
Best ResponseYou've already chosen the best response.3:) yes lol dw:1433574618995:dw put around that just wherever you want text do \text{ }

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oooooh how did you know that?? :O

freckles
 one year ago
Best ResponseYou've already chosen the best response.3just a little experience with LaTeX

freckles
 one year ago
Best ResponseYou've already chosen the best response.3I had to look up some things and also there is a LaTeX group if you want to get really good at it

freckles
 one year ago
Best ResponseYou've already chosen the best response.3http://openstudy.com/study#/groups/LaTeX%20Practicing!%20%3A) there are some tutorials you can find somewhere in these threads they have posted

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thats great!! Thanks for the link! It'll be useful! :D

freckles
 one year ago
Best ResponseYou've already chosen the best response.3By the way I do not claim to be a genius at it

freckles
 one year ago
Best ResponseYou've already chosen the best response.3I just know some basic things

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It's still a lot more that I know :P

yrelhan4
 one year ago
Best ResponseYou've already chosen the best response.0The "beautiful formula" thing kinda made me laugh. :P Nice explanation though. :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Haha @yrelhan4 yeah same here xD and yes, @freckles explains perfectly!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0^_^ just being honest :D

freckles
 one year ago
Best ResponseYou've already chosen the best response.3goodnight and thanks good luck with calculus

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@freckles G'night and thank YOU for helping me out so much! Thanks! :)
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