## 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

1. 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?

2. freckles

$\frac{\pi \cdot r_1^2 -\pi \cdot r_2^2}{r_1-r_2} \\ \pi \frac{r_1^2-r_2^2}{r_1-r_2} \\ \pi \frac{(r_1-r_2)(r_1+r_2)}{r_1-r_2} \\ \pi (r_1+r_2)$

3. anonymous

2pi(2) + 2pi(3) ------------- is this right? 2

4. anonymous

for part (i)

5. 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

6. freckles

all you have to do is add your r's and then multiply the result by pi

7. anonymous

Ahhh I see! That makes sense!

8. freckles

like I started with the one formula change of area divided by change or radi

9. freckles

$\text{ average rate iof change of area}=\frac{A(r_1)-A(r_2)}{r_1-r_2}$

10. freckles

but was able to simplify this to that really pretty formula

11. anonymous

Right, and that gives us the avg rate of change of area

12. anonymous

Oh that sure is a beautiful formula *_*

13. freckles

right if you wanted instantaneous rate of change at some r you would find the derivative then plug in that r

14. anonymous

Ohhh true!!

15. sepeario

how do you type text like that in the formula thing?

16. anonymous

@freckles thanks again!! :)

17. anonymous

@Sepeario click on 'equation'

18. sepeario

yeah but it always italicises the text

19. freckles

$\frac{ \text{ kitty eats kitten food} }{\text{ how to do } 5+\frac{6}{7} \text{ in a fraction }}$

20. freckles

\frac{ \text{ kitty eats kitten food} }{\text{ how to do } 5+\frac{6}{7} \text{ in a fraction }}

21. sepeario

how do you write normal text like that inside the equation thing?

22. anonymous

Ohh hmm I have no clue, @freckles should know :P

23. freckles

:) yes lol |dw:1433574618995:dw| put around that just wherever you want text do \text{ }

24. anonymous

Oooooh how did you know that?? :O

25. sepeario

oh thanks so much

26. freckles

just a little experience with LaTeX

27. freckles

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

Awesomeness ;D

29. anonymous

Oh is there?

30. freckles

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

Thats great!! Thanks for the link! It'll be useful! :D

32. freckles

By the way I do not claim to be a genius at it

33. freckles

I just know some basic things

34. anonymous

It's still a lot more that I know :P

35. anonymous

than*

36. yrelhan4

The "beautiful formula" thing kinda made me laugh. :P Nice explanation though. :)

37. anonymous

Haha @yrelhan4 yeah same here xD and yes, @freckles explains perfectly!

38. freckles

awww how kind

39. anonymous

^_^ just being honest :D

40. freckles

goodnight and thanks good luck with calculus

41. anonymous

@freckles G'night and thank YOU for helping me out so much! Thanks! :)

42. freckles

It was no problem

43. anonymous

:) Sleep well