Question

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

Answer 1

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?

Answer 2

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

Answer 3

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

Answer 4

for part (i)

Answer 5

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

Answer 6

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

Answer 7

Ahhh I see! That makes sense!

Answer 8

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

Answer 9

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

Answer 10

but was able to simplify this to that really pretty formula

Answer 11

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

Answer 12

Oh that sure is a beautiful formula *_*

Answer 13

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

Answer 14

Ohhh true!!

Answer 15

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

Answer 16

@freckles thanks again!! :)

Answer 17

@Sepeario click on 'equation'

Answer 18

yeah but it always italicises the text

Answer 19

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

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

:) yes lol


put around that

just wherever you want text do \text{ }

Answer 24

Oooooh how did you know that?? :O

Answer 25

oh thanks so much

Answer 26

just a little experience with LaTeX

Answer 27

I had to look up some things and also there is a LaTeX group if you want to get really good at it

Answer 28

Awesomeness ;D

Answer 29

Oh is there?

Answer 30

http://openstudy.com/study#/groups/LaTeX%20Practicing!%20%3A)

there are some tutorials you can find somewhere in these threads they have posted

Answer 31

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

Answer 32

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

Answer 33

I just know some basic things

Answer 34

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

Answer 35

than*

Answer 36

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

Answer 37

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

Answer 38

awww how kind

Answer 39

^_^ just being honest :D

Answer 40

goodnight and thanks
good luck with calculus

Answer 41

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

Answer 42

It was no problem

Answer 43

:) Sleep well