system (03:49:22:004 PM): Mod2 entered the Room2 chat room.
system (04:08:17:048 PM): hayley entered the Room2 chat room.
system (04:08:27:426 PM): hayley left the Room2 chat room.
system (04:12:23:547 PM): racshattuck entered the Room2 chat room.
Mod2 (04:12:36:641 PM): do you feel better about pi now, rachshat?

system (04:12:41:161 PM): Ian entered the Room2 chat room.
Ian (04:12:48:643 PM): Hi rac
racshattuck (04:12:50:512 PM): hello i need help with mutiplactation
system (04:12:55:305 PM): mijitpride entered the Room2 chat room.
Ian (04:12:58:769 PM): Can you give me an example?
mijitpride (04:13:07:898 PM): hey ian ... i have a question
system (04:13:08:983 PM): omega entered the Room2 chat room.
Ian (04:13:13:797 PM): Hi mijit.  rac is having trouble with multiplication.
racshattuck (04:13:32:641 PM): 34578 times 567
Mod2 (04:13:44:730 PM): Sure... racshat... what don't you understand?

Ian (04:13:59:387 PM): That's a big one.  Are you okay on smaller ones?  Like 57 times 8?
racshattuck (04:14:09:859 PM): well it is hard
Ian (04:14:10:824 PM): Try that one.
racshattuck (04:14:54:317 PM): 456
Ian (04:15:01:984 PM): Excellent!  What if it was 57 times 80?
Mod2 (04:15:03:862 PM): are you sure about your answer, racshat?

racshattuck (04:15:47:782 PM): 4560
racshattuck (04:16:03:885 PM): that was easy you had to add a 0
Mod2 (04:16:04:294 PM): what about 57 times pi?

Ian (04:16:21:723 PM): Dealing with bigger numbers is mostly about adding zeros. 
racshattuck (04:16:25:617 PM): i do not know how 
Ian (04:17:07:889 PM): What does the 100 represent?
racshattuck (04:17:40:557 PM): radius
Ian (04:17:50:319 PM): I thought 10 was the radius.
Mod2 (04:18:08:593 PM): Hint:  an easy way to erase a small area of the whiteboard is to draw a white, filled 

 rectangle on top of itracshattuck (04:18:20:595 PM): it is but you have to times 10 times 10
Ian (04:18:34:031 PM): Oh, were you finding the area of the circle?
racshattuck (04:18:46:040 PM): yes
Mod2 (04:19:16:263 PM): Ah!  you seem pretty good about multiplications, ratshack!

Ian (04:19:19:620 PM): Okay, so it looks like you're on the right track.
mijitpride (04:19:42:313 PM): hey ian
mijitpride (04:19:59:169 PM): can you show me algrebraically what this is equal to ....
system (04:21:26:627 PM): racshattuck left the Room2 chat room.
Ian (04:22:09:824 PM): I don't know offhand what that's equal to.
Ian (04:22:13:558 PM): Maybe we can figure it out. 
omega (04:22:20:866 PM): I need to find the simplest form of..

omega (04:22:45:268 PM): do I add the exponents of multiply?

omega (04:22:49:751 PM): or*

Ian (04:22:50:899 PM): You know that m^4 = m*m*m*m, right?
omega (04:22:56:352 PM): Yeah

Ian (04:22:58:751 PM): And m^2 = m*m?
omega (04:23:05:979 PM): I just forgot if I add or multiply the exponents

Ian (04:23:07:451 PM): So what if you multiply those together?  What do you get?
Ian (04:23:33:072 PM): Try actually doing it: (m*m*m*m)*(m*m) = ?
omega (04:23:53:989 PM): huh

omega (04:24:02:943 PM): I'm terrible at algebra.

Ian (04:24:34:497 PM): Here's a similar example:  (m*m*m)*(m*m) = m*m*m*m*m
Mod2 (04:26:13:020 PM): So, that was m^3 * m^2 ritht, Ian?

system (04:26:53:228 PM): omega left the Room2 chat room.
Mod2 (04:27:22:044 PM): Oops, we lost omega... hopefully he got his question answered

mijitpride (04:28:47:939 PM): thanks for that website ian
Ian (04:29:14:856 PM): So this is kind of like Euler's equation.
Ian (04:29:29:284 PM): You write down something using symbols you have, and it may or may not make sense... but you see where it goes.
mijitpride (04:30:04:156 PM): yea yea ... definitely
Ian (04:30:18:530 PM): What else have you been wondering about lately?
mijitpride (04:30:37:132 PM): how long would it take to teach someone to integrate ....... hence ....
Ian (04:30:57:329 PM): It depends on how well they have to know it.
Ian (04:30:59:915 PM): :^D
Ian (04:31:12:404 PM): I mean, you could learn what integration _means_, and how it works, in about 5 minutes.
Ian (04:31:35:493 PM): But then there are all kinds of specific techniques for specific integrals, and that takes years.
mijitpride (04:31:43:401 PM): i just want to learn something new ... yea .. im not even in calc yet .. i was just wondering cause my brother was showing me his diff eq work
mijitpride (04:36:01:382 PM): you still there>?
Ian (04:36:10:993 PM): Sorry, yeah.
Ian (04:36:17:694 PM): Suppose we have that curve I just drew.  It's equation is y = -(x-1)^2 + 1
Ian (04:36:24:888 PM):  Suppose you wanted to find the area under it.  How could you do that?
mijitpride (04:36:55:925 PM): integrate?
Ian (04:37:10:066 PM): Right, but you don't know how to integrate.  What else might you try?
mijitpride (04:37:31:616 PM): if i want a close answer but not exact i would
mijitpride (04:37:51:170 PM): and so on
Ian (04:38:00:655 PM): Right. 
Ian (04:38:10:446 PM): SO how could you calculate that?
mijitpride (04:38:53:628 PM): (a1)(b1)+(a2)(b2)+ ......
Ian (04:39:06:078 PM): What are your a and b terms?
mijitpride (04:39:30:345 PM): x and y values for each rectangle under the curve
Ian (04:40:26:247 PM): One is width, and one is height?
mijitpride (04:40:50:020 PM): yea
Ian (04:41:29:709 PM): I guess you can just choose the width.  But how would you find the height of each one?
mijitpride (04:42:35:851 PM): determine the slope of the curve at the top of it and somehow derive the y value
Ian (04:43:02:916 PM): How does the slope help you?
mijitpride (04:44:14:871 PM): you could plug an x value into the equation
Ian (04:44:22:862 PM): Which equation?
mijitpride (04:44:55:797 PM): the equation for the parabola
Ian (04:46:32:423 PM): So, if you know that x is the lower left corner of one of those rectangles, and w is the width of each one, what is the height?
system (04:47:06:958 PM): mijitpride left the Room2 chat room.
system (04:54:22:890 PM): mijitpride entered the Room2 chat room.
Ian (04:54:28:900 PM): Hi,  Where'd ya go?
mijitpride (04:54:40:724 PM): my compuet screwed up
Ian (04:54:57:113 PM): Windows machine?  :^D
mijitpride (04:55:49:816 PM): nahh ... mac ... i dont do windows
mijitpride (04:56:10:504 PM): its cause im downloading music ... it always freezes
Ian (04:56:58:743 PM): Can you still see the whiteboard, with the stuff you drew?
mijitpride (04:57:24:834 PM): yea .. its still there
Ian (04:58:26:716 PM): So, suppose each rectangle has width w.  What is the area of the nth rectangle from the left?
mijitpride (04:59:55:582 PM): ((w-1)^2 +1) x w
Ian (05:00:37:975 PM): Since w is constant, that looks like every rectangle has the same area. 
mijitpride (05:01:47:832 PM): oh word .. true that ... ummm ... ya got me then
Ian (05:02:12:240 PM): If you look at the nth rectangle, you can use n and w to find x, right?
mijitpride (05:03:08:869 PM): yea ... its just that n has to have a limit because eventually it peaks so thats where i got confused
mijitpride (05:03:56:858 PM): i didnt know if it was w+n or (w)(n) or what
Ian (05:04:04:835 PM): n can be anything from 1 up to the number of guys of width w who will fit between x=0 and x=1.
Ian (05:04:40:674 PM): For example, if w=1/2, then n can be 1 or 2.  If w=1/4, n can be 1, 2, 3, or 4.  
mijitpride (05:05:19:800 PM): but im saying at the axis of symmetry, the parabola has its greatest y value and if the y value is a function of x and n then there has to be some limit .. doesnt there?
Ian (05:05:23:645 PM): To look at it the other way, if we choose a maximum n, that determines our value of w.
Ian (05:06:03:732 PM): You don't need to drag a limit into it.  If you have a value for x, the rectangle is just whatever you get when you plug x into the function.
Ian (05:06:56:475 PM): It doesn't matter where the rectangle is, as long as you don't let x get past 1.
mijitpride (05:07:12:779 PM): arite .. i gotcha
Ian (05:07:47:159 PM): So can you write the expression for the nth area?
mijitpride (05:09:35:297 PM): ((n)/(w)-1)^2+1??
Ian (05:10:24:509 PM): If I'm looking at the nth rectangle (where I count from 1)...
Ian (05:10:37:507 PM): I think the x value is x=(n-1)*w, isn't it?
mijitpride (05:11:31:534 PM): i think so
Ian (05:13:10:549 PM): Okay, so if y=-(x-1)^2+1, then the area is w*[-((n-1)*w)^2 + 1], right?
mijitpride (05:13:39:841 PM): yea yea
Ian (05:13:56:171 PM): So your approximation to the area would be 
Ian (05:14:39:981 PM): It's too hard to write!
Ian (05:15:13:083 PM): Anyway, you'd have this sum, where you index n from 1 to 1/w, and you have that expression.  
Ian (05:15:56:846 PM): So that's an approximation to the area.
mijitpride (05:16:21:585 PM): but you can have infinitely small rectangles to aproach a more accurate area right
Ian (05:17:11:021 PM): Right.  
Ian (05:17:27:247 PM): So if you take the limit, as the number of rectangles goes to infinity, you get the _exact_ area.
Ian (05:17:32:472 PM): And that's integration. 
mijitpride (05:17:52:370 PM): it doesnt seem that hard
Ian (05:18:22:544 PM): The idea isn't hard at all!
mijitpride (05:18:38:481 PM): but lke everything else .. its gets hard
mijitpride (05:18:43:125 PM): i assume
Ian (05:18:44:133 PM): It's just doing it in practice that's hard.
Ian (05:19:14:887 PM): Because there are a lot of special cases.
Ian (05:19:47:947 PM): The idea  behind derivatives is kind of the same way.
Ian (05:19:54:805 PM): Have you learned about those yet?
mijitpride (05:20:21:606 PM): nope ... not at all
Ian (05:21:15:051 PM): Can I clear the canvas?
mijitpride (05:21:24:052 PM): yea
Ian (05:21:51:540 PM): So let's say we have a curve, like this. 
Ian (05:21:56:837 PM): And we pick two points on it.
Ian (05:22:46:854 PM): How can you find the slope of the line that connects the two points?
Ian (05:24:37:592 PM): Right. Now, what if you write x_2 as (x+d)?
mijitpride (05:25:00:872 PM): why would you
Ian (05:25:37:174 PM): Try it, and you'll see.
Ian (05:25:50:919 PM): (I know, that's a terrible answer!)
Ian (05:26:37:430 PM): Okay, a better answer is:  we'd like to try to express as much as we can in terms of some difference in the x values, because we're going to shrink that down eventually.  It's kind of like how in integration, we wanted to express everything in terms of w, so we could shrink that down.
Ian (05:27:29:254 PM): Good.  So if y_1 is f(x_1), what's y_2? 
Ian (05:29:48:862 PM): I'm having trouble reading what you wrote. 
mijitpride (05:30:02:786 PM):  can i clear it?
Ian (05:30:29:398 PM): sure
Ian (05:32:04:663 PM): Don't you mean y_2=f(x_1+d)?
system (05:34:56:160 PM): krishara entered the Room2 chat room.
mijitpride (05:35:01:093 PM): ok i follow now .. i read what you wrote wrong
Ian (05:35:20:839 PM): Yeah, this isn't the greatest environment for talking about this stuff...
Ian (05:35:32:075 PM): So, does the thing I just wrote belog make sense?
mijitpride (05:35:33:371 PM): seriously
mijitpride (05:35:40:406 PM): yea .. perfect sense
Ian (05:36:33:483 PM): So, if you let d shrink down to zero, what happens?
Ian (05:36:46:981 PM): Hi Krish,
Ian (05:37:04:722 PM): Is there something math-related you'd like to talk about today?
mijitpride (05:37:08:172 PM): the function is undefined ... it approaches an asyptote
Ian (05:37:15:088 PM): Really?
mijitpride (05:37:21:604 PM): shouldnt it
mijitpride (05:37:32:280 PM): oh shit .. i see
krishara (05:37:37:017 PM): Hello i need help solving a problem. Here it goes If the volume of a bubble is 15cm how many bubbles would fill the cylindrical bubble room if it is 2,100cm tall and has a diameter of 800cm?
Ian (05:38:07:500 PM): Do you mean 15 cubic cm?
mijitpride (05:38:12:421 PM): as d shrinks to zero the slope shrinks to 0
Ian (05:38:39:397 PM): It's hard to see it from just the abstract formula.  Try it for some function, like f(x) = x^2.  
krishara (05:39:22:925 PM): well i'm only in the 6th grade i don't understand
Ian (05:40:06:037 PM): Let's try something simpler.  Suppose I have a container that holds 12 cups of liquid, and I have a glass that holds 2 cups.  How many times can I empty the glass into the container.
krishara (05:40:46:298 PM): yes
Ian (05:40:58:449 PM): Yes?
krishara (05:42:47:951 PM): will it be 6
Ian (05:42:57:714 PM): Cool.  How did you get that?
krishara (05:43:50:736 PM): i divided  by 2
krishara (05:44:26:575 PM): lan are you still there
Ian (05:44:35:476 PM): Yes.
Ian (05:44:42:467 PM): You divided 12 by 2?
Ian (05:44:51:360 PM): So you divided the total volume by the volume of each thing, right?
krishara (05:45:07:990 PM): yes
Ian (05:45:21:624 PM): So would that same idea work for your original problem?
Ian (05:45:36:959 PM): The room is like the container, and the bubble is like the glass.
Ian (05:46:34:877 PM): Does that make sense, krishara?
krishara (05:46:54:406 PM): kinda
Ian (05:47:34:008 PM): Suppose we made it look like this.  There are 300 cubic cm in the room, and a bubble is 15 cubic cm.  How many bubbles would fit in the room?
krishara (05:48:50:929 PM): give me 1 minute please
krishara (05:49:53:965 PM): i think the answer is 20 is that correct
krishara (05:50:23:835 PM): lan are still there
Ian (05:50:29:471 PM): Still here.
Ian (05:50:40:261 PM): That's right.  
Ian (05:50:53:309 PM): Are you getting the basic idea? 
Ian (05:51:35:509 PM): If so, what remains is to figure out the volume of the room.
krishara (05:52:01:778 PM):  to divide
Ian (05:52:34:278 PM): Right, this is one time when you want to use division.  When you want to know how many times something fits into some larger space. 
Ian (05:52:45:481 PM): Do you know how to find the volume of a cylinder?
krishara (05:53:00:798 PM): kind of
krishara (05:53:35:961 PM): hello you still there
Ian (05:53:48:177 PM): Still here.  
krishara (05:53:53:606 PM): ok
Ian (05:54:10:863 PM): We have a cylinder with a diameter of 800 and a height of 2100.  What would the volume be?
krishara (05:54:42:216 PM): 1 mintue please
Ian (05:55:16:050 PM): Sure, take your time.
krishara (05:56:16:774 PM): now i divide and i don't under stand
Ian (05:56:56:062 PM): Did you get the volume?
krishara (05:57:10:984 PM): no i think i need some help
Ian (05:57:21:291 PM): Okay. 
krishara (05:57:30:984 PM): 
Ian (05:57:34:190 PM): Let's say I have somethign like a cereal box.
krishara (05:57:41:541 PM): ok
Ian (05:58:26:242 PM): That's a bad box, but do you recognize it?
krishara (05:58:53:847 PM): yeah you did the best you could i like it
Ian (05:58:59:474 PM): The base is a rectangle, with dimensions 3 inches and 4 inches. 
Ian (05:59:06:841 PM): So what's the area of the base?
krishara (05:59:20:299 PM): 12 i think
Ian (05:59:25:689 PM): Right.  
Ian (05:59:45:654 PM): If the height is 5, what's the volume?  It's the area of the base, times the height.
Ian (05:59:48:756 PM): So what would that be?
krishara (06:00:01:274 PM): 60 i think
Ian (06:00:11:278 PM): Perfect.  
Ian (06:00:32:142 PM): In general, when we have something that goes 'straight up' like this, the volume is the area of the base, times the height.
Ian (06:01:03:295 PM): A cylinder is kind of like that, except the base is a circle instead of a rectangle.  
Ian (06:01:25:592 PM): If the radius of the circle is 2 inches, can you find the area?
krishara (06:01:48:729 PM): yes i think
Ian (06:02:34:596 PM): Give it a try.  Let me know what you get.
krishara (06:02:50:713 PM): i'm guessing 4
Ian (06:03:00:488 PM): Did you use a formula for that?
krishara (06:03:19:536 PM): what do you mean
Ian (06:03:42:049 PM): How did you get 4?
krishara (06:05:55:390 PM): what i'm trying to figure out is the volume of a bubble is 15 cubic cm how many would fill the cylindrical bubbleroom if it is 2,100cm tall and has a diameter of 800 cm
krishara (06:06:44:277 PM): how i got 4 i multply
Ian (06:09:02:445 PM): With the bubble room, if you knew the volume of the room, you could divide by the volume of the bubble to get the number of bubbles, right?
krishara (06:09:23:507 PM): right
Ian (06:10:17:578 PM): So you need to find the volume of the room. 
Ian (06:10:32:192 PM): You know the height of the room, so you have to find the area of the floor.
krishara (06:10:38:588 PM): so wouldn't i divide
Ian (06:11:00:797 PM): To find the area?
Ian (06:11:37:439 PM): I promise we'll get back to the bubbles, but for now, if you have a circle with radius 2, can you tell me the area?
krishara (06:11:53:688 PM): so i divide 2,100 and the diameter which is 800 cm
krishara (06:12:26:713 PM): sorry it doesn't say an area
Ian (06:12:41:031 PM): Right.  Remember the cereal box?
krishara (06:12:59:940 PM): yes i remeber
Ian (06:13:01:483 PM): We got the volume from the area and the height.
Ian (06:13:10:387 PM): volume equals area times height.
krishara (06:13:24:435 PM): so the area was the numbers
Ian (06:13:27:141 PM): So we want to do that with the cylinder, too:  volume = area times height.
Ian (06:13:33:843 PM): We know the height.  We have to find the area.
Ian (06:13:58:225 PM): All we know about the circle at the bottom is that the diameter is 800 cm.  
Ian (06:14:06:320 PM): We need to use that to find the area.
krishara (06:14:07:634 PM): or do we divide the 15 and 800
krishara (06:14:44:414 PM): ok you still there 
Ian (06:14:56:954 PM): Yes.
krishara (06:15:18:942 PM): oh yeah or do we add all the numbers and divide by 3 or no
Ian (06:15:53:508 PM): What I'd like to do is go back and look at some basic stuff about circles.  Can we do that?
krishara (06:16:03:290 PM): can you draw me a picture please
krishara (06:16:22:003 PM): sure we can do that
Ian (06:16:28:430 PM): This is a circle.
krishara (06:16:32:367 PM): ok
Ian (06:16:32:538 PM): (More or less.)
Ian (06:16:44:918 PM): That's the radius.
krishara (06:16:50:246 PM): ok
Ian (06:16:53:570 PM): It's the distance from the center of the circle to the outside.
krishara (06:17:12:764 PM): ok which is half and diameter is all
Ian (06:17:17:249 PM): To find the area of the circle, we multiply pi by the radius squared.  For example, if the radius is 2, 
krishara (06:17:39:260 PM): ok
Ian (06:17:41:029 PM): then the area is (pi*2*2), or (pi*4).
Ian (06:17:47:813 PM): You're familiar with pi?
krishara (06:18:04:250 PM): yes which is 3.14 right
mijitpride (06:18:16:785 PM): is everyone still here
krishara (06:18:24:520 PM): yes
Ian (06:18:33:380 PM): Krishara and I are still here.
system (06:18:44:273 PM): mijitpride left the Room2 chat room.
system (06:18:47:291 PM): krishara left the Room2 chat room.
Ian (06:18:48:630 PM): Right. 
system (06:20:17:981 PM): Ian left the Room2 chat room.
Mod2 (06:20:19:253 PM): were did they go?

Mod2 (06:21:09:293 PM): Ian?

system (06:24:04:285 PM): Mod2 left the Room2 chat room.