March 16, 2007

SCRIBE POST: DAY 89

The plan was to have this up by Friday. Sorry guys. Anyway, I haven't been scribe for quite some time, so it took me awhile to get back into it...

We started class by talking about our due dates for our DEVELOPING EXPERT VOICES assignment. Remember guys: you can always move your due date earlier than expected. We also talked about the rubric for this assignment. Remember that changes must be made no later than Friday, March 23rd.

Let's get the math started...
To solve for a you simply plug in 1 for k. To solve for b, c, and d, you must integrate it from 1 to the number of items. We start with 1, because this is where the domain of the function begins. If you plugged 0 into the function, you would get 23 minutes. This doesn't make sense; it shouldn't take 23 minutes to make nothing. Once you know the integral, the rest is just punching it into the calculator. The answers can be found on the bottom of this page. http://3.bp.blogspot.com/_tlF3qs3v9cw/RfmQ9vFtnUI/AAAAAAAAAIA/ymR08nIwBLc/s1600-h/AppsOfTheIntegralExerc.jpg Note: This is a good exercise to practise for the unit test.


With the help of Fooplot http://www.fooplot.com/, we were able to see what the graph looked like. Points of intersection tell you where to integrate.


1. To find the area of S, we simply find the integral from 0 to 4. Because the function f(x) is on the bottom, we subtract it from g(x).

2. To find the volume of S, we first find the volume of one piece. We take an arbitrary slice, and find its area. In this case, the shape of the slice is a semi-circle, where the radius is the top function, g(x), subtract the bottom function, f(x). Once you have the area, you must write the integral. You then apply this integral to find the volume of the whole thing.


3. Because we S is rotating, you can imagine a solid being formed with a hole in the middle. To find the area, we must take the area of the smaller circle and subract it from the area of the bigger circle. Questions a, b, and c are all the same question; the only difference between them is how the radii are formed.

a)


b)

c)
d) In this case, the solid is rotating around the y-axis, therefore the shape of the arbitrary slice is no longer a circle. It becomes a prism. The width of the prism is the circumference. (remember: the paper towel) Its thickness is dx, because we want the slice to be infinitesmally small. Its height is simply the top function, g(x), subtract the bottom function, f(x).

So that brings us to the end. If you're still having trouble, the slides from Thursdays class http://www.slideshare.net/gofull/30241/1 are up.. thank goodness for our super-di-duper smartboard!!! HMWK for the weekend is EXC 8.5 # 1,3,5,11,15. And by the way, MARK is the scribe for Monday! Enjoy the rest of your weekend guys =)

3 comments:

Mr. H said...

Great use of images Linger. I am impressed with the detail that they show. Thanks for being a great scribe.

Harbeck

Sargent Park School

Lani said...

Hi Linger,

Your annotations with the clear illustrations are really important to understanding the content. This scribe should be a good one to assist with review.

Best,
Lani

lindsay said...

WOO LINGER! that scribe was awesome. i have a better understanding of what we've been talking about. HALL OF FAME! =) and...bonus marks? ;)