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Tuesday, March 22, 2011
hw #8-2 Multiplying Polynomials, Factoring with GCF, FOIL & Area Model
hw #8-2
pg 483 #9-25, 39 Odd
USE BOTH FOIL AND the AREA MODEL
(the book discusses the "distribution" and a table method, both are very similar to what we have done in class, so just use any method you are comfortable with)
pg 489-490 #21-41 Odd
WHO can EXPLAIN why that formula works... i.e. what are the components of the surface area of a cylinder and how do they match up with the components of the formula?
To find the surface area of a cylinder you need to add the surface area of each end plus the surface area of the side. It's easier than you think. Each end is a circle so the surface area of each end is πr^2. r is the radius of the end. There are two ends so their combinded surface area is 2πr^2. The surface area of the side is the circumference times the height, which is 2πrh. Once again, r is the radius and this time there is h, which is the height of the side.
So, when you put everything together, you get:
2πr^2 + 2πrh
I think I should get a BEANIE BABY for my amazing explanation of why the formula for the surface area of a cylinder works!!!
To find the surface area of a cylinder you need to add the surface area of each end plus the surface area of the side. The side is the tube part of the cylinder. If you flatten out the tube you get a rectangle. Obviously, the area of a rectangle is l*w, which is equal to 2πr * h. 2πr is the length, l. h is the width, w. Simplified, you get 2πrh.
When you add everything together you get:
2πr^2 + 2πrh
-Julian
Hint: You need to think of the cylinder as a group of ordinary geometric shapes. 2 circles and a rectangle.
For #18: Yup! For w: Yup! For Julian: A BEANIE BABY!!
Julian, you should make youtube video of your explanation, right down to the flattening of the cylinder.
I hope everybody read Julian's explanation. He described a geometric concept known as a "flat pattern" or "net." Any 3d object, including a sphere, can be cut and laid out in a flat pattern. Julian did a very nice job of describing the process in his own words.
For the example problem (it applies to #29) how do you factor out the 2pi (which there are 2 of) and only still end up with 1 2pi on the outside of the parentheses?
Just in case anyone was wondering, the surface area for a cylinder is 2 π r2 + 2 π r h, for number 29 on page 490
ReplyDeleteWHO can EXPLAIN why that formula works... i.e. what are the components of the surface area of a cylinder and how do they match up with the components of the formula?
ReplyDeleteDo we only use FOIL on the questions that are (a+b)*(c+d)? Or ones that have more constants?
ReplyDeleteOh & Thanks Tyler!
ReplyDeleteAnd no, Mr.C, I don't. =)
Hehehe!
For #9, I don't understand how to use FOIL for that.. For one thing, I don't really understand how to use FOIL!
ReplyDeleteAlso, for #9, would a fully simplified answer be x^2+4x
ReplyDelete?
And I don't know how to use FOIL for the other ones either.. Only the (a+b)*(c+d)..
ReplyDeleteWould it, for those ones, just be (if the problem was a(b+c)) ab+ac?
ReplyDeleteWhat would -w^2 * w be?
ReplyDeleteWould it just be.. um.. -w^3?
That doesn't seem right though..
Is there even a GCF for #18?
ReplyDeleteDARN! I just did #9-25 ALL! Oh well =)
ReplyDeleteFOIL is for binomials ONLY. The AREA MODEL works for everything.
ReplyDeleteTake another look at #18... I think I see something that each term has in common... do you?
ReplyDelete-w^2 * w?? Is someone overthinking?
ReplyDeleteYou can always break it up into component parts (aka FACTORS)... remember, a neg sign just means multiplication by -1, yes?
-1 * w * w * w
can u answer ur own q now?
Gosh... nobody wants to explain the surface area formula for cylinders... I'm disappointed!!
ReplyDeleteWHY IT WORKS:
ReplyDeleteTo find the surface area of a cylinder you need to add the surface area of each end plus the surface area of the side. It's easier than you think. Each end is a circle so the surface area of each end is πr^2. r is the radius of the end. There are two ends so their combinded surface area is 2πr^2. The surface area of the side is the circumference times the height, which is 2πrh. Once again, r is the radius and this time there is h, which is the height of the side.
So, when you put everything together, you get:
2πr^2 + 2πrh
I think I should get a BEANIE BABY for my amazing explanation of why the formula for the surface area of a cylinder works!!!
-Julian
How can you explain why the area of the "side" is 2πrh?? And what "side" are you talking about anyway... I thought it was more like a tube??
ReplyDeleteWHY IT WORKS (REVISED):
ReplyDeleteTo find the surface area of a cylinder you need to add the surface area of each end plus the surface area of the side. The side is the tube part of the cylinder. If you flatten out the tube you get a rectangle. Obviously, the area of a rectangle is l*w, which is equal to 2πr * h. 2πr is the length, l. h is the width, w. Simplified, you get 2πrh.
When you add everything together you get:
2πr^2 + 2πrh
-Julian
Hint: You need to think of the cylinder as a group of ordinary geometric shapes. 2 circles and a rectangle.
For #18: Oh! a? Right?
ReplyDeleteWould -w^2*w=-w^3? Right?
ReplyDeleteFor #18: Yup!
ReplyDeleteFor w: Yup!
For Julian: A BEANIE BABY!!
Julian, you should make youtube video of your explanation, right down to the flattening of the cylinder.
I hope everybody read Julian's explanation. He described a geometric concept known as a "flat pattern" or "net." Any 3d object, including a sphere, can be cut and laid out in a flat pattern. Julian did a very nice job of describing the process in his own words.
Hahaha!
ReplyDeleteGO JULIAN!!
(No more complaints..) =)
Oh & for #29, you don't substitute 3.14 for pi, do you?
ReplyDeleteFor the example problem (it applies to #29) how do you factor out the 2pi (which there are 2 of) and only still end up with 1 2pi on the outside of the parentheses?
ReplyDeleteFor #29, I'm in the process & I'm stuck. I have:
ReplyDelete2π(x^2+4x+4)+2π(x^2+7x+10)
I don't know what to do!!
For a binomial * trinomial do you use FOIL?
ReplyDeleteI'm having trouble coming up with a polynomial for #35..
ReplyDeleteI repeat... FOIL is for binomial*binomial ONLY... why won't you use the AREA MODEL?????????????
ReplyDeleteOkey doke! I did!
ReplyDeleteAnd the other questions..?
We'll save #29 for class tomorrow... it's so much FUN I wouldn't want ANYONE to miss it!
ReplyDeleteI BET IT WAS PAUL W. WHO SAID:
ReplyDelete"Hahaha!
GO JULIAN!!
(No more complaints..) =)"
:)
Well that's JOLLY! I will BE THERE tomorrow! =)
ReplyDeleteNope Nope, Julian, it was Lotta =)
ReplyDeleteTHAT WAS MY NEXT GUESS!!!!!!!!! JK
ReplyDeleteIf I thought a BEANIE BABY would stop Julian from complaining, I would have given him one two months ago!!! I just don't think anything will work!!
ReplyDelete