Another long day doing Aleks stuff. Anyway, Go Packers.
I went to school 2 out of 5 days last week, so forgive me if I'm not sure what I'm talking about.
No one really went over 12-1, so I don't what that's all about. Something about lines. I don't know. So I guess that leaves Matrices. And I'm going to use 1x2's because anything bigger just looks ridiculous.
ex.
H = [2 3]
G = [4 5]
Find H + G
H + G = [6 8]
ex. 2 Find H x G
You can't really multiply them because they're dimensions don't work. The "inside" numbers have to match. ex. 2x3 3x4
*On a side note, Division requires you to multiply the matrix by the other's inverse. Again, that still requires the dimension's "inside" numbers to match.
Sunday, February 6, 2011
Nathan's blog
Okay, so section 12-1 involved drawing little lines and connecting them. That's about it for that section. So, since that can't get me 150 words, I will just review matrices again. You can add, subtract, or multiply matrices but you can't divide them.
Adding Matrices:
[4 5] + [-9 2] = [-5 7]
[7 8] [5 -3] [12 5]
Subtracting Matrices:
[7 18] - [5 4] = [2 12]
[9 4] [-8 2] [17 2]
Multiplying Matrices:
[2 5] X [3 10] = [11 30]
[7 6] [1 2] [27 82]
That's only some of the things on matrices. You also have scalar multiplication, Cramer's rule, and finding the inverse and determinant of a matrix.
Cramer's rule is:
Dx/d
Dy/d
Scalar multiplication is when you solve without using Cramer's rule.
The determinant of a matrix is ad-bc.
The inverse of a matrix is 1/ the determinant of the matrix.
That's all I got on matrices. Next time I will probably review something different.
Adding Matrices:
[4 5] + [-9 2] = [-5 7]
[7 8] [5 -3] [12 5]
Subtracting Matrices:
[7 18] - [5 4] = [2 12]
[9 4] [-8 2] [17 2]
Multiplying Matrices:
[2 5] X [3 10] = [11 30]
[7 6] [1 2] [27 82]
That's only some of the things on matrices. You also have scalar multiplication, Cramer's rule, and finding the inverse and determinant of a matrix.
Cramer's rule is:
Dx/d
Dy/d
Scalar multiplication is when you solve without using Cramer's rule.
The determinant of a matrix is ad-bc.
The inverse of a matrix is 1/ the determinant of the matrix.
That's all I got on matrices. Next time I will probably review something different.
BLOOGGGGG
This week, we learned about matrices, which was reallllyyrealllyy realllyy easy whereas what i'm attemping to learn in aleks is driving me crazy. i mess up once and then fix it because it'll be an arithmetic error or i would have just typed it wrong on the last on before its "done" but then it says "oh, do it two more times". AHHHHHHHHHHHHHH. i'm gonna show you some of this maddness.
The thing i was stuck on was a number +/- a fraction OVER another number +/- another fraction! its so confusing!
but i don't have any problems to show you! i can make one up and show you the procedure, but i'm not gonna work it all the way through because its not gonna be pretty.
5-6x/2x^2
-------------
2+3/8x
say this is your problem, you have to find a commom denominator of the fractions inside the fraction. which would be 8x^2
then you multiply everything by this common denominator!
you would get:
45x^2-48x^3/2x^2
-------------------
16x^2+8x^2/8x
then you can reduce and get:
45x^2-24x
-----------
16x^2+x
then usually on aleks, it can be factored and reduced to a simple fraction, but i'm not gonna try mine, have fun once all ya'll get to that part of the aleks.:)
The thing i was stuck on was a number +/- a fraction OVER another number +/- another fraction! its so confusing!
but i don't have any problems to show you! i can make one up and show you the procedure, but i'm not gonna work it all the way through because its not gonna be pretty.
5-6x/2x^2
-------------
2+3/8x
say this is your problem, you have to find a commom denominator of the fractions inside the fraction. which would be 8x^2
then you multiply everything by this common denominator!
you would get:
45x^2-48x^3/2x^2
-------------------
16x^2+8x^2/8x
then you can reduce and get:
45x^2-24x
-----------
16x^2+x
then usually on aleks, it can be factored and reduced to a simple fraction, but i'm not gonna try mine, have fun once all ya'll get to that part of the aleks.:)
Kaitlyn's blogg
This week we did a test on matrices and we learned 12-1. We also worked on aleks a lot, which is good because its pretty easy and will help bring up everyone's grades in that class. I forgot how to do 12-1 and i forgot to bring my binder home, so i will go over matrices :)
Adding and subtracting matrices is pretty straightforward. you just add or subtract the number across from it in each matrix.
Ex:
[2 3] + [7 5] = [9 8]
[1 5] [1 0] [2 5]
When you multiply matrices, you must make sure the dimensions are correct. if you have a 3x2 matrix and a 2x1 matrix, you can multiply this because the two middle numbers (2 and 2) are the same.
Ex:
[2 3] x [7 5]= [14+ 3 10+0]= [17 10]
[1 5] [1 0] [7+5 5+0] [12 5]
Adding and subtracting matrices is pretty straightforward. you just add or subtract the number across from it in each matrix.
Ex:
[2 3] + [7 5] = [9 8]
[1 5] [1 0] [2 5]
When you multiply matrices, you must make sure the dimensions are correct. if you have a 3x2 matrix and a 2x1 matrix, you can multiply this because the two middle numbers (2 and 2) are the same.
Ex:
[2 3] x [7 5]= [14+ 3 10+0]= [17 10]
[1 5] [1 0] [7+5 5+0] [12 5]
lawrence's blog
there really isnt much to say about what we did this week. this week all we did was take a test on matrices and went over chapter 12-1. we also spent alot of time on aleks which is good because it will bring up alot of our grades. for those who didnt understand matrices it was pretty easy.
imma show yall if a matrix is able to be multiplied. for example:
3x2 2x2 you can multiply these because the last and first number are the same and you will have a 3x2
4x8 9x7 you cant multiply these because the first and last number arent the same
now imma add one just to be nice :)
2 5 7 + 4 5 6 = 6 10 13
3 9 1 6 7 8 9 16 9
that is all for now and if you need help with anything just let me know. i can help
imma show yall if a matrix is able to be multiplied. for example:
3x2 2x2 you can multiply these because the last and first number are the same and you will have a 3x2
4x8 9x7 you cant multiply these because the first and last number arent the same
now imma add one just to be nice :)
2 5 7 + 4 5 6 = 6 10 13
3 9 1 6 7 8 9 16 9
that is all for now and if you need help with anything just let me know. i can help
Friday, February 4, 2011
Taylor's Blog Review
REVIEW TIME!!!
These are the review notes on what we learned in section 7.5
You will need to know the following so that you can work out the equations.
Tan Theta=y/x
Cot Theta = x/y
Sec Theta = r/x
Csc Theta = r/y
Ok now that we know what Tan, Cot, Sec, and Csc are lets use them to solve the following equations.
Since Sin Theta = 2/8 0<> 90 degrees find the meaning of the other five trig functions.
(REMEMBER I DON’T KNOW HOW TO PUT A GRAPH ON THE COMPUTER SO I WILL JUST TYPE IT OUT.)
Ok, we know the since Sin is positive then the y needs to be positive and that can only happen on the second and first quadrant. Also since 2/8 is supposed to be less than 90 degrees we need to be in the first quadrant. Ok now we need to find x. You can draw a triangle and put in the info that you know to help you.
A^2+2^2=8^2
We will use the Pythagorean theorem to help us find x.
A^2+4=64
a^2=60
We will then use the exponents to get theses answers and then we will subtract 4 from 64 and get 60 then we will find the square root of a and 60 and the answer will be the square root of 60.
Now we just fill in the blanks.
Cos x/r= square root of 60/8
Tan y/x= (since we can’t have a square root at the bottom we will multiply it by the square root of 60 and reduce and get this) square root of 60/30
Cot x/y= square root of 60/2
Sec r/x=(since we can’t have a square root at the bottom we will multiply it by the square root of 60 and reduce and get this) 2 times the square root of 60/15
Csc r/y = 8/2 (reduced is) 4
Now lets try to find the reference angle of tan.
Find the reference angle for Tan 43 degrees.
First we find what quadrant its in. Which is the first because of the degrees which means tan is positive.
Tan 43 degrees
Since 65 degrees is already in-between 0 and 90 degrees we don’t need to subtract and since it’s not on the Trig chart that means that Tan 43 degrees is your answer.
That is 7.5 review Until next time!
These are the review notes on what we learned in section 7.5
You will need to know the following so that you can work out the equations.
Tan Theta=y/x
Cot Theta = x/y
Sec Theta = r/x
Csc Theta = r/y
Ok now that we know what Tan, Cot, Sec, and Csc are lets use them to solve the following equations.
Since Sin Theta = 2/8 0<> 90 degrees find the meaning of the other five trig functions.
(REMEMBER I DON’T KNOW HOW TO PUT A GRAPH ON THE COMPUTER SO I WILL JUST TYPE IT OUT.)
Ok, we know the since Sin is positive then the y needs to be positive and that can only happen on the second and first quadrant. Also since 2/8 is supposed to be less than 90 degrees we need to be in the first quadrant. Ok now we need to find x. You can draw a triangle and put in the info that you know to help you.
A^2+2^2=8^2
We will use the Pythagorean theorem to help us find x.
A^2+4=64
a^2=60
We will then use the exponents to get theses answers and then we will subtract 4 from 64 and get 60 then we will find the square root of a and 60 and the answer will be the square root of 60.
Now we just fill in the blanks.
Cos x/r= square root of 60/8
Tan y/x= (since we can’t have a square root at the bottom we will multiply it by the square root of 60 and reduce and get this) square root of 60/30
Cot x/y= square root of 60/2
Sec r/x=(since we can’t have a square root at the bottom we will multiply it by the square root of 60 and reduce and get this) 2 times the square root of 60/15
Csc r/y = 8/2 (reduced is) 4
Now lets try to find the reference angle of tan.
Find the reference angle for Tan 43 degrees.
First we find what quadrant its in. Which is the first because of the degrees which means tan is positive.
Tan 43 degrees
Since 65 degrees is already in-between 0 and 90 degrees we don’t need to subtract and since it’s not on the Trig chart that means that Tan 43 degrees is your answer.
That is 7.5 review Until next time!
Charlie's.
This week we reviewed & took a test on matrices [Chapter 14].
& like everyday we did aleks.com thingy.
(i still have like a wholeee bunch left to 'master')
& we just started chapter 12 yesterday.
chapter 12 is something weird.
i honestly already fergot how to do it.
the only thing i know is that you draw things,
& then if it says to add them, you connect the two arrows.
& on the two arrows thingy, there's a head and a tail.
so, since i totally fergot how to do it ALREADY.
i'll just do an example of matrices.
EXAMPLE:
[ 2 8 1 ] [ 8 2 7 ]
[ 6 5 7 ] + [ 4 6 9 ] =
[ 8 1 3 ] [ 4 6 2 ]
[ 10 10 8 ]
[ 10 11 16 ]
[ 12 7 5 ]
& like everyday we did aleks.com thingy.
(i still have like a wholeee bunch left to 'master')
& we just started chapter 12 yesterday.
chapter 12 is something weird.
i honestly already fergot how to do it.
the only thing i know is that you draw things,
& then if it says to add them, you connect the two arrows.
& on the two arrows thingy, there's a head and a tail.
so, since i totally fergot how to do it ALREADY.
i'll just do an example of matrices.
EXAMPLE:
[ 2 8 1 ] [ 8 2 7 ]
[ 6 5 7 ] + [ 4 6 9 ] =
[ 8 1 3 ] [ 4 6 2 ]
[ 10 10 8 ]
[ 10 11 16 ]
[ 12 7 5 ]
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