easter reflection

wealp, its time for another blog
i'm just gonna talk about somethin we learned a long time ago
the way that you can use g for x^2 when the degree is 4
so simple

x^4-4x^2-12=0

1. g=x^4/2
g=x^2
g^2-4g-12

2. (g^2-6g)+(2g-12)
g(g-6)+2(g-6)
(g+2)(g-6)
g=-2 g=6

nothin rly new
happy easter

easter reflection

so we started chapter 12 last week, and i have to say it is pretty easy

vectors:

basically you are given 2 points

A(3,7) B(1,4)

To find the components of vector AB, subtract A from B

1-3 , 4-7

AB = (-2,-3,)

To find the magnitude of a vector, use the distance formula

D= sqrt (x1 - x2)^2 + (y1 - y2)^2

to add vectors, add components
to subtract vectors, subtract components
etc.

so far this is the easiest chapter i think

reflection

Vectors:
u = (1,2) v = (4,3)

1. u + v
(1+4) (2+3)
= (5,5)

2. u - v
(1-4) (2-3)
= (-3, -1)

3. 3u + v
(3+4) (6+3)
= (7, 9)




yay i actually get it :)

reflection 4/4

So, it's Easter again. HAPPY EASTER, and my Daddy decided to show up for the first time in about A YEAR, so yeah.. i almost forgot this blog!

So, this week we started learning Chapter... 12?
Hm, that sounds right... anywayssss it was vectors.

This is a pretty simple chapter, and hopefully it stays that way!

Ex. 1)
A(-3,-5) B(-5,1)

a) Find the components of the vector AB
~subtract the components of B-A
~ -5-(-3),1-(-5)
~(-2,6)

b) Find the magnitude
~to find magnitude first you have to determine whether you're dealing with two points or if you're dealing with a vector
~distance formula time!
~sqrt of (-5+3)^2 + (1+5)^2
~which is the sqrt of 40
~and that simplifies to 2sqrt10.< magnitude!

Ex. 2.)
u=(3,1) v=(-8,4)

a) Find u + v
~add the components of u and v
~(-5,5)

b) Find 2v + u
~First you have to multiply the components of v by 2, then you add it to the components of u
~(-16,8) + (3,1)
~And you add those components together ^^
~So you get (-13,9)

Makeup reflection 1

hmmm, trig chart timeeee!

0 = 0 degrees
pi/6 = 30 degrees
pi/4 = 45 degrees
pi/3 = 60 degrees
pi/2 = 90 degrees

sin 0 = 0
sin 30 = 1/2
sin 45 = square root of 2 over 2
sin 60 = square root of 3 over 2
sin 90 = 1
cos 0 = 1
cos 30 = square root of 3 over 2
cos 45 = square root of 2 over 2
cos 60 = 1/2
cos 90 = 0
tan 0 = 0
tan 30 = square root of 3 over 3
tan 45 = 1
tan 60 = square root of 3
tan 90 = undefined
cot 0 = undefined
cot 30 = square root of 3
cot 45 = 1
cot 60 = square root of 3 over 3
cot 90 = 0
sec 0 = 1
sec 30 = 2 square root of 3 over 3
sec 45 = square root of 2
sec 60 = 2
sec 90 = undefined
csc 0 = undefined
csc 30 = 2
csc 45 = square root of 2
csc 60 = 2 square root of 3 over 3
csc 90 = 1

Reflection 4/4

HAPPY EASTER EVERYYONEE :) yayyyy, we got B-rob back! We really did not learn that much stuff this week and it was short, but i pretty much got everything that we learned.

______________________________________________________

Vectors:
u = (1,2) v = (4,3)

1. u + v
(1+4) (2+3)
= (5,5)

2. u - v
(1-4) (2-3)
= (-3, -1)

3. 3u + v
(3+4) (6+3)
= (7, 9)
_______________________________________________________

EXAMPLE:

* If u=(1,-3) and v=(2,5) find... (a) u+v , (b) u-v , (c) /2u+3v/.

(a)= (3,2)
(b)= (-1,-8)
(c)= /(2,-6) + (6,15)/
= /(8,9)/
= squareroot 8^2 + 9^2
= squareroot 145
______________________________________________________

I pretty much understood everything, but if anyone wants to give examples, i'm down! THANKSS :)

REFLECTION 4/4

Soooo I definitely almost forgot all about this blog you guys. Anyway this past week we started learning Chapter 12 which is vectors. To say a little bit about vectors, they represent movement, the letters u and v are usually used to represent them, and they're pretty easy. First we learned the basics like drawing them, adding and subtracting components, and finding the magnitudes. Then we learned how to find vector equations. I pretty much understood everything so far in this chapter so here's a few examples:

Ex. 1.) A(-3,-5) B(-5,1)
a.) Find the components of the vector AB
*to do this all you have to do is subtract the components of B from the components of A
*So you get -5-(-3),1-(-5)
*So that gives you (-2,6)
b.) Find the magnitude
*to find magnitude first you have to determine whether you're dealing with two points or if you're dealing with a vector
*in this case, you're dealing with two points, so to find the magnitude you're going to use the distance formula
*So you get sqrt of (-5+3)^2 + (1+5)^2
*which is the sqrt of 40
*and that simplifies to 2 sqrt of 10, and that's your magnitude

Ex. 2.) u=(3,1) v=(-8,4)
a.) Find u + v
*All you have to do is add the components of u and v
*So you get (-5,5)
b.) Find 2v + u
*First you have to multiply the components of v by 2, then you add it to the components of u
*So you get (-16,8) + (3,1)
*And you add those components together ^^
*So you get (-13,9)

For the most part, I thought this was a good week. Even though it went by soooooo sloowwwwwwww. Nothing was unbearably hard to catch on to, but I'm a little confused with finding velocity and speed still. If anyone would like to help me out that would be great (:

Hope everyone has a great holidays (:

Reflection

Sooooooo Happy easter everyone :)

This week we started learning chapter 12..I think. And it was vectors so far its been pretty easy but everything always gets harder, of course. We started of learning about vectors. There are vectors and points, you can tell it's a vector by looking at it because there will be a U or V before the numbers. If it ask you to find AB with an arrow over it your just subtracting the 2nd points from the first points. It might also ask you to add or multiply, but you just plug U & V to it. Also if you have to find absolute value, after doing the problem you have to square root the answer. **If it ask to find the magnitude you just do the distance formula.
^This is all that we learned towards the beginnging of the week.

I didn't bring my book home so here's some examples I made up:

Vectors:
U=(3,4) V=(6,5)

U+V= (3,4)+(6,5)
=(9,9)

U-V= (3,4)-(6,5)
=(-3,-1)

--------------------------

I understood everything we learned!

Reflection #33

I'm going to review the areas of different triangles:

Area of a right triangle: A=(1/2)(base)(height)
Area of a non-right triangle: A=(1/2)(leg)(other leg)sin(angle in between the two legs)

Examples:
visualize a right triangle: DEF (left to right)
D=90 degrees, d=8, e=6...Find the area.
So, you know your base is e, which is 6.
Now, to find your height, or f, use: a^2 + b^2 = c^2
c is always to hypotenuse, which is d (8).
6^2 + b^2 = 8^2
36 + b^2 = 64
b^2 = 28
b = 5.292
Your height is 5.292
Now, plug into the formula.
A = (1/2)(6)(5.292)
A = 15.875

Now, visualize a non-right triangle: HIJ (left to right)
H = 65 degrees, j = 2, i = 6
Plug into the formula.
A = (1/2)(2)(6)sin(65)
A = 5.438

For comments, just add more examples.