Flatland Chapters 5-8

1. They are all lines in a 2D perspective. This was the point of looking at a penny. You aren't above the shape to be able to see it. You are even with a side so you can only see one side at a time.

2. hearing, feeling and color.

3. The shapes painted themselves to be able to distinguish themselves. This is related to the class they are in. Therefore, it is similar to our fashion choices. The brand of clothing does this in our society. In addition, we use color and style to stand out from everyone else or to blend in.

4. This is an opinion. As long as you support it correctly it is right. However, the narrator is a middle-class square. Some people did not realize this. In addition, it has to be supported with facts from the book! Saying he is a nice guy or that he seemed to know what was going on is not adequate.

5. This is an opinion. However, satirize means to poke fun at something while still trying to make a point. Utopian means perfect. Is this society really perfect with the limitations placed on women and lower classes?

Writing Activity: Make sure this is at least a paragraph... Mrs. Mustian would be appalled that some paragraphs are two sentences.. However, if everyone is a line, how can you animate that?

Reflection 27

Well I'm finalllllly back from orlando for nationals for danceteam. Sorry for this blog being late but I didn't have a computer out there haha. Anyways i'll just explain something from a really long time ago that's super easy. Plus I remember it,
I'll explain Inequalities. There are two types of inequalities, regular inequalities and absolute value inequaties. In absolute value inequalities there are two different types determined by the signs if it is not an equal sign. They can either be and/or inequalities. And inequalities always have a less than symbol and or inequalities always have a greater than symbol. *In absolute value inequalities you always get two answers. *Also remember if dividing by a negative the greater/less than sign will switch to the opposite.

Examples:

1. 4x + 1 > 13

*For this problem you only get only answer because it isn't absolute value.

*Subtract 1 from 13 and you get 4x > 12

*Divide by 4

*Answer x > 3

2. 3x - 4 + 5 <22

*Subtract the 5 over from the 27 and you get 3x - 4<22

*Solve the equation first by adding 4 over to all sides -18<3x<26

*Divide by 3 on all sides your final answer is -6

Reflection following mardi gras week

I'm gunna review some stuff about circles, cuz i remember it even tho its really ole.

Equation of a circle in standard form is:
(x-h)^2+(y-k)^2=r^2
center(h,k) radius(r)
If not in standard form, you must complete the square to put into standard form.
If given the center and a point, you can use the distance formula to find the radius.
To find the intersection of a line and a circle:
first, solve for y.
second, substitute it in your circle equation.
third, solve for x.
fourth, plug y in to get y.
NOTE: if your x-value is imaginary there is NO INTERSECTION.
Ex:Find center and radius:
1. (x-3)^2+(y+7)^2=19
center: (3, -7)
radius: (square root of 19)
2. PUT IN STANDARD FORM TO FIND CENTER AND RADIUS:
x^2+y^2+16x-12y+5=0
COMPLETE THE SQUARE:
x^2+16x+y^2-12y=-5
x^2+16x+64+y^2-12y+36=-5+64+36
(x+8)^2+(y-6)^2=95
CENTER:(-8,6)
radius: (square root of 95)

Reflection #27

Okay, let's review chapter 1 and completing the square:

Step 1: Move c over
Step 2: Divide by quadratic coefficient
Step 3: Divide b by 2, then square it and add to both sides
Step 4: Factor
Step 5: Square root both sides
Step 6: Solve for x
Step 7: put in point form (#,#)

Ex. x^2+x-2=0
x^2+x =2
x^2+x =2
(1/2)^2=1/4 x^2+x+1/4=2+1/4
(x+1/2)^2=9/4
x+1/2=+/-3/2
x=-1/2+/-3/2 x=1 x=-2
= (1,0) (-2,0)

Back to basics! :)

2nd Mardi Gras Reflection

I don't really know what to blog about anymore. Did we even have to read over the break. I don't know anything, hah. I wish someone would tell me if we needed to read. I am on chapter four so far, and this book is not one bit interesting. Can anyone tell me what chapter we are supposed to be on? I really hope that we weren't supposed to read because i'm going to be behind!
So, about the houses in Flatland. The most common form for the construction of a house is five sided or pentagonal, as the annexed figure. The two NOrthern sides RO, OF, constitute the roof, and for the most part have no doors; on the East is a small door for the Women; on the West is a much larger one for the Men; the South side or floor is usually doorless.
Square and triangular houses are not allowed, and for this reason. THe angles of a Square being much more pointed than those of a pentagon, and the lines of inanimate objects, such as houses, being dimmer than the lines of Men and Women, it follows that there is no little danger lest the points of a square or triangular house residence might do serious injury to an inconsiderate them: and as early as the elevnth century of our era, triangular houses were universally forbidden by Law, the only exceptions being fortifications, powder magazines, barracks, and other state buildings, which it is not desirable that the general public should approach without circumspection.
So, if anyone would still like to expalin this book to me, i would appreciate it. I still am a little confused to about what is going on. And does anyone know if we are supposed to do comments too? I have no idea. I am so oblivious haha, THANKSSS!

another relfection

So these are the six trig functions and the unit circle:
Six trig functions:
sin: y/r
cos: x/r
tan: y/x
cot: x/y
csc: r/y
sec: r/x

Unit Circle:
90(pi/2): (0,1)
180(pi): (-1,0)
270(3pi/2): (0,-1)
360(2pi): (1,0)

And here are a couple identities:
csc x = 1/sin x
sec x = 1/cos x
cot x = 1/tan x
sin (-x) = -sin x
cos (-x) = cos x
csc (-x) = -csc x
sec (-x) = sec x
tan (-x) = -tan x
cot (-x) = -cot x

reflection

Im gonna show you something in chapter 2. Solving anything bigger than a quadratic usuing quadratic form. To use quadratic form you have to have 3 terms only. The first term must equal the 2nd exponentx2, and the last term must be a constant. The first thing you do is make g=x^exponent/2 so that you would get g^2+g+#. The second thing is to do the quadratic formula, factor, or complete the square. The the last thing is to plug back in for g. (Whenever you do step three you are basically just plugging back into step one. g=x^2)

An example:
x^4-4x^2-12=0
1. g=x^4/2
g=x^2
g^2-4
g-12
2. (g^2-6g)+(2g-12)
g(g-6)+2(g-6)
(g+2)(g-6)
g=-2 g=6

Happy mardie gras

Okay for this reflection, I'll just review a whole bunch of random things that I can come up with off the top of my head. haha. And hopefully I'm still explaining all of this correctly.
So to start off, I'll give some examples of sequences and series stuff that we learned in Chapter 13.

Ex. 1.) If t1 = 2, t2 = 6, and tn-1 + 2tn-2, what is t5?
*Okay first off, the "n-1" and "n-2" are subscripts, just to clear that up
*So first you notice that you are given what the 1st and 2nd terms are. In order to get to the 5th term that they're asking for, you have to also find the terms in between before you find that one.
*So first you're going to solve for the 3rd term. "t3"
*Well the way ms robinson taught this in class was to read "n-1" as the "previous term" and "n-2" as the "previous previous term", butttttttttttt I got confused with that soooo this is how I did it: (it's pretty much the same, but it's easier for me to understand.)
*So first we want to find t3 right? So all I do is plug in a "3" wherever there is an "n" in the equation given to us.
*So you would get t3=t3-1 + 2t3-2
*Simplifying that you get t3=t2 + 2(t1)
*Then all you have to do is plug in the actual numbers for the "t's".
*So you get t3 = 6+2(2) Sooooo t3 = 10
**Okay for these next two terms, you're going to do the same thing, but I'm just not going to waste my time explaining every single step because I did it once already (;
*Soo now you want to find the next term "t4"
*plugging into the equation you get t4=10 + 2(6) Sooo t4 = 22
*Now to find t5!! woohhoo
*plugging into the equation you get that t5=22 + 2(10) So t5 is 42

Ex. 2.) Find the sum of the first 12 terms for the sequence/series (whatever it is): 3,6,9,12,...66
*First you need to find out whether this is arithmetic or geometric.
*It's arithmetic because you are adding 3 each time
*This is not an infinite series because it tells you the last number which is 66
*Soooo you are going to use this arithmetic sum formula to find your answer: Sn=n(t1 + tn)/2
*And you just plug in the numbers you are given
*So you get S12=12(3+66)/2
*12(69)/2
*The sum of the first 12 terms in the series/sequence is 414

Second Mardi Gras Reflection

To convert radians to degrees you take the radian and multiply by 180/pi.

Ex: 225 degrees x pi/180 = 5/4 pi

3pi/4 x 180/pi=135 degrees

In 7-3 you have to know the unit circle and chart.

The Chart:

Sin=y/r Csc=r/y
Cos=x/r Sec=r/x
tan=y/x Cot=x/y

Ex:

Find all 6 trig functions of (-3,4).

Sin=4/5 Csc=5/4
Cos=-3/5 Sec=-5/3
tan=-4/3 Cot=-3/4

The unit circle:

90 degrees= pi/2 and (0,1)

180 degrees=pi and (-1,0)

270 degrees=3pi/2 and (0,-1)

360 degrees= 2pi and (1,0)

First Mardi Gras Reflection

This is my mardi gras reflection about something we learned a while back.



sum and difference formulas for sine and cosine

cos(a±B)=cos(a)cos(B) ± sin(a)sin(B)
sin(a±B)=sin(a)cos(B) ± cos(a)sin(b)




sum and difference formulas for tangent

tan(a+B)=(tana+tanB)/(1-tanatanB)
tan(a-B)=(tana-tanB)/(1+tanatanB)



half angle and double angle formulas

sin2a=2sinacosa
cos2a=cos^2a-sin^2a=1-2sin^2a=2cos^2a-1
tan2a=2tan∂/(1-tan^2a)
sina/2=±√((1-cosa)/2)
cosa/2=±√((1+cosa)/2)
tana/2=±√(1-cosa)/(1+cosa)=sin∂/(1+cosa)=(1-cosa)/sina

Ex problem: Find the exact value of cos25 cos5-sin 25 sin5.

1. You use the sum and difference formulas for sine and cosine.

2.Then you add 25 + 5 when you look at the formula and that gives you sin 30.

3. When you look at the trig chart sin 30 gives you 3/2 as your answer.

Random Reflection

law of cosines
(opp leg)=(adj leg)^2 + (other adj leg)-2(adj leg) (adj leg) cos (angle between)

it is used when solving for non-right triangles
SOHCAHTOA is also the law of sines
law of sines
EX: angle B=30 degrees, angle A=135 degrees, and side b=4 ...find C and a and c.
find your other angle, so add 30 to 135 together and get 165, then you subtract that from 180 and get 15 so angle C is 15 degrees.
next, find another side...since you have pairs, you ca use that in the law of sines
your equation would be sin(30/4)=sin(135/a)
cross multiple and get asin(30)= 4sin15........which means that c=2.071

I know i just did law of sines but its easy and I like it so i did it again. and btw CONGRATULAIONS ON THE BABY

Reflection # *insert random number here*

blah, bloggin about math from the week before........when we didnt even have school.........BLASPHEMY!!!

haha

only math related thing that happened.....was a math competition.....so i guess ill just put math we learned before brob left?

i guess ill just do that........*findin some kind of math in this confusing mind*..........blah.......

so...ill talk about series(es) and ∑ stuff....i guess :/

Give each series in expanded form

4
∑ 5K 5+10+15+20
K=1

6
∑ n^2 9+16+25+36
n=3

Express the series in sigma notation

1+2+4+8+16+32
5
∑ 2^K
K=0

48+24+12+6+...
∞
∑ 48(1/2)^c
c=0

you see, the basics of ∑ are:
the top # is where the series ends
the bottom variable and variable's value are where the series starts
and the equation on the right of the ∑ is.....well its the equation for the series

with many numbers, finding the series is a task that requires a lot of numerical logic
u kno, stuff like:

if x^0=1, find x
its pretty obvious that this answer can be anything from -∞ to ∞
anything^0 always equals 1

and i cant think of any other pieces of numeric logic right now.......but u get the picture

anyways......i rly cant remember much more about the last few bits of math that we learned recently.....but i do know this.......in a game of Scrabble......New Hampshire has the highest point value out of all the states......

well....since i cant remember alot....ill just say that i dont understand.......why people love Avatar

reflection 27

This is my reflection for the second sunday during our mardi gras break. This week has been nice being off but it hasn't really felt like i have been off because i have softball everyday and i still have to wake up early and go to school and everything. But anyway, im ready to go back to school because that means that it is that much closer to being SUMMER:) and i know everyone is excited about that. And congratulations to Mrs. Robinson on having her baby this week i think. a baby girl?:) im pretty sure it is. Sooo..on this reflection im going to review some of the things from chapter 13. I think I'll do section 13-5, with the Sums of Infinite Series. Heres the only formula you will need to know i believe...s=t1/1-r

EXAMPLE 1:
Find the sum of the infinite series. 9-6+4-
r=-6/9 = -2/3
r=4/-6 = -2/3
-2/3<1
s=9/(1-(-2/3))
=27/5

EXAMPLE 2:
For what values of x does the series converge?
1+(x-2)+(x-2)^2+(x-2)^3+

r=x-2
x-2<1
-11

reflection 26

This is my reflection for the first sunday on our mardi gras break. I didn't even think about doing the reflection, ha i totally forgot. But I'm pretty sure that i did pretty good on my chapter 13 test. I thought i knew almost everything in each section. And i don't think that flatland isn't going to be that bad of a book, i actually got pretty into it on thursday when we were reading in class. And 20 vocabulary words isn't bad at all for the whole entire book. For this reflection im going to review a little bit of chapter 13, section 1. Here are the 2 formulas: ARITHMETIC-tn=t1(n-1)d, and GEOMETRIC-tn=t1xr^(n-1).

EXAMPLE 1:
Find the formula for the nth term of the arithmetic sequence. 3,5,7...
tn=3+(n-1)(2)
tn=3+2n-2
tn=1+2n

EXAMPLE 2:
Find the formula for the nth term of the sequence. 3,4.5,6.75...
r=4.5/3=3/2
6.75/4.5=3/2

tn=3x(3/2)^n-1

Reflection

I'll just talk about stuff we learned in chapter 13 for this blog. In chapter 13 we learned about sequences, many formulas, sigma notation, etc.
Sigma Notation

100 - 1 & 100 are called the limits of summation.
sigma n^2 - n^2 is the summand
n=1 - the bottom variable is called the index, which is K.

- To evaluate-plug in the numbers between your limits of summation into the summand.
Adding each term to form a series.

- Examples:
Give each series in expanded form

1) 4
sigma 5K = 5+10+15+20
K=1

2) 6
sigma 9+16+25+36
n=3

Express the series in sigma notation

1) 1+2+4+8+16+32
5
sigma 1X(2)^K
K=0

2) 48+24+12+6+...
infiniti
sigma 48(1/2)^c
c=0

For some reason i am still having trouble with sequences even though it super easy, i guess i need to know the formulas better.

reflection!

flatland is a never ending sheet of paper that is home to a population of a variety of different shapes. The shapes in flatland identify the social statuses of the people that live there; triangles are lower class, squares are upper class and throughout generations the squares' offspring gain one extra side, until they become circles, the highest class people of flatland. flatland is seen through human perspective only if they can look at it the right way; the book suggests placing your eye at table level and looking at a regularly three dimensional object; in this case, a penny. it'll appear as a line, which is how the people of flatland live there. the plot sequence didn't kick in yet, but this is basically the general information from the introduction of the book.

Reflection 27

Flatland is where the story takes place. It is a two dimensional world, and its inhabitants include several types of shapes. Isosceles triangles are the lowest social class in flatland. Pointed Acute triangles are the soldiers, and the children of squares and up will supposedly gain an extra side each generation, leaving the circles as the highest rank. The people of Flatland live in pentagons, originally triangles but they became too dangerous. Flatland is theoretically a never ending sheet of paper, and the perspective the people see in is as if you line your eye up with the surface of a table and look at a coin, making them near invisible. Women in Flatland are lines, so they could make the perfect soldier because they are invisible, and sharp. So far we only have an introduction to the book but soon we should get to plot development soon.

REFLECTION #27

Okay for this reflection, I'll just review a whole bunch of random things that I can come up with off the top of my head. haha. And hopefully I'm still explaining all of this correctly.
So to start off, I'll give some examples of sequences and series stuff that we learned in Chapter 13.

Ex. 1.) If t1 = 2, t2 = 6, and tn-1 + 2tn-2, what is t5?
*Okay first off, the "n-1" and "n-2" are subscripts, just to clear that up
*So first you notice that you are given what the 1st and 2nd terms are. In order to get to the 5th term that they're asking for, you have to also find the terms in between before you find that one.
*So first you're going to solve for the 3rd term. "t3"
*Well the way ms robinson taught this in class was to read "n-1" as the "previous term" and "n-2" as the "previous previous term", butttttttttttt I got confused with that soooo this is how I did it: (it's pretty much the same, but it's easier for me to understand.)
*So first we want to find t3 right? So all I do is plug in a "3" wherever there is an "n" in the equation given to us.
*So you would get t3=t3-1 + 2t3-2
*Simplifying that you get t3=t2 + 2(t1)
*Then all you have to do is plug in the actual numbers for the "t's".
*So you get t3 = 6+2(2) Sooooo t3 = 10
**Okay for these next two terms, you're going to do the same thing, but I'm just not going to waste my time explaining every single step because I did it once already (;
*Soo now you want to find the next term "t4"
*plugging into the equation you get t4=10 + 2(6) Sooo t4 = 22
*Now to find t5!! woohhoo
*plugging into the equation you get that t5=22 + 2(10) So t5 is 42

Ex. 2.) Find the sum of the first 12 terms for the sequence/series (whatever it is): 3,6,9,12,...66
*First you need to find out whether this is arithmetic or geometric.
*It's arithmetic because you are adding 3 each time
*This is not an infinite series because it tells you the last number which is 66
*Soooo you are going to use this arithmetic sum formula to find your answer: Sn=n(t1 + tn)/2
*And you just plug in the numbers you are given
*So you get S12=12(3+66)/2
*12(69)/2
*The sum of the first 12 terms in the series/sequence is 414

Ex. 3.) Now here's an example with sigmas. *Again I'm going to use "E" as sigma because I don't know how to put an actual sigma on this thing..

Put 1,5,9,13,17 in sigma notation
*First figure out whether it's arithmetic or geometric.
*It's arithmetic because you're adding 4 each time
*Now you have to find the equation for it ,*which will be the summand of the sigma
*So you're going to use the arithmetic formula tn=t1 + (n-1) d
*And plugging in the numbers you have you get >> tn=1 + (n-1) (4)
*tn = 4n - 3 (Soo that's the summand)
*Now to find the index. *All you do is plug in a number for "n" that will give you the first number of the series you're given. *Most of the time when it's arithmetic the index is 1, and in this case it is
*Now to find the top number of the sigma thing you count the numbers in the series you're given starting with 1. And you get 5, so that's your top number
*This is what it would look like:

5
E 4n-3
n=1

Alright I'm done reviewing..