# mathgeek15

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## Blog Entries posted by mathgeek15

"Whats up physicist?" (Penny, Big Bang Theory)
So a few weeks ago was my birthday (delayed much?) and I have some really awesome friends who got balloons for me. So nice, right? Well as I am looking at the balloons, I noticed one of them had a limit on it. What this super awesome friend of mine did was write happy

th
Birthday!! Totally cool huh? Turns out the limit equals my age, which is really cool and NERDY!!!!
Thanks Alpha Geek!
So, I am aware that you guys have been doing E&M for a while, so while this is a little late, it should still help. Now, I know that not everyone likes E&M (just ask Mr. Fullerton how much I liked it ). Well, I too am taking E&M (for the third time), and I have finally cracked the code for success (took me long enough). Now I, the girl who cannot do the right-hand rule (still), is not only understanding E&M, but solving it CORRECTLY.
How you ask? Well, here are some tips:

1. Don't read the book. Seriously. People who say they read the book and found it helpful either a) didn't read the book b ) are lying or c) is Mr. Fullerton. Instead, DO THE PRACTICE PROBLEMS. The book has some really good example problems that are similar to the ones you do in class, but different enough for practice, and then you have the step by step answers. Plus, some of the examples are actually the derivations for electric fields, and trust me, it's a good idea to do those again.

2. Ask questions. Think you understand what you did in class? Think again. Very few people that I know understood E&M perfectly the first time. Mr. Fullerton doesn't bite, so ask him questions. (The worst that he will do is throw you out a window )

3. Actually do the homework. I mean do the homework on your own, not do the homework with the answer right in front of you so you can glance at it for every step or copy someone else's procedure and plug in your numbers. You may think, Oh, I'm not going to do that. I will only look at the answer key when I need to. I know. I was you. But I stopped doing that because I realized that I was looking at the answers too frequently for it to be MY work. Now I'm not saying don't use the answers. I love answer keys (just ask Mr. Muz). But don't become so dependent on them that you can't solve the problem on your own.

4. Ask for help. The most important of them all. If you need help, you are not going to learn anything by ignoring it, hoping it goes away. In E&M, your worst nightmares never just "go away". They linger in the background and attack when you least expect it, causing you to have a mini breakdown. I know. I've been there. Two days ago. But then I went to my professors office hours and it turned out I knew more than I thought. Shocker, I know.

These things have helped me to survive E&M (barely). And if I can survive, so can you.

PS: Since I am taking E&M this semester, I will post helpful tips, problems, derivations, equation dumps, anything that I think might help you, the new Physics C students, to survive... As long as I have time. I do have my own homework.
I'M BAACCCKKKKK!!!! As stated in my last entry, though it be several months ago, college wont stop me from blog posting. And with my new found wisdom of college life, I thought I should give some advice to the new prisoners, I mean physics C students.
The first thing you learn in physics c is vectors, along with the dot and cross product. LEARN, MEMORIZE, MASTER, REPEAT. Not only will they continue to pop up throughout the year in physics, they will continue to pop up in college. I was one of the many that learned and memorized it at the beginning of the year for the first test, then forgot about it the next day. DON'T DO THAT. I am currently taking calculus III and Fullerton's lessons on it are my lifesaver. I am the one explaining the notes to others instead of being extremely confused. Also, Fullerton's method for solving the cross product is very useful, so while it may seem confusing or overly complicated now, it will simplify the more difficult questions in the future.

Alright, I think that enough of now, I don't want to scare you newbies away already!!!
So senior year has finally come to an end and we all are saying goodbye. So I thought I would discuss the physics of senior year. The year has had so much physics enwrapped in it, in and outside the classroom. We got to use physics in physics c (duh), calculus, and technology for those who take these classes. With a basic understanding of physics, these classes became easier to learn and master.
Outside the classroom, physics was used by every athlete in the school in some shape or form from lacrosse involving torque, to hockey with rotational motion. But there is so much more. Physics was used every time the students went up and down the stairs, or when we used the computers or cell phones (which of course none of us would ever do). There's when we go to the nurses office and they use the thermometer, or when we do our locker combinations to get our stuff.
Physics can even be applied to our work effort. the more energy that we used throughout the year, the less potential energy we had to use. Hence, the moment APs were over, almost the entire class stopped working, using at times only the most minimal of effort.
Finally, there was the excitement factor. Like with electromagnetism, the closer we got to the end of the year, the more energetic we got, buzzing with excitement for graduation.
On that note, I would like to say good luck to everyone in their future, whether that be in college or high school or whatever it is you do, and to continue with physics and stay nerdy!!!
So my dog just growled and I thought I should do a blog post on her since I cannot think of any ideas. I was just playing fetch with Pearl in my house, which has hard wood floor (the real kind). Pearl ran on the area carpet onto the hardwood, but when she tried to stop, she ended up skidding past the ball into the fireplace (its just a hole in the wall made of brick so she was unharmed).

So here's the play-by-play:
When Pearl was running on the carpet, she was able to get enough contraction to accelerate forward.
Once Pearl hit the hardwood floor, she couldn't accelerate or decelerate as easy as when she was on the carpet without the friction on her paws.
When she reached the ball, she attempted to stop abruptly, however, the with the low friction on the hardwood floor, she slid past the ball into the fireplace.

While my dog is very smart, she is not smart enough to learn physics. But if she could, Pearl would probably not slide into the fireplace every time we play ball. At least I can get amusement from she sliding all over the place.
Ok, I think everyone knows that sequels are rarely as good as the original, but I think The Physics of Roof Trusses II is way better than the first, but that's mostly because I thought that this roof truss was way cooler. So the very last thing I did in my independent study was build a scissor roof truss. The reason why I like this one so much is because of the awesome shape, even if the angles were butts. Anyways, it usually spans up to 20 meters or 65.51 feet and is most commonly found in cathedral ceiling and other architectural projects. Seems like I'm not the only one who thinks it looks cool. What's nice about this truss is that it eliminates the need of a bearing beam (a support beam that goes horizontal), but it has poor insulation and is very expensive. Maybe that's why churches are always so cold....

Hey look! there are people in the background!
PS sorry for the poor quality
As most people know, I can't stand cats, and constantly joke about kicking them. So, I thought it would be appropriate if I did a blog post on it!!
I am by far not athletic, so top speed I could probably kick a soccer ball at 15 m/s or 33.354 mi/hr (This is the average low for kids 11-17 ). I also don't kick at much of an angle, but for this we'll say 20 degrees.

So here's the math:
y- component:
height: ?
acceleration: 9.8
velocity initial: 15sin20= 5.13
velocity final: 0
time:?

vf= vo + at
0= 5.13 + -9.8t
5.13= 9.8t
t= .5235 --> Total Time: 1.047 seconds

Y= vot + .5at2
Y= 5.13(.5235) + .5(9.8)(.5235)2
Y= 2.686+ 1.343
Y= 4.028 meters --> 13.22 feet

x-component:
velocity: 15cos20= 14.10
time: 1.047
distance: ?

x= vt
x= 14.1(1.047)
x= 14.758 meters --> 48.42 feet

DANG! That's far. Now I wanna try this. Anyone got a cat I can borrow?
As my second to last blog post ever (for a grade, you can't get rid of me that easy!!!), I thought I should simply talk about how physics is in everything we do. so Here are some summer activity examples most people would not think of:
Playing on the playground (teeter totter, slides, swings, etc)
Computers/ video games
Cell Phones
Flying a kite
Water gun wars
Swimming
Driving
Packaging for college (Force required to pull/carry it, increasing mass)
Baking/ throwing cupcakes
Sports (Baseball, football, soccer... btw you have to be playing not watching sports)
Shopping (carrying shopping bags, the production of the clothes)
Sleeping (See The Physics of Sleeping)

And there is so much more! So as we all enjoy our last summer before we all go to college, think about how physics is used in everything that we do.
Next year I will be going to college for civil engineering and I can't wait. One of the people in my physics class is always asking me if I'm going to build an Atlantis. Ever since, I have been interested in the idea of building a floating city on water, called seasteading, which is what Atlantis was before it sank supposedly. Current engineers are looking into the idea, using a similar set up as oil rigs, which are held up on platforms that go down to the bottom. The issue is the cost and the politics of it.

There are floating bridges in existence, which use multiple air compartments so that in the case of a leak, the bridge will not collapse. However, these bridges are mostly used temporarily because it is not always the most stable or reliable. Thus, this same technology would not be possible. Not to mention that a car is a whole lot lighter than a city.

So are floating cities a possibility? I don't know, but I want to try. Even if it means taking all the floaties in the world and building a city on top. Think it will float?
So Friday night was Senior ball!!!! I hope everyone had lots of fun. I sure did, and like many of the girls, came in high heels. However, I tried my best to stay in them for as long as possible, dancing in a knee-length dress in 3-inch heels. It's a lot harder than it sounds. When you wear high heels, the center of body mass vertically shifts upward. Because of this shift, your posture becomes unstable, and increasingly so as the height of the heel increases and with increased amounts of movement. Therefore, with the significant displacement of the center of mass and dancing, which involves lots of movement, its only a disaster waiting to happen. Thankfully, I ditched the heels before that happened, although a certain friend who was pretty in pink did have to face the physics. And the floor.
Ok, I'm going to be honest... I am waiting for my hair to dry before I go to bed, and I have nothing better to do than to do a blog post. This might take a while.
Well, in the meantime, since this was the last day of real physics c, I decided to say the top ten tings I have learned from taking this course (fyi, they are in no specific order, only in the order they pop into my wet head)

1. Rotational kinematics/energy/momentum/ everything is without a doubt the coolest subject in the course. Not that I'm biased.
2. E&M is the most evil thing in the world
3. Maxwell's Equations are the best thing in the world of E&M and the only reason why I (sort of) understand E&M
4. Drag Force is definitely the hardest thing you learn in the entire course, and once you finish the course you realize it isn't that hard in the first place
5. Calculus is your saving grace- if you know calculus, it will make the course 10000000X easier.
6. Don't underestimate the book. Even when the words don't make sense (they never do), do the sample problems and they will go a long way.
7. No one is as good at physics as Mr. Muffin Man. Don't bother trying, you will lose. (If I have the screen name wrong let me know and I will fix it)
8. Walter Lewin makes the best dotted lines. Don't deny it, it's true.
9.Batman is the coolest way to apply physics.
10. The right hand rule is unteachable to me. I have had two teachers, several friends, and multiple books attempt to teach it to me, and its no use. It's a lost cause.

Well, that's my top ten. I hope you guys can learn something from it! ( To all future physics c students: see #3. There is hope.To all future professors: see #10. There is no hope)
I must have a thing for thinking about blog posts in the middle of the night. So last night I woke up at 3:00 am because of my sore throat, which makes it extremely painful to swallow, cough, yawn, etc. So, as I lied in bed unable to fall asleep, I thought about the mythbusters episode I watched about making someone wet the bed by sticking their hand in water. But what stuck out to me was that they used the frequency of the brain waves to determine how deeply asleep Adam and Jamie were.

As you can see, the brain waves are much faster and active when awake, but when asleep the frequency slows down, making it easier to pull a classic camp prank on someone. Spoiler Alert: it doesn't work. Pretty cool how waves is applied to the real world huh? Unless you're me, then your brain waves look like this:

Ok so I think it's fair to say that no one wants to read a textbook, especially a physics one. Me personally, the words just kinda go in one ear and out the other. So here's my tip on how to read the textbook: Don't read the textbook.
A lot of you are probably thinking, "YES! I've been doing that all year!" Well, there's more too it. Mr Fullerton is right when he says the textbook can be very helpful, but the way I "read" the textbook is by doing the problems. Obviously you can't just open the textbook and do all the problems at once on the first day of the unit, but go through them along with the class. It gives the stuff you learn in class something to base it off of.
Now, I definitely would not go and do every single problem in the book; some of them are unnecessary or just dumb (aka unnecessary). So, since we have a magnetism text coming up, here are the problems I thought were helpful focusing on the stuff we just learned:
28.1, 28.3, 28.4, 28.6, 28.7, 28.9, 28.12, 28.13, 28.14, 29.4, 30.1
After doing these problems, I feel a lot better about this unit (not magnetism in general, just this unit). Hope this helps you and good luck on the test!!
After talking so much about my favorite engineering field, I decided to create a QUIZ to find your perfect field of engineering. A nerdy-version of a personality quiz. WIN.
By the way, please post your results, I am curious to know how accurate my quiz is.

1. Other than physics, what is your favorite subject?
a. Biology
b. Chemistry
c. Technology
d. Math/ Calculus

2. What do you like to do in your free time?
a. Logic puzzles
b. Tinker
c. Go out with friends
d. Go for a walk/ do sport things

3. People would describe you as:
a. Perfectionist
b.Caring/ Kind
c. Innovative
d. Logical

4. As a Child you loved:
a. The loud electronic robots that made shooting noises
b. Building the marble race tracks (with the plastic pipes)
c. Playing outdoors
d. Video Games

5. During a group lab, you usually:
a. Set up the lab
b. Collect the Data
c. Calculate the necessary numbers

6. You hate:
a. Disorganization
b. Carelessness
c. Selfish People
d. Things done incorrectly

a. Spiderman
b. Batman
c. Aquaman
d. Ironman

8. What is your favorite unit in Physics?
a. Work, Energy, Power
b. Electricity and Magnetism
c. Dynamics
d. Fluids
e. Statics (Combination of torque, dynamics, and vectors)

9. Would you rather be responisble for:
a. A company
b. People's lives
c. Improving the world/ country
d. The community

10. Why do you want to go into engineering?
a. To protect the environment and people
b. To manage things efficiently
c. To help people
d. To advance the world we live in

Biomedical: 1a/b, 2c, 3b, 4c, 5d, 6b, 7a, 8d, 9b, 10c
Civil: 1c, 2a, 3a, 4b, 5c, 6d, 7b, 8e, 9b, 10a
Electrical: 1c, 2b, 3d, 4d, 5a, 6a, 7d, 8b, 9c, 10d
Environmental: 1a, 2d, 3b, 4c, 5b, 6c, 7c, 8a, 9d, 10a
Industrial: 1d, 2a, 3c, 4b, 5b, 6a, 7b, 8c, 9a, 10b
Mechanical (Robotics): 1c, 2b, 3c, 4a, 5a, 6b, 7d, 8a, 9c, 10d
As promised, I looked into how fast the Batmobile would go on a frictionless plane instead of the roads of Gotham. To compare the difference, I used everyone's loving friend, Energy.
uk= .8
aB= 60 mph in 2.4 seconds (after some conversions....)= 11.17 m/s
mB= 4500 lbs (FYI, I was wrong, a tank weighs 135,000 lbs)

F-Ff= mBa
mBaB- ukmBg= mBa
(4500) (11.17) - .8(4500) (9.8)= 4500a
a= 10.376 m/s
They may not look like a big difference; well, its not in the short distance.

x= 1 mile= 1609.34 m
x= .5at2
t2= 2x/a
t2= 2(1609.34)/ (10.376)
t2= 310.2
t= 17.65 s
vs.
t2= 2x/a
t2= 2(1609.34)/ (11.17)
t2= 287.999
t= 16.97 s
So, obviously, when it comes to short distances, the friction on the car is almost negligible. However, if Superman decided to play a prank on Batman (his attempt to be funny), he could put the Batmobile in space, where the car can infinitely accelerate without friction, where the Batmobile will become the Batrocket. Let's hope the brakes are working.
Wow. That title is a mouthful. Kinda like the equations in this unit because THERE ARE SOOO MANY. So I am going to help everyone (and myself) and create a list.
FM= qv x B --> FM= qvBsinᶿ
F= I x B
FM= FC --> r= mv/ (qB)
Velocity Selector: FM= FE --> v= E/B
FB= ʃI (dl x
B= μoI/ (2πr) μo= 4π e-7
Maxwell's 2nd Equation: ʃB·dA= 0
σInduced= (1-(1/k)) σFree
B-Field due to Current Loop: B= μoI/ (2r)
ʃB x dl= μoIpenetrating
B= NμoI/ L
μ= NIA μ= magnetic moment
τ= μ x B τ= torque
B= μo(qv x r)/ (4πr2)

Huh. Maybe there aren't as many as I thought, they are just more complicated than normal. Guete Gelueck! (well, technically Alles Gute....)
Its after midnight and I'm tired. So here are some cartoons about Schrodinger's Cat, which I have been thinking about a lot lately for some reason...

[ATTACH=CONFIG]651[/ATTACH][ATTACH=CONFIG]653[/ATTACH]

Cartoon #1: "We may, or may not, have cloned Schrodinger's cat"
Cartoon @2: "Being simultaneously dead and alive in the box gave me an incredible perspective over the "life, the universe, and everything". And I am here to tell it to the world!"
Ok, so I totally got this blog idea from denverbroncos, though after thinking about it the two reseaches are not the same like I thought (my bad). Anyways I decided to do this anyways because its uber-physicsy and funny. Basically, Penny wants to learn what Leonard does for a living, and Sheldon's teaching her. This is gonna be interesting...

Oh my gosh I am crying on the inside. I was creating a really awesome blog post that everyone would love and I went to backspace a letter and it returned to the home blog page. I lost everything. So I am going to explain why when you are tired you do stupid things such as not save.

According to scientists, during sleep your brain sorts through and stores information, replaces chemicals, and solves problem from the day. When you are tired, it's your body's way of saying, "AAAHHHH me tired." Just like when exercising any other muscle, after a certain amount of time that muscle becomes sore and cramped (headache), in desperate need of a break. However, instead of tightening up and not being able to move that muscle, the brain begins to make poor decisions, make mistakes, and neglect certain details. In addition, many people become more emotional due to lack of sleep, they also become hyper-alert in a negative way: aware of the problems youre facing, but not able to focus on any one topic. An interesting "fact" (i googled it so i could be wrong), but when tired your brain acts in a similar way to when you're tired, slower reaction rate, temperamental, and poor judgement. Another really cool "fact" is that your body/brain sends signals to go to sleep, which requires more energy to fight the urge, which makes you more tired.

Long story short, give up and go to bed. Which is what I will do now... maybe. I apologize if i repeated myself or if the facts are false.
As many people know I plan to go to college for civil engineering. Whenever I tell people this, they always ask me what exactly civil engineering is. So, to kill two birds with one stone, I'm going to explain via blog post!

So basically, to put it in simplest terms, civil engineering is the physics of structures.... sort of. Civil engineering, like engineering in general, has many many many different sections within it. For example, there's structural, geotechnical, materials, construction, transportation, water resources, sewerage, and so much more. Even environmental engineering is considered a subset of civil engineering, although personally I think they should just give environmental its own group, but that will probably happen in the near future with the increase in demand for alternative energy. I am interested in structural engineering, which includes anything from homes to bridges.

As a structural engineer, I would be in charge of a variety of things. The dictionary definition is an engineer who "analyzes, designs, plans, and researches the structural components and systems." So during a project, I would need to work with other engineering professions and architects constantly to create a design and during the construction of the project.
Civil engineers use trigonometry a lot because almost all structures involve trusses, but as for physics there are several "units" that can be used. For example:
Dynamics: Newton's laws, free body diagrams. The purpose of free body diagrams is actually to find the force on each beam of a truss (not to make our lives miserable)
Linear Momentum: Center of mass, this is used a lot for I beams and of beam types.
Finally Rotational Momentum: Torque. Torque has everything to do with trusses because you what static equilibrium in all structures. How safe would you feel if the building shook every time there was a gust of wind? I would be very scared.

One of the final things a civil engineer could be responsible for is overseeing the construction, especially paying attention to the details when the project is being finalized. When I went on a shadowing day, I visited a site with a civil engineer, who kept talking to his partner about certain details that the construction workers screwed up, which irritated him a lot. Not only did I find that humorous, that moment I knew that civil engineering would be perfect for me.
Ok, I gotta admit, that last blog post stunk like my dog's farts. In fact, other than the physics of faradays cage, they all have been pretty bad. Well, I am going to tell you what the best and the worst have in the blog posts.
The best:
Humor is a good thing. Physics at times can be rather boring, and if you couple it with some humor, it can be more entertaining for the viewers.
Have it on an interesting topic. Let's face it, a bad topic is a bad blog.
Connect to the "real world." Dont just talk about school and physics class, but connect it to the outside world. It gives the blogs a sense of meaning.
Ad finally, Make it meaningful. I know lots of you are only trying to get these done at the last second, but if you are just randomly posting things hoping to get credit, the post is going to be a dud, except on those rare occasions where it turns out amazing (aka the physics of faraday's cage).

The Worst:
Dry. There's no spice, no excitement. If you simply have a dry subject, try adding in colors or fun faces. It adds character and draws the eye.
No Physics. Yes, the are times where the blog posts are simply people rambling. Come on, weve all done it (the physics of tetris by me, not mrmuffinman). Make something up, find some connection, just put physics in it! ***Warning: lame physics is better than no physics, but still won;t do well
Bore-fest. As sad as it is there are certain topics that people dont care about, like my independent study. Not that I blame people....

I think the most important part of making a blog post is to be excited for it!!! Put a little of yourself into the blog posts, just like in English voice is key.
Well, I hope I have helped make you all better bloggers!!! Ready, Set, Blog!
I have been waiting to do this blog post for a long time, and I am excited to do this. I dont know about anyone else, but I like to keep track of my highest viewing blog posts and try to get the most as possible. After (semi) extensive research, I am ready to share my findings with you!!!!
So, to start off, blog post views increases the same way as the learning curve, slow at first, then increases a a faster rate until the acclereation begins to slow down until it plateaus. However, the difference between the learning curve and the "blog curve" is thatthe blog curve never really plateaus because there are always new people entering the internet and this website, searching for an amusing blog post or specific information.
[ATTACH=CONFIG]631[/ATTACH]
So, last quarter when I did my blog posts I recorded the number of views I had after two weeks. I have now created different groups to dicuss the success of each blog post. Keep in mind that the numbers I use are from my blog posts only, so that can be different for other people. Here are my "catagories" based off the numbers:
High viewers ( a hit): 100+
Middle Range (a good blog): approx. 65-99
Low viewers (Better luck next time): >65

I figured this blog post is boring enough, so check my posts later for advice on creating blog posts. Have fun!
Hey people, i know that it's not a fan favorite but i haven't done a blog post on my independent study. Recently I finished a roof truss called a double cantilever (or a type C truss), a model for the technology room. This specific type of roof truss is used mostly in commercial and industrial buildings. It spans on average 16 meters, or 52.5 feet. That's really all I know, but I'm really proud of my work which I think is very cool. Hope you guys agree!!
(Again, sorry about the extreme size of the picture, I still cant figure that out....)

Ok, to be completely honest I came up with this idea thanks to Mr. Fullerton and Goalkeeper0.
Anyways, whenever someone talks about Faraday's Cage, I think about that scene in Sorcerer's Apprentice. Not only is it a funny movie, but it's got physics in it. Not to mention Nicholas Cage (hahaha Nicholas Cage, Faraday's Cage, no pun intended). What's not to love? So here's a clip from the movie, which is a great and really cool example of Faraday's Cage. Enjoy the Show!

Ok, I have been working really hard to finish the AP Physics Review Packet, but I haven't really compared answers with anyone else. So I thought it would be helpful for everyone if I posted my answers. I personally think they are right, but if you have a different answer, SAY SO!!! I would gladly compare notes to find the correct answer, helping everyone out. If I missed any questions, let me know.
[TABLE="class: grid, width: 500"]
[TR]
[TD]Pg 1
1. A
11. B
[/TD]
[TD]Pg 2
14. A
15. E
2. E
65. C
5. C
[/TD]
[TD]Pg 3
1. E
3. D
3 (below). C
[/TD]
[/TR]
[TR]
[TD]Pg 4
5. C
19. D
[/TD]
[TD]Pg 5
2. E
26. C
27. C
10. C
[/TD]
[TD]Pg 6
25. B
7. E
3. D
[/TD]
[/TR]
[TR]
[TD]Pg 7
6. E
9. E
5. C
[/TD]
[TD]Pg 8
19. A
9. D
[/TD]
[TD]Pg 9
34. B
4. E
7. E
[/TD]
[/TR]
[TR]
[TD]Pg 10
34. A
14. C
6. B
[/TD]
[TD]Pg 11
15. E
17. A
8. B
10. E
[/TD]
[TD]Pg 12
18. A
32. B
15. E
[/TD]
[/TR]
[TR]
[TD]Pg 13
18. D
16. A
18 (Right). B
[/TD]
[TD]Pg 14
19. C
8. A
13. A
14. A
[/TD]
[TD]Pg 15
31. E
17. B
12. C
17 (Right). E
[/TD]
[/TR]
[TR]
[TD]Pg 16
29. B
31. E
[/TD]
[TD]Pg 17
6. A
28. D
12. C
13. D
[/TD]
[TD]Pg 18
20. C
27. A
29. B
30. E
[/TD]
[/TR]
[TR]
[TD]Pg 19
23. D
1. D
5. C
[/TD]
[TD]Pg 20
14. B
15. A
9. D
35. A
[/TD]
[TD]Pg 21
32. E
33. B
32 (Right). D
35. E
[/TD]
[/TR]
[TR]
[TD]Pg 22
30. B
26. D
26 (Bottom). E
[/TD]
[TD]Pg 23
10. A
11. D
12. B
12 (Top). E
20. D
[/TD]
[TD]Pg 24
32. A?
22. C
21. C
[/TD]
[/TR]
[TR]
[TD]Pg 25
22. D
11. E
20. A
35. B
[/TD]
[TD]Pg 26
10. E
3. C
30. A
34. C
9. D
[/TD]
[TD][/TD]
[/TR]
[/TABLE]
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