Last Day of November

Today is the last day of November. A lot of things are good because of this. First of all, I'd like to mention that since today is November 30 and there is no 31st of November, it means that tomorrow is December 1, the first day of December and the day of Green Team's field trip. My group, Group 2, is going to the Federal Reserve, which is a bank. It may sound a little tedious, but I think it's going to be an okay trip. There are many reasons for me to say so.

1. There is math involved.
2. Mr. Yellen has said that it is supposed to be fun, I don't know.
3. Mrs. Batchelder said that there were going to be gifts.
4. It skips most of school (we're still having C Block).
5. There is even more math involved.
6. Ditto the first reason.

This month, I have posted 32 posts, including this one. That means that I have posted more posts than the number of days, 30. I must have done a lot of work! I can't believe that I managed to do that and do all my school work and do all the chinese school homework and practice the piano every night and do math team and winter running and do orchestra and do band and study latin! That's just like impossible! But it is, I've done it...

Skipping Math

Yay! I just missed (not skipped like it says in the title) a math class. Well, I also missed Spanish, but that's not the real point of importance here. There was a test in math class. Since I was going to miss it, I took it in the morning before school started. I only had about 15 minutes, but that's basically how long it took me to take the test. It was a loooooooot easier than I thought. I just have to finish checking the test later.

I had to swear that I wouldn't tell anyone what was on the test or how hard it was. But somehow, everyone seems to know that I took the test early. I'm still wondering how they found out. Please tell me if you know! So many people came up to me and asked if the test was hard, and I either said, "I'm not allowed to tell" or "I don't know, you find out yourself when you take it." (This message is especially for you Tyler, Linnea, Alex (maybe, I forgot), Seong-Tae, David (a.k.a. Jimmie), and a countless number of other people that I didn't mention.

Math is a lot easier subject than most people think it is. It only has one answer for every question. (Well, there are some exceptions, for example, quadratic equations usually have two answers, but that's beyond the point and you'll probably learn that in ninth or tenth grade.) I'll bet you anything that if I tutored any of you in my class for two weeks, you could be as good as me! I'm serious!



By the way, it's not too late to answer the POTW question. Only two people have gotten it correct. About three other people all did it wrong. I was very surprised.

Create Account

There is now the ability to have your own private account on my blog. There is a login screen in the toolbar that you can log in to. If you are new and would like to create an account, just follow the instructions beneath the Login screen. This is a very complicated software that uses Javascript and HTML. Note that capitalization does not matter. Also, please give credit to Google Docs and Spreasheets for offering the seperate web pages. It is a very simple precess and only takes five minutes of your time. This a a very new thing, so please excuse any errors in the program.

POTW #4

The entire figure at the above is a right triangle. Angles ABC and BDA are right angles. Lines BA is 15 units and line BC is 20 units. Find, if possible, the lengths of l and m. If you think it is impossible, then explain why it is so.

Email all answer to twang7888@yahoo.com.

Difficulty level: 3

Source: Totally original, so forget about finding the answer on the web, but there's always the possibility that someone else has coincidencially posted it on the web.

About POTW Scoring

A various number of people have asked me about how the POTW points are scored. It is very simple, but seems complex. Here is the starting list:

First place: 5
Second place: 4
Third place: 3
Fourth place: 2
Fifth place: 1

Then, you take that number and you multiply by the difficulty level. So if a POTW question has a difficulty level of 4, then first place would be worth 20, second place, 16, third, 12, etc. FYI, the difficulty level is at the end of every POTW.


NOTE: THIS SCORE GUIDE IS SUBJECT TO CHANGE AND YOU WILL BE INFORMED WHEN IT IS DONE SO. AFTER THIS PARTICULAR POTW ROUND IS OVER, (every POTW round is five questions) THE POINT VALUE WILL CHANGE BECAUSE I HAVE NOTICED THAT THERE ARE MANY PEOPLE WHO DON'T GET POINTS BECAUSE THERE AREN'T ENOUGH PLACES FOR THEM.

Announcement Banner

There is a new Announcement Banner in the toolbar. It is the very first thing. It says all the current announcements. I thought of this because people keep asking me when the next POTW is coming out. Just to inform you, POTWs come out on Tuesdays, exceptions may be made and it will say so on the new Announcements Banner. One thing that I really like about it is that it scrolls over, so it attracts attention. That is important! I noticed that even after it has been posted, people have left comments saying "When is the next POTW coming?" Well, now you know. Check the announcements!

Miniclip Games

Below is the Twangsite Miniclip Game Room. It's really cool, and I found out how to post it onto my blog. This Game Room will be updated weekly. After a while, this post will be pushed downward on my blog because I will have many new posts that will be above it. I have taken this into consideration and put this on the toolbar to the right of this post. You can also put this onto your blog by clicking here. However, it will appear too big for your blog because the window isn't large enough (there might be an exception as Blogger now allows templates that are stretched). I have solved this problem myself very easily. However, you may have a more difficult time shrinking the image because chances are that you don't know HTML (Hypertext Markup Language). You can email me and I will email you the the revised HTML text and then you can post it onto your blog as well. My email is twang7888@yahoo.com. Anyway, here is the Twangsite Miniclip Game Room:

POTW #3 Answer and Explanation

The problem is actually a lot easier than you think, you just need the right way to look at it. Notice that the triangle's hypotenuses (is that the plural for hypotenuse?) have different slopes. In the original picture, the slope of the upper triangle is steeper than the lower one. Because of this, the hypotenuse bends slightly inward, making the area smaller than it appears. In the rearranged triangle, the the triangles switch, so the lower triangle is the one with the steeper slope and the upper one has the more level slope. This makes the hypotenuse slightly outward, which makes the area of the area of the triangle slightly larger than it seems. Since the rearranged triangle is exactly one unit bigger than the original triangle. Therefore, there is a hole of one unit!


By the way, the source of this puzzle was Exidor's Logic Puzzle Place, but you will probably find it in many, many other places too.

1000 Hits

I have recently discovered some good news. My blog has been visited 1000 times! It happened yesterday on Thanksgiving. You can see for yourself on my web counter on the very bottom of the toolbar. It probably has a little more now because other people have already added on the the number of hits there are.

Funny Math

Here are some funny math pictures you an look at during Thanksgiving. I didn't make these up.

Thanksgiving!

It's Thanksgiving! School just got out and I just got home from taking the bus. I have a party tomorrow and another one on Saturday. Tomorrow's party is going to be better because it has one of my friends, and Saturday's party is going to be my parents' friends. We get four days off of school. During this time, I'm definitely going to finish my the English Short Story Writing Assignment. That's all for now!!!

POTW #3

As you can see, the top figure is split into four parts. The bottom figure uses the same four pieces, but has a hole in the middle. How can this be possible?

(Note: You can click on the images to get an enlarged view.)

Email all answer to twang7888@yahoo.com

Difficulty Level: 4

Source: Not actually original, but I'll tell you the source on the answers...

Chapter 3 Science Homework

Part of the Chapter 3 science homework is now available my blog. Click here to view it now. It is now totally complete.

This was brought to you by Google Docs and Spreadsheets.

5-Star Practice Test

I'm making a 5-star practice test for the math class. It's actaully turning out to be really fun. I'm currently in the process of typing the questions and making sure I didn't make any stupid errors or mistakes. I was thinking of posting it onto my blog, but then I remembered that equations can't be displayed on Blogger. It would be too complicated to use HTML for it (I'm not even sure you can do that), so I'm just not going to bother. If your in my Accelerated Math Class, then you can see it. This is probably my first real blog entry in a while. When I say "real," I mean something about my life, not math homework answers or POTWs.

POTW #2 Answer and Explanation

This problem involves compound interest. In order to solve this problem, you would have to understand some vocabulary. When something is "compounded", it means that the interest is added on to it. For example, if something was compouded monthly at a rate of 5%, then you would add 5% every month. Also, "compounded triyearly" means that it would be compounded three times per year, so about every four months. You would also have to know the form of an exponential equation, a*b^x, where a is the starting number (in this case, 1000), b is the growth or decay rate, and x is the number of times it is compounded.

To start, you would have to write an expression for each of the three different interest plans:
1. 1000*1.012
2. 1000*1.001^12
3. 1000*1.0035^3

Then, just solve each of the equations and see which one is bigger:
1. $1012
2. $1012.07
3. $1010.54

According to the work, John should pick choice two for his interest plan for his bank account. This would give him the most money, $0.07 more than the first choice. Every penny counts!

November 15 Math Homework

Here's the November 15 Math Homework.

Again, it's thanks to Google Docs and Spreadsheets that it's here.

November 14 Math Homework

Here's the math homework for today.

Again, curtesy to Google Docs and Spreadsheets.

Science Homework Posts

Math homwork is easy to post because they are usually in the book, so I have to write them up anyway. Now, our science teacher has given us work to do from the book. So I might as well post it to my blog. I will probably do this every time unless the homework is not from the book. Social Studies and English could be coming soon, but I doubt English would work, because we hardly get any homework anyway!

POTW #2

John has $1000 and he decides to start a bank account. The bank offers three different types of deals for interest rates. They are listed below:

1. An interest rate of 1.2% compounded yearly

2. An interest rate of 0.1% compounded monthly

3. An interest rate of 0.35% compounded triyearly

Which deal should John pick if he stores the money in the bank for one year and wants to get the most money?

Note: Every penny counts!!!!

Solved the problem? Then email it to twang7888@yahoo.com.

Click here for more information about problem of the weeks such as grading criteria, answering, etc.

Difficulty level: 3 (out of 5)



Source: Original, but the idea of compounding money was taken from math class about two weeks ago.

POTW #1 Answer and Explanation

Since the POTW is closed, I decided to give the answer now because anyone else that finishes the problem will not deserve any credit, only the first five do (This time, first six because Tyler E. was an exception). I know it has only been about 3 days, but so what?



The perimeter of the rectangle would be 56 inches. The length was 16 inches and the width was 12 inches. There were many ways to do this, but the easiest would be to use algebra. However, you would have to know how to simplify quadratic equations, which average eighth graders wouldn't know. Here's a step-by-step process of solving this question the algebraic way.

First, you would get the equation:
x(x+4)=192 where x stands for the width

Distribute the x:
x^2+4x=192

Make the equation equal 0:
x^2+4x-192=0

Simplify the quadratic equation: (Note: if you do not know how to do this, then you couldn't have solved this question the algebraic way)
(x-12)(x+16)=0

Solve for x: (Note: There are usually two answers for a quadratic equation)
x=12 or -16

Use your logic, the width couldn't be a negative number, so the width would be 12.
Now, if the width was 12, the the length would be four more, or 16. Thus the perimeter would be 12+12+16+16=56

(Note: please be sure to find out what the question is asking for. A few people gave me 12 and 16, which were the dimensions of the rectangle. However, the problem asked for the perimeter. I did not take off for this error because this was the first POTW (Tyler E. is an exception). I will take off 2 points in the future though.)


Any questions or comments? Post a comment or email me at twang7888@yahoo.com.

POTW Leader Board

The Problem of the Week Leader Board is in the toolbar to the right
----------------------------------------->

POTW #1

A rectangle's area is 192 square inches. The length of rectangle is 4 inches longer than it's width. How many inches are in the perimeter of the rectangle?


Please email me the answer at twang7888@yahoo.com! Do not post a comment, or else everyone will know the answer! 2 points off for resubmissions!

Click here for more information about answering the question, grading criteria, points, and others.

Dificulty Level: 3 (out of five)



Source: Original

The Mathster and the Candy Craving Child

Recently, our class has written a story in class that had to end with "And the moral is, be careful what you wish for." I was really bored today and decided to put this on my blog. It is very long, so again, I used Google Docs and Spreadsheets, which by now has become my favorite Google thing. Here it is: The Mathster and the Candy Craving Child

Hope you like it!

Problem of the Weeks (POTW)

I'm going to post some problem of the weeks on this blog. Of course, they are math questions. However, I think just math questions are a little tedious, so I'm going to have a competition. Everytime you answer the problem of the week, you get a certain amount of points, depending on how quickly you submit your answer.

The grading criteria is a little complicated. The first person to submit their answer gets 5 points. Second person, 4 points. Third, 3 points. Fourth, 2 points. Fifth, 1 point. Sixth and above, 0 points! this score is then multiplied by the difficulty level, which means that the harder the problem, the more points it's worth. After every five problems, I announce the winner and then I reset the scores. Any wrong answers will deserve a 0 and will not count as a place number.

Please email me your answers. One smart thing to do would be to click on the email post button under the problem and email me the answer in the "Message" box. Please leave a name. (Note: I know that not everyone likes to publicize their name on the Internet, so you can just give a screen name like "Koolfool" or "DDOG123". However, you must be sure to use the same screen everytime, or else your points won't add up.) Two points off for resubmissions!

The difficulty level criteria goes as follows:

5: Very difficult, could take 15-30 minutes for an average eighth grader
4: Difficult, could take 10-15 minutes for an average eighth grader
3. Average, could take 2-10 minutes for an average eighth grader
2. Below average, could take 1 minute for an average eighth grader
1. Extremely easy, could take less than a minute for an average eighth grader

Note: All POTW questions are bold, italic, and highlighted in blue.


Any questions or answers to be given? Email me at twang7888@yahoo.com.

Top 5 Viewers and Commenters

To the right of this post in the sideline, there is now two slots that have the top 5 viewers and top 5 commenters. If you read this blog a lot or post many "useful" comments, then your name gets put into the sideline.

I just thought this was a fun thing to try. Any thoughts about it?

November 9 Math Homework

Here's the link to November 9th Math Homework.

I used the Google Docs and Spreadsheets, as I have mentioned before. This is the second post that I used it. I hope you think it's better.

Google Docs and Spreadsheets

The homework that I've posted for math class is helpful, but someone told me that it was unclear and the exponents were all wierd. To solve that problem, I decided to use Google Docs and Spreadsheets because it shows more advanced symbols. Also, it is on a blank sheet with so sidelines or ads so that you can print it out and have your own copy of the answers. I hope this is useful and makes your life easier.

November 8 Math Homework

November 8 Math Homework

I used Google Docs and Spreadsheets. It's really cool.

November 7 Math Homework

Pg. 193-194 Problem Set D

(Note: For problems 1-4 with the tables, the numbers don't match up because I didn't want to take the time to put tables in. Sorry for the inconvinience.)
1.
(x,y) (0,0) (4,4) (36,16) (25,0.25) (0,100)
√(x)+√(y) 0 4 10 5.5 10
√(x+y) 0 √8 √52 √25.25 10
The table shows that you cannot distribute the square root symbol over the addition because the values are not the same.
2.
(x,y) (0,0) (5,5) (9,25) (0.64,100) (0,100)
√(x)*√(y) 0 5 15 8 0
√(x*y) 0 5 15 8 0
The table shows that you can distribute the square root symbol over the multiplication because the values are not the same.
3. (x,y) (0,0) (4,4) (81,49) (25/9,16/9) (0,100)
√(x)-√(y) 0 0 2 1/3 -10
√(x-y) 0 0 √32 1 Undefined
The table shows that you cannot distribute the square root symbol over the subtraction because the values are not the same.
4. (x,y) (0,2) (3,3) (4,16) (4/9,2.25) (0,100)
√(x)/√(y) 0 1 0.5 4/9 0
√(x/y) 0 1 0.5 4/9 0
The table shows that you can distribute the square root symbol over the division because the values are the same.


Pg. 195 Problem Set E

1. 5√3
2. 2√15
3. Cannot be simplified
4. 0.5√0.5
5. 5x√2x
6. 6(a^2)(b^2)√2b
7. √12
8. √72
9. √75y^2
10. √(3/16)x^5


Pg. 196 Problem Set F

1. No √2+√2+√2 = 3√2 = √18
√6 = √6
2. No 3√2+√3 do not simplify to anything.
3. Yes √50+√98 = 5√2+7√2=12√2
12√2 = 12√2
4. Yes √45+√20-7√5 = 3√5+2√5-7√5 = -2√5
(-1/2)√80 = -2√5
5. √75-√27
6ai. √3
6aii. √3
6aiii. 5√2
6aiv. 5√2
6b. Yes, i and ii are equivalent
iii and iv are equivalent



Note: It is possible that there is a typo or that I have made a calculation mistake. I do not take any blame for wrong answers.

Sorry, no results found

This is personally to the person who requested Mendelssohn Violin Concerto in e Minor:

Dear Sheet music wanter,

I am sorry, but even with all it's famousness, it was not in the list of sheet music I have. There are many reasons for this. For one, this piece may have not given permission to anyone to legally put it on the web for free. Two, I'm just not looking hard enough.


Sorry for the inconvience,
Twang

November 6 Math Homework

Pg. 178-180 Problem Set G

1a. Yes, growth
1b. Yes, decay
1c. No
1d. Yes, decay
1e. Yes, growth
1f. No
2a. II and III cannot describe a linear relationship. II cannot because is has more than one place that it curves. III cannot because it is a parabola.
2b. I involves growth and IV involves decay.
3a. No, you cannot
3b. No, there is not
4a. No
4b. Yes, it would involve growth because the interval that y increases by is getting higher and higher each time x increases.
4c. Yes, it would involve decay because the interval that y increases by is getting smaller and smaller each time x increases.
5. Yes, the relationship between the number of days since the scientist began growing the culture and the number of amoebas is exponential; the growth rate is 2.
6. No, the relationships between the number of days since Sydney began hiking and the number of miles she has hiked is not exponential because she hikes 15 miles everyday, which makes it linear.


Pg. 180-181 Problem Set H

1.
Days Culture 1 Culture 2 Culture 3 Culture 4
0 100 100 100 100
1 300 50 70 500
2 900 25 49 2500
3 2700 13 34 12500
4 8100 6 24 65200
2. Culture 1: 3
Culture 4: 5
3. Culture 2: 0.5
Culture 3: 0.7
4a. Culture 1: p=100*3n
Culture 2: p=100*0.5n
Culture 3: p=100*0.7n
Culture 4: p=100*5n
4b. They all start with the constant 100 and all have a number to the nth power.
4c. They all have a different number as the base of the exponent.
5a. Graphs not available.
5b. Graphs not available.
5c. The graphs that grew started low and went higher and higher. The graphs the decayed started really high up and eventually got lower and lower.
5d. They have the same form and shape just reflected across the y-axis.
5e. For the growth graphs, the graph the increases at the faster rate has a greater growth factor, while the graph he increases at a smaller rate has a lower growth factor. For the decay graphs, the smaller growth factor decreases faster than those with a larger growth factor.


Pg. 183-184 #9-16

9. No
10. Yes, growth factor of 4
11. Yes, growth factor of 4
12. No
13. Yes, decay factor of 0.25
14. No
15a. 133.3 mg
15b. 200*(2/3)n
15c. 200*(2/3)n
16a. IV
16b. I
16c. II
16d. III
16e. V



Note: It is possible that there is a typo or that I have made a calculation mistake. I do not take any blame for wrong answers.

Math Homework Posts

I am going to start putting the daily math homework on my blog. I will try to do it for every day, but it is hard to type the math homework because there are a lot of symbols and other wierd things like fractions, square root symbols, etc. However, I could use HTML codes but that takes a lot of time. One major problem is exponents. I don't think HTML can even place exponents onto variables and numbers. Some of the answers will look wierd. For those, either take a good guess at what it should say or do it yourserlf! Please don't rely on this for answers all the time.

Warning!!!!! I do not take blame for any wrong answers due to typos or miscalculations. I am human.