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
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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.

X-Country Meet

We had a meet at school today against Acton and Oak Hill. It was really fun and our team won! I was especially happy because I ran really, really well today. I broke my personal record by 47 seconds. I don't know how much you know about running, but that's a lot of time to lose in one race. Our course is 1.8 miles long. My best time is now 13:13 (minutes:seconds). We have our all city championship meet in two days, Wednesday. I can't wait to see how well I will run by then. I'll update my blog when the time comes.

The New Sheet Music Toolbar

There is not a toolbar on the sideline to the right of this posting that has sheet music postings. I will post sheet music onto it for music that is requested. I have already gotten one request and I will get it on soon. All the music on the toolbar will be in alphebetical order by last name of composer. You can request a piece by posting a comment to this posting. Enjoy!

Music Update and Free Sheet Music!

Fantasie Impromptu is the piece that I'm playing on the piano right now. No, there there is no third Fantasie Impromptu, I'm only saying #3 because there are also two other posts on my blog that have to do with it. I can play the whole thing now, but I haven't worked hard to perfect it because right now, I am improving my technic. Bach's Inventions are a very good way to do that. I have free access to popular sheet music for all instruments! Just email me or post a comment and I will put a link to it on the sideline of this blog (to the right). The quality isn't the best, but at least it's music you can read!

Wow, My Math Grade is High

There aren't many important things going on in my life. We had a math test yesterday and and I got a 91 out of 80 (the most you could get was 92)! I couldn't believe it. I was sure that I would mess up somewhere. Anyway, it actually boosted my grade up 1%. You can see my updated math grade in the subtitle of this blog. I've changed the look of my blog by updating it to Google Beta Blog. You can do it to; just get a Google account. If you already have Gmail, GTalk, or something similar to that, then you already have one. I already made the background white again because the bluish color was too bright and hurt your eyes after staring at it for a while. Nothing much more.

I Came Back

I'm back from my trip to Europe. I'm going to try to find some extra time to post all my adventures. I have a lot of homework right now, so I can't do it now. Note to all readers: all the posts that have red text have to do with my trips. That way it will be easy to locate on the page.

Plane Writing

Yesterday, which was Wednesday, was my last day of schools before my journey to Europe. I got some of my final homework assignments and said good-bye to all my friends. I got picked up by my parents instead of taking the bus because so that I could get home quicker. After packing some last minutes stuff, we went outside to wait for our cab coming to pick my family up at 3:45 PM. When 3:45 came and the taxi hadn’t come yet. My dad said that drivers are usually late. Then 4:00 came and it still wasn’t here. My mom called again and the lady said that the cab was stuck in traffic, but should come in the next five minutes. At 4:10, the taxi finally arrived. After putting all the luggage in the truck, we got in and set off for the airport. We got to the check-in line and was relieved to see that there was no line, period. That made up for all the time that was were waiting for the taxi, so we were on time again. For all our flights this trip, we would be taking Swiss Airlines. We checked in, got to our gate, and boarded the plane. After waiting about twenty minutes in line for the runway, the airplane took off. Our first stop in Germany was Zurich, where we would then be switching planes to go the Geneva, also in Germany. The plane ride was actually a lot better than I had expected. It was at least ten times better than our plane trip to China. For one, it was much shorter, only about six to seven hours. Also, there were video games this flight, which entertained my brother and I for almost the entire trip. I slept for about one hour and when we finally landed, I was so happy that all that time on the plane was already over. When we got to Zurich, it was already Thursday, the fifth of October. The time there is six hours faster than EST (Eastern Standard Time) which I live in, so I had to get used to the jet lag. We then switched planes to go to Geneva. The flight to Geneva was the shortest flight I had ever taken. It was only about half an hour. On that flight, I got my first experience of Swiss Chocolate. It tasted sooooooooo good. It was a million times better than Hershey’s Chocolate. We then picked up our luggage and took the train from the airport to Geneva Main Station. My dad bought tickets for train ride to Basel (on the edge of Switzerland), then to Freiburg (in Germany), where we would finally take a rest from our travels and stay in a hotel for a while. While waiting for the train, I finally got my first experience of people speaking fluent French; not the uneducated French learners in my school (no offense to those people). The train ride was better because there was more leg room, but there weren’t any televisions or entertainment to keep us occupied for the four hour train trip. I mostly slept to make up for the major loss of rest and did a little of the homework that my teachers had assigned while I was away. That’s about my travels to Europe. Read more to find out about all my exciting adventures there.

Another one???

In a few days, I will be going to Europe to have a vacation. The whole family is going; my dad, mom, my brother, and I. First, we are going to Germany. After a few days of having fun, Last time I went on vacation, which was during the summer when I went to China, I have to admit that I didn’t think about writing anything. I was having a blast, so who would think about it? This time, I’m going to be ready. I’m going to bring a stack of papers so that I can take some notes about what I did each day so that I can post them for the world to read! I’ll have plenty of time on the planes and trains and at the hotel when there’s nothing to do for a while. When I come back, I can post them since I don’t have access to a computer in Europe. At this very second that I’m clicking away on my keyboard, I suddenly thought of something. I will be going on two vacations with less than a month in between each one. It feels like just yesterday when I was on the plane soaring across the world. It’s going to be fun skipping a lot of school. I’m going to be missing seven days of school. There’s a bad part to it to. I’m going to have a loooooooooot of make-up work to do to catch up with the rest of the class while I was absent. That’s why I have already asked for a lot of the homework from most of my teachers. I still haven’t gotten around to my English and Spanish teachers, but I hope to see them on the coming Tuesday. The most homework is in math class, but I won’t have too big of a problem with that because the math we do in school is pretty easy.

School is going okay for the beginning of the school year. There isn’t a big homework load, but I hear from former eighth graders that there is the most homework in November and December right before Christmas vacation. After that, it shouldn’t be a big strain on homework. After school, I run Cross-Country. Cross-Country is just long-distance running. You need a lot of endurance to run Cross-Country. Anyway, our team had our first meet last Wednesday against Oak Hill at home. I actually did pretty good considering that fact that my both my ankles were hurting a little. The course is 3 kilometers, or 1.8 miles. I came in twelve place, running a time of 14:38 (minutes:seconds). The coach hopes that by the end of the season, I will beat 13:30. I highly doubt that I will success, but who knows?

My math grade changed again (see the blog title above) to a 115% because of two more extra credits. I know that because our math teacher, and most others math teachers, post the students’ grades online so that kids can check their grade often. I wish all of our teachers did that. It’s really useful when it gets to the middle of the term, because that way, you can tell which things need improving. For example, if I have all A’s for tests, quizzes, projects, and participation, but I have a B for homework, then homework is obviously something that I need to work on. I know I wrote a lot, because I’m trying to make up for the whole month of September where I only wrote one entry.