Ch. 2 - Solving Equation in One Variable

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Ch. 5 - Determining Number of Triangles

Exploration 1. Case #1
Exploration 1. Case #2, 3

Exploration 2. Case #1, 2


Exploration 2. Case #3

Exploration 3.


Question 1: Explain why sin C is the same in both triangles in the ambiguous case (exploration 3). This is why the Law of Sines is also ambiguous in this case.

SinC is the same in both triangle because SinA remains the same since according to the law of sin, sinA= sinC.

Question 2: What did you discover about the number of triangles you can make given SSA (two sides and an angle)? Summarize the "rules" for all cases.

If angel A is obtuse and...

• BC > AB....1 triangle
  
• BC = AB....0 triangle
• BC <>

If angel A is acute and....

• BC <>
• BC = h....1 triangle
• BC > AB > h....1 triangle
• AB > BC > h....2 triangles
  

Remedial College Classes

Many high school students don't seem to take advantage of the free classes being offer at high school and master all the basic skills that they need to take advance classes in colleges. So what happen when they go to college? They have no choice but to take remedial courses, but those courses are costly and also time consuming. Although it is true in most cases, some other cases are just simply due to the school or the teachers. Some teachers are just not fit for teaching that particular subject at that particular level or the students don't feel enough motivation to do their best. They give out easy work (maybe even no work at all) and not giving out the work that are suppose to prepare students for college. As the results, students can pass by those classes with some easy A's without doing much work and not being fully prepare for the "real" thing in college. Now I'm not saying that the teachers are entirely to blame, there are, indeed, some students who just don't take advantage of the good offers and just simply slack off. But there are some students who are taking lots of AP classes so they have lots of challenging homework to complete compare to just regular classes. So to say, it is nearly impossible for students to fully taking time on their homework/classwork to study the materials and master them with that much amount of homework piling on them and not much time to do them, especially those that have jobs or living independently.
To resolve these problems, I think there need to be more programs that can help students prepare for colleges during/outside of school time such as Upward Bound and incorporate the classes' lessons to other things that are relating to that topic so students would be able to know more. And also, if there are fewer classes a day, then students can absorb more and learn more for each subject. In addition, I think lessons should go a bit slower so students can practice more and fully grasp the standards instead of trying to cramp a lot of things and not being able to understand them completely. But of course, that won't be able to happen but it's a nice idea to look forward to.

Cyber Bullying Bill Jan. 1, 2011

Cyber bullying has always been a major issue concerning about the internet. Cyber bullying can lead to serious consequences such as suicides and homicides, and I think that the new laws might be able to prevent some cases from happening, but it needs to take on higher measures to completely prevent such tragedies. I feel that people that bully others are probably cowards or they may feel powerless within the real society that they needed to act like "trolls" to vent out their frustrations that they don't dare to confront. They need to stop doing that because I think it's stupid and pointless trying to make the victims look bad online.
In some cases, cyber-bullying cause unnecessary troubles to other people beside the bullies and the victims. For instance, if you're under the age of 18, your parents are somewhat hold responsible for your action by paying your fine, etc. Furthermore, it goes into your records which wouldn't be goof for your job/college applications. People have the rights to voice their opinions, but when people abuse that rights, it is not only unacceptable, but also a disgrace and involve innocent people for their actions.

Ch. 4 - Solve Problems with Trigonometry

Ch. 1 - Modeling with Functions and Regression Equations

Chapter 1 talks about different types of functions and how each function look like when we graph them. For this project, we will be focusing on the 2 most common functions (or equations) that we see over and over again throughout the courses of math: linear and quadratic equations. Linear function can be represent by f(x)=x and can be written as Ax+B in equation form from our previous chapter. Meanwhile, a quadratic function is represented as f(x)= x² and can be written as Ax²+Bx+C.

In this project, we're trying to graph the given data with the most accurate function as possible. The line on the graph that model the most relative to the given data is called the regression line. But in order to find the regression line, we need to consider the correlation coefficient "r" and coefficient of determination "R²", where R² is needed to predict the future outcome base on the relative data. However in this case, both r and R² will be the correlation coefficient where the closer the number gets to 1, the better the curve fits the data.

• First of all, we need to input the data (years) into the table of the graphing calculators. To do that, hit STAT > EDIT > ENTER. A table will appear with the headings L1, L2, etc. For this problem, L1 will be the input x-values in years. And L2 will be the output y-values in average hour earnings.

• After you have entering all the data, you're ready to find the regression equations. In order to find the regression equation (for now we just need to find the linear and quadratic regression equations), we hit STAT > CALC > 8:LinReg(a+bx) > ENTER to find the linear regression equation.

• After the linear regression appear, hit 2ND > 1 (for L1), 2 (for L2), > VARS > Y-VARS > 1:Function > ENTER > 1:Y1 > ENTER. If you follow the steps correctly, you should be able to get the first picture. Press ENTER again to get the second picture where you will see the equation of linear regression and the correlation coefficient "r". (The equation also appear in Y1 if you go to Y= )

• The same procedures apply for finding quadratic regression equation. Only instead of choosing 8:LinReg, you hit STAT > CALC > 5:QuadReg > ENTER. Continue following the rest of the steps from linear regression and you should be able to get something like the pictures below.

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Ch. P - Applying Linear Equation in Two Variables

Chapter P talks about the linear equation. A linear equation can be represented by the general form Ax+By+C=0 which you can use to find the x-intercept and y-intercept. The equation can be transform into different forms, such as point-slope form or slope-intercept form, depending on what information is given and what you're trying to find. Point-slope form gives you a point and the slope and can be use to find a linear equation. While, the slope-intercept form gives you the slope and y-intercept and can be use to graph a line in a graphing calculator.

Ch. P - Graphing Function

1. For this graph, I used the original function of y=√x (square root of x) which is shown in black marker with the original function boxed in the first quadrant.
2. Next, I translated the function (y=√x) 3 units down along the y-axis to create a vertical translation of y=√x-3. The translation is shown in red marker in the fourth quadrant.
   
3. Then to create a horizontal translation, I moved the function 4 units to the right along the x-axis to create y=√(x-4). The translation is shown in blue marker in the first quadrant.
4. And to combine both vertical and horizontal translation, I transformed the original function into y=√(x+6)+3 where the graph moved 6 units to the left of the x-axis then 3 units up the y-axis. The translation is shown in green marker in the second quadrant.
5. Then I did a reflection where I reflected the original function across the x-axis to create y= -√x which is shown in purple marker in the fourth quadrant.
6. Lastly, I created a transformation by combining the vertical and horizontal translation and the reflection across the x-axis to move the original function reflected across the x-axis, translated 8 units to the left and 2 units down to make y= -√(x+8)-2. The transformation is shown in black marker in the third quadrant.

About "Dan"

Background:

• Education.}

1. Elementary School.........Đuốc Sống (1st - second semester of 4th grade) // Franklin (4th - 5th grade)
   
2. Middle School...............Roosevelt (6th - 8th grade)
   
3. High School.................Oakland High (9th - current)
   

• Work & Volunteer.}

1. Oakland Main Library
2. Coastal Clean Up
3. Link Crew

What I want to be:

• Cultural anthropologist or...
• Animator

Interests:

• Drawing Japanese anime characters
• Cats (especially black ones)
• Study abroad
• Travel to England, Italy, Japan, and Korea
• K-pop / K-rap (EPIK HIGH!!!)
• Historical fiction