Chapter 2 Project

How to do Determining the number of Triangles in the Ambiguous case (SSA): A construction exploration

Exploration 1a:

AC = 120 degrees

AB = 6 cm

BC = 7 cm

1) Draw a 120 degree angle, 7 cm, 6 cm, and 5 cm line (6 and 5 cm line also used for other two diagrams in exploration 1)

2) Copy angle A

3) Fix compass to length 6 cm. Place pointy end on A and pencil end on the intial side. This will be point B.

*Step 1-3 are also used to start the other two diagrams of exploration 1

4) Fix compass to 7 cm length. Place pointy end on B and make an arc that intersects the terminal side (ray AC) The intersection will be point C.

5) construct a perpendicular to form height.

Exploration 1b:

Exploration 1c:

1) Repeat Step 1-3 of first diagram of exploration 1
2) Fix compass to 5 cm length. Place pointy end on B and make an arc that intersects ray AC. The arc did not intersect AC, it intersected AB. Therefore creating a line, not a triangle.

Exploration 2a:

1)Draw 30 degree angle with a protractor

2) Copy 30 degree angle

3) Draw ray AC and AB

4) AC can be any length, in this case, I fixed the compass to length 7 cm

5) Construct a perpendicular from AC to ray AB to form a altitude

*These 5 steps are the same for the other two triangles in exploration 2

6) First Case, let BC be less then height, which eventually, it won't form a triangle, because if BC is less than h then BC won't touch ray AB (point B is nonexistence)

Exploration 2b:

Exploration 2C:

Exploration 3:

1) Draw a 30 degree angle, 7 cm line segment and 6 cm line segment

2) Copy the 30 degree angle
3) Fix compass to 7 cm length. Place pointy end of compass on angle A, then place pencil end somewhere along the terminal side of the angle. That point will be AC.
4) Fix compass to 6 cm length. Place pointy end on C, then place pencil end to the left of C and right of C. Make arcs. These will be the two B points.

5) Construct altitude by constructing a perpendicular bisector.
6) Measure h.

Questions:

1) Because sin A remains the same in the ambiguous case, sin c also remain the same

2) If angle A is obtuse, then side BC (long side) has to be greater than side AB in order to form a triangle. A triangle cannot form if BC is less than or equal to AB.

In a right triangle, side BC has to equal the height of the triangle. BC cannot be less than h.

BC could also be greater than h, but BC also has to be greater than AC as well and angle A has to be acute. Though this is not a right triangle, one obtuse triangle and two acute

California "Cyber-Bully" Bill Takes Effect

Bullying, a word that is just gross.
The Internet is used for work, convenience, research, and fun for all ages, but some people are found impersonating other people. This act will hurt the victim and also the impersonator. Thanks to this new law, impersonators on the internet will receive the punishment of heading to prison and expected to pay a fine of $1000.
This act of cyber bullying is just plain pathetic, don't people have much better things to do?

A solution to this is just to seek out the impersonator and punish them. Another possible solution is to shut down the pathetic websites that are posting these comments and place strict laws to creating a website. Why must there be impersonators? I know that there are many type of conflicts in an individual's life, but does it have to lead to the case where people use the internet to abuse another person? Why can't these people just find a solution to their problems by using some common sense? Overall, any form of bullying is just plain pathetic and would just cause even more problems to occur. Bullying is not the way to solve problems.

Remedial college classes cost billions

This sort of news is frustrating to be heard for college students and California. It is sad to see many high school students graduating then finding they are unprepared to meet the standards in college/univeristy. Many college freshmen today that just entered college finds that they are unprepared and are placed in remedial classes and the numbers of remedial classes in California are increasing. I believe that remedial classes are helpful in helping college students to become more prepared, but remedial classes are just too time consuming and frustrating. I think the reason why college freshmen don't have the skills they need for college is because they didn't put enough effort in their work when they were in high school. Many high school students who say high school is too hard has no clue that there is another level of education that is even harder. I think the reason why high school students believe that the work is hard is that they don't get the material. Some reasons why they don't get the material are they don't pay attention in class, don't complete their assignments, don't do well on tests, socialize too much on their phones and internet, and cut classes. It is not to say that high school students should over work their abilities, but at least high school students should put more time and effort in their work so they can understand the material and not have to worry that they are unprepared for college classes.

I believe this news is a warning for high school students to put as much effort they can in their work so they can be prepared for college courses and not have to worry about being placed in remedial classes. With more students putting more effort in their work, there would be less stress in the future, less remedial classes, and more money could be saved to be used for improving school districts.

Ch 4 Project Solving Problems with Trigonometry

Ch 1 Project: How to do Modeling with Functions and Regression Equations

The Exploration says first I have to draw in the diagonals of the seven shapes, excluding the triangle, because triangles don't have diagonals. I connected the segments of each nonadjacent points for the seven shapes.

Then I entered the data into my graphing calculator. I placed the values, n, which is the number of sides, in List 1 (L1) and the corresponding values, d, which is the number of diagonals, in List 2 (L2).

Next I made a scatter plot of the data.

Then I used my calculator to figure out the linear regression, power regression, quadratic regression, cubic, and quartic regression.

I found out that the Quadratic Regression best fits the data. The equation is 0.5x^2 - 1.5x. The R^2, or correlation coefficient, is 1. The R^2 tells the strength and direction of the scatter plot. Since R^2 is positive 1, then the scatter plot has a positive association. Since all the data points fit exactly on the curve, then the strength is very strong, because 1 in correlation means that the scatter plot is very strong.

Finally, I used the Equation 0.5x^2 - 1.5x to find how many diagonals there are for a 200-gon. My calculations tell me that a 200-gon has 19700 diagonals.

Ch P: How to do Applying Linear Functions in Two Variables

Chapter P Opener Problem Part C
Option 4

First, I have to search online to find the light speed from Earth to Jupiter.
After I found the light speed from earth to Jupiter, I formed a question that I need to solve: Approximate the distance between Earth and Jupiter.

The Procedures:
1) I used the linear equation d = r times t (distance equals rate times time). First, I found the values of r and t, not d, because I'm trying to find d.

r = 186,000 miles/second
t = 34.98 minutes
d = ?

2) Then, I converted 34.98 minutes to seconds to keep the units the same. I multiply 60 and 34.98 minutes and got 2098.8 seconds.

3) Lastly, I plug the three numbers in to my equation (d = r times t) and got distance equals 390,376,800 miles, which approximately equals 390 million miles.

Ch P: How to do Graphing Functions

Graphing Functions / Transformations
Back to School Night Extra Credit

Well, since my mom didn't completed her education when she was young, she had no clue what she was asked to do on this assignment. So, I have to show her how to do a vertical and a horizontal translation combined.

First, I asked her to graph the Absolute Value parent function in black. I had to show her how to draw the function, because she seems clueless on what to do.
Then, I asked her to translate the graph 3 units to the right and use red to trace. This is the horizontal translation.
Lastly, I asked her to translate the graph 6 units up and use purple/violet to trace. This is the vertical translation.

When we were finished, my mom feels kind of happy that she drew a graph, but she still ís clueless about the purpose of the graphing functions. Overall, I'm proud to see her at least try to sketch the graph.

Graphing Functions / Transformations

1) First, I graphed the Absolute Value parent function.
y = "Absolute Value of X"

2) Then, I did a vertical translation in the color red. I translated the parent function 10 units up along the y-axis and got the new graph,
y = "The Absolute Value of X" plus 10

3) Next, I did a horizontal translation in the color blue. I translated the parent function 6 units to the left along the x-axis and got the new graph,
y = "The Absolute Value of X plus 6"

4) I already did a vertical and a horizontal translation, now I did a vertical and horizontal translation combined in the color green. First, I translated the parent function 10 units to the right and 2 units up, and got the new graph,
y = "Absolute Value of X minus 10" plus 2


5) Next, I did a reflection over the x-axis in the color purple. All I did was flipped the Absolute Value parent function upside down, to get the new graph,
y = - "Absolute Value of X"

6) Lastly, I combined a reflection, vertical translation, and horizontal translation in the color black. First, I translated the graph 10 units to the right, 2 units up, and then reflected the graph over the x-axis to get the final graph,
y = - "Absolute Value of X minus 10" plus 2

Altogether, I did five transformations.

About "Denny"

Background:
Education -
- Oakland Senior High School'12
- Roosevelt Middle School: 2005-2008
- Garfield Elementary School: 2002-2005
- Daniel Webster Elementary School (San Francisco): 1999 - 2002

Work Experience -
- Oakland Public Library Asian Branch Intern: From July 2010 - August 2010

Volunteer Experience -
- Oakland Public Library Teen Volunteer: August 2010 - Present

What I want to be:
I want to become an Engineer when I graduate college

Interests:
- Draw
- Watch TV

Photo of me: