Graphing Polynomials

Another Fun round of Math!

I know math is not the fun class but I am really enjoying study the subject this year, within 2018 – 2019 I got to learn about Precalculus, which includes algebra and trigonometry at a level which is designed to prepare students for the study of calculus. Ever thought, algebra and trigonometry is not my strength I still want to build those skill into my strength. This round we are studying in Chapter 3 (Polynomial and Rational Functions), which include seven smaller subjects. I would like to show some example in the small subjects that related to Chapter 3.

In Chapter 3.2 (Polynomial Functions and Their Graphs) we learn the polynomial functions simply as polynomials. The following polynomial has degree 5 leading coefficient 3, and constant term -6

We also need to understand how the graph of a basic polynomial function look like and which graph is not a polynomial function.

Example: P(x)=x^4 − x^3 − 6x^2

First, we’ll need to factor this polynomial as much as possible so we can identify the zeros and get their multiplicities.

P(x )= x^4 − x^3 − 6x^2 = x^2(x^2 − x − 6) = x^2(x − 3)(x + 2)

Here is a list of the zeroes and their multiplicities.

X = −2 (multiplicity 1)

X = 0 (multiplicity 2)

X = 3 (multiplicity 1)

So, the zeros at x = -2 and x = 3 which will correspond to x-intercepts, that cross the x-axis since their multiplicity is odd. The zero at x = 0 will not cross the x-axis since it multicity is even. The y-intercept is (0,0) and notices that this is also an x-intercept.

The coefficient of the 4th-degree term is positive and so since the degree is even we know that the polynomial will have a positive infinite bound at both ends of the graph.

Finally, here are some function that helps to the graph, We need to plug in a random number to help identify the behavior of the graph. Normally, we would have one point in between the zeros.

P(−3) = 54

P(−1) = −4

P(1) = −6

P(4) = 96

Here is a sketch of a graph

S’more Stoichiometry Lab

FUN! FUN! Another day for Lab! FOOD!

You’ve ever cooked a meal from a recipe, you will have noticed they come with serving amounts, in fact, this number can be off, and you’ll end up with either less or more food than you anticipated. A number of things can take an account for this difference – food spillage prior to cooking, leaving ingredients too long on the stove top, using the wrong measuring cup, and so forth.

The similar can happen at whatever point we have an experiment in the chemistry lab to make a compound. We first make a calculation for how much of a compound we’ll end up with, in fact, these calculation are made under ideal conditions. They don’t account for experimental errors or personal errors of the experimenter. In the end, your prediction is often different from what you have actually made.

In Chemistry, we have learned about theoretical yield, which is the amount of the product calculated from the limiting reactant. The limiting reactant is the reactant in the chemical reaction that limits the amount of product that it can produce. The actual yield is the actual amount of the product, which the experiment produces.

The difference between theoretical yield and actual yield can be calculated by using percent yield, which we can use this formula:

In order to use this formula, the theoretical yield and actual yield need to have the same unit. If the actual yield in gram, the theoretical yield also need to be in gram. If the actual yield in mole, the theoretical yield also need to be in mole. If one has a different unit, we need to perform a conversion if we are giving one measurement in term of the unit.

We had conducted an experiment (S’more Lab). In order to make this S’more, we need substance, so teacher provide us Cracker, Chocolate, and Marshmallow.

 Substance Symbol Graham Cracker (half of a cracker) Gc Marshmallow M Chocolate Piece (individual piece of chocolate) Cp S’more  (2 crackers, 3 pieces of chocolate, 1 marshmallow) Gc2MCp3

We need to follow a certain step to create S’more

Step 1: Balance the equation

Cp + M + Gc → Gc2MCp3 to 3Cp + M +2Gc → Gc2MCp3

Step 2: Calculate the theoretical yield

In the experiment, I weight the substance. I got Graham Cracker (Gc) 8 grams, Marshmallow (M) 5 grams, Chocolate Pieces (Cp) 9 grams. I added all up, it has 30 grams of the substance

Step 3: Roast your marshmallows and chocolate on the Bunsen burner

Step 4: Putting the marshmallows and the chocolate between the cracker

Step 5: The ACTUAL (experimental) mass of one s’mores: 28.5 grams

Step 6: Calculate the percent yield

Experimental Yield = 28.5 grams

Theoretical Yield = 30 grams

% yield = (Actual yield / Theoretical yield) * 100

28.5/30 = 0.95 * 100 = 95%

Percent yield = 95%

Step 7: EAT YOUR S’MORE!!! (:

Engineer Biography of Alexandre-Gustave Eiffel

General Information

Alexandre-Gustave Eiffel was the Architect and French engineer born on December 15, 1832, in Dijon and died at age 91 years old on December 28, 1923, in Paris. His parent was Catherine Melanie Moineuse and François Alexandre Boenickhausen. He famous for Architect, Civil Engineer, He also a founder/ Co-Founder: Eiffel & Cie.

Childhood & Early Life

The family came from a region near the Eifel mountains and adopted the name “Eiffel”. He spent most of his childhood with his grandmother. He studied at the ‘Lycee Royal’ in Dijon and earned his baccalaureate in science and humanities. He also had friend and uncle to teach Gustave philosophy, theology, chemistry, and mining.

To prepare himself for the difference entrance exams of engineering colleges he joined the College Sainte-Barbe in Paris. In 1855 he completed his graduation earning the thirteenth position out of eighty candidates.

Career

After completing his graduation he did an unpaid job for a few months to assist his brother-in-law in a foundry. He got his first paid job as the secretary of Charles Nepveu, a railway engineer. When the company of Nepveu became bankrupt, he arranged for a bridge design work for Eiffel that was to be constructed for the ‘Saint Germaine’ railway. His reputation as an architect and civil engineer got him more projects and he established his own workshop in 1866 and undertook projects in different countries. One such project was an all-metal construction of the church of San Marcos in Arica, Chil

Various parts of the project were manufactured in France and shipped to the site to be assembled there. His technical innovations were path-breaking (specially prefabrication of cantilever constructions).

His most noted masterpiece that bears his name and went on to become one of his prominent works is the ‘Eiffel Tower’. Eiffel is most famous for what would become known as the Eiffel Tower, which was begun in 1887 for the 1889 Universal Exposition in Paris. The tower is composed of 12000 different components and 2500000, all designed and assembled to handle wind pressure. If it were melted down, the tower’s metal would only fill up its base about two and a half inches deep.

The Eiffel could build the world’s tallest structure(at 984 feet) in just two years and torn by the tower’s unique design, most deriding it as hideously modern and useless. The tower also directed Eiffel’s interest in the field of aerodynamics.

Eiffel turned his interest to meteorology in his final years, studying the subject at length before his death on December 28, 1923

Awards & Achievements

Thought out Eiffel career he designed and constructed a number of great structures, in one of the structures was the most famous and iconic structures is the world-famous Eiffel Tower. Also in 1912, the ‘Smithsonian Institution’ honored him with the ‘Samuel P.Langley Medal for Prodromic’ award.

Personal Life & Legacy

On July 8th, 1862 he got married to Marie Gaudelet. They remained married for fifteen years and had five children together (three girls, and two boys) before Marie caught pneumonia and died in 1887. Gustave never married any woman again. On the day Gustave dies, on December 28, 1923, while in his mansion on ‘Rue Rabelais’ in Paris and was buried in ‘ Levallois-Perret Cemetery’ in the family tomb.

3 defining principles/characteristics/values

Some characteristics that he had that make his goal success, are have, He becomes a high earning graduate students so people truth him and give him chance. He also determines to study day in and day out until he great at it. He is an intelligence how he works and how his think, He also put his full effort into every project that he had been working on. “In 1855 he completed his graduation earning the thirteenth position out of eighty candidates.” He many interests in the variety of subject. In his early life, he takes many interests like philosophy, theology, chemistry, and mining, even before his death that other subject with him. This makes him become a success people by having more knowledge so he can do anything he wants by using the skill that he had After the Eiffel Tower was built he had changed his interest in meteorology in his final years, studying the subject at length before his death on December 28, 1923. In his life, he had married with a woman and stay loyal to her all the time. So that makes people truth him and had him rise about everyone else. Other may think he loyal to his hard work with his job. He loyal because they saw the project like his life, If he to do it he will give it everything to finishing it with loyalty.

Works Cited

“Alexandre Gustave Eiffel.” American Society of Civil Engineers (ASCE), www.asce.org/templates/person-bio-detail.aspx?id=11166.

“Alexandre Gustave Eiffel Facts.” YourDictionary, biography.yourdictionary.com/alexandre-gustave-eiffel.

“Gustave Eiffel.” Wikipedia, Wikimedia Foundation, 11 Sept. 2018, en.wikipedia.org/wiki/Gustave_Eiffel.

TheBiography.us. “Biography of Alexandre-Gustave Eiffel <Small>(1832-1923)</Small>.” TheBiography.us, thebiography.us/en/eiffel-alexandre-gustave.

“Who Is Gustave Eiffel? Everything You Need to Know.” Childhood, Life Achievements &amp; Timeline, www.thefamouspeople.com/profiles/gustave-eiffel-6809.php.

Flame Change Color When Have Contract With Chemical!

When an element get heated with the flame, heat will excite the electrons in the atom.  This allows the electron to travel from the ground states to a higher energy level. So the atom becomes unstable and it will release energy to move into it ground stand back. In this releasing energy will match wavelength that it will energy emit and it also corresponds to the color of the visible light in a form of electromagnetic radiation.

I had an explanation about the concept of the idea with word now how can we see it with our eye, so we need to conduct an experiment that called the flame test lab in our chemistry class.

In the experiment, we had six different compounds of salt (Copper, Strontium, Barium, Lithium, Calcium, and Potassium). Each of them was placed on a popsicle stick that will be heated on the flame of a burner. All of the salt compounds emitted different colors and then we find the wavelength that corresponds to the color of the salt compound that was identifies.

Nevertheless, in an experiment, they would not be conducted with a perfect resolve. One possible source of error can be how we observed the color. Color is really tough to identify with our eye. This would lead us to an inaccurate of the color, that would affect the wavelengths we would find at the end. In the next experiment, I would avoid this error by using colorimeter can be used to accurately measure the wavelength.

Forever Give

This poem was inspired by the trash dump at Stung Meanchey. I wrote the poem from a perspective of a trash.

If I could be a tree …

I would turn myself big and cover you up

I would turn my leaves into cash and chase you toward the ending sky

so you would understand wonder.

If I could be a mountain …

I would kneel down and lift you up

I would turn my ground into a house so you can see all the wonderful places

so you would understand freedom.

If I could be an ocean …

I would transfer you across the great seas with my heart waves

You would swim with the dolphins and turtles in the growing waters,

So you would understand hope.

If I could be the sun …

I would warm you up

After the orange light turn out before the dark light turn in

I would gaze to the sky

show you the wonder, freedom, hope that it provided.

But who I am is who I am …

I am trash…

Love you until the end

Until the place close down…

Until the mountain kneels down and lift you up ….

Until the ocean transfer you across the great seas ….

Until orange light burns out ….

That how much I love you !!!

Forever and never want anything in return!!!!

SAT Preparation

On the first two weeks of the school year, we did PSAT Bootcamp. We had Amanda and Kim to be our mentors. For the two weeks we work with Kim and Amanda, they taught us many skill and strategy about SAT. I found the Reading and Language section was the hardest subject that blocking me from getting a high score when they took the test for the second English learner.

We took three PSAT over two weeks of practice with a website called Khan Academy, I can see really clear the improvement that I made when working with Kim and Amanda beside learning by myself. Also, I use the strategies that I learn with them to improve my score. After the first two weeks of the school year, in math class, we are still practicing for PSAT, by that we have independent time to work on some small subject like complex number and circle theorem. So that we can extend to a rage of math knowledge beside learning about the strategies.

Abstract Art

On my summer holiday, I have been taking some of my time to work on my Blender skill. I had in my mind, “I don’t know what I should do.” I go online and found artwork that has colorful color and there doesn’t have a shape that like a drawing or a model. It is the abstract art so I take the picture and turn it into a 3d abstract art. When I finish the abstract art I went on to work with food. I decide to pick a food that everyone likes it and also it with my level of learning then I choose to make pizza. Making pizza it a struggle for me to adjust the texture of the cheese. There some more artwork in the picture below. I hope you enjoy my artwork.

Changing Cambodia

As a kid that lives with a family that struggles with poverty, My parents never gave up a dream of getting their children a great education as possible but they can never do that. I only get to learn from the government school, it’s not safe, But one day, there was a magical school that appears from nowhere, it was Liger Leadership Academy school. My parents tried their best to get me into there by running to everywhere, asking everyone about this school, and buying items for me to take the test.

If I were to relate to what I had changed Cambodia by now, I can see that I am a part of the change in the society. If I would reclaim my life story from the beginning of this topic I would be said that I can’t afford a really high-quality school. So then I had this amazing exploration called Bambujaya, this name is coming from this new Cambodia private school-Bambujaya located in Phnom Penh, that hopes to offer an affordable option to government school students, so I got hired by the founder to adopt grade 3 textbook, into supplemental activities which mean that we are not trying to change the Khmer curriculum; rather, we are adapting it by writing activities called “add-ons” that are more engaging, hands-on, and address multiple learning styles. So they can have it for teaching the student in the school.

The add-ons allow the students to study also having fun with the activity that we provide to them. So if I was born again it won’t be hard for my family to find a high-quality school also affordable.

Also, people around us always busy that they don’t really care about the awareness of our surrounding that can help them with idea or knowledge that can help them in the future. Like the awareness of Rabies that spread by dogs and cats that live strong with you all the time. We always knew that Rabies come from dogs and cats but we don’t know how to prevent it from spreading it to human. The awareness that we facing it can solve we just need to the action by go them and talk about the problem and how to solve it. So we had this amazing team that working with Animal Recule Cambodia too, run out to the community and tell them about Rabies with the poster, information card, and by month.

But we didn’t stop there.

We got our self a final task, it was going out and vaccinate dogs and cats in our community for free; by the donation from Animal Rescue Cambodia (ARC). In this case, we need to get an abundance of jobs done in time to get this happen. I was assigned to communicate with the village chief for the permission to allow us to vaccinate dogs and cats and we need the village chief to spread the word to a different family in order to get this mission a success. By the end of all the hard work -communication with the village chief and villager- now it time for the fun time with hard work involved.

We had to go out and vaccinate cats and dogs through two villages, which are Chompous Kaek and Koh Krobey. For both villages, we got to vaccinate 126 dogs and cats combined. So this a really successful day that I had to help my village -Koh Krobey- and nearby village for getting Rabies. This is just a small area village but it can make a fair amount of difference.

This is just a small project that we learn about that help to create a small change in some area that could make a gigantic difference in the future. Although change doesn’t happen immediately I believe it will pay off one day.

I greatly cheer up for anyone who believes in yourself cause you have the ability to did, it not other who that you that. You can be anyone or anything by you try to become that person. If you want to be a change agents for your country. Don’t wait for the right time, make the time wait for you to do it.

Whenever I struggle with something I always say this to myself “All is well, if I’m happy, it fine for me and it also fine for other cause they can’t see inside of me”

Wonder Woman Physics

Dianna of the mascara is certainly wondrously crafted by the gods themselves she is incredibly strong and agile quick enough to matrix-style visualize bullets and block them just being fast and just being strong isn’t enough to do what Wonder Woman does she have to be really smart too.

Wonder Woman’s abilities have been to use her indestructible to deflect incoming projectiles in most cases bullets. It seems straightforward to identify the bullet and block it but it’s not that easy and that’s where the wonder comes in. To block the bullet, we need the reaction time to do so and you need to be strong enough to withstand the impact so first what does blocking a bullet feels like well right.

Right before impact; bullet has two-quantities that can help us determine what the force would feel like when you block a bullet the first is momentum (MV) then Kinetic Energy (1/2MV^2).

Before we get into Dianna shoot blocking, we need to understand the feel of blocking a shot. Base in the movie of Wonder Woman, the German using the gun call Gewehr 98, that had a bullet weight of 9.9-grams with a velocity of 878 m/s and with time travel of 1/24 s because in the sense of Wonder Woman movie it takes about that time.

So we can use the F=MA to measure how much force did Diana had felt every time she blocked a shot of a Gewehr 98. Base on the calculation she needs to experience 210 N every time. F = MV/T, F = 9.9*878/1/24 s, F = 210 N.

The kinetic energy of bullets is an important metric weaponry because it describes how far a bullet will go how far it will penetrate into some object before it is slowed down by the forces impressed upon it but Dianna’s braces are impenetrable so instead we are gonna use momentum which describes how long it will take a bullet to be slowed down to zero by some force based.

She can block a bullet without reacting to and so her reaction time would have to be incredibly fast. War scene it is about 800m with a reaction time of 0.9s. With beach scene is less than 100m she had a reaction time of 0.1s. It the scene she saves a person with 5-meters away, she had a reaction time of 0.01s. That is twice as fast as our brain can tell us to move our limbs. Blocking bullet like Wonder Woman it not just require strength or speed in have to be a gigantic physics nerd.

Bambujaya Exploration

Bambujaya school is a new private school in Phnom Penh, that hopes to offer an affordable option to government school students. It is unique in that it will use the government school curriculum, but with innovative and engaging adaptations. So this is where we come in to play! Writing supplemental activities using grade three Khmer curriculum. This means that we are not changing the curriculum; rather, we are adapting it by writing activities called “add-ons” that are more engaging, hands-on, and address multiple learning styles. These add-ons should also be specific, observable, measurable, and simple for the teacher to understand. Finding cross-curriculum activities→ apply knowledge or value to more than one academic. When students can be shown that topics or subjects are connected, it will be more relevant and meaningful to students. Bambujaya wants activities that are STEM-based using light resources to supplement their curriculum. In this Exploration, we have grade 3 books, that 3 topics, Khmer, Science and Societal study, and Math. So I chose the Khmer textbook to write about. So below is some of the add-ons that I wrote in my exploration.

Book: Khmer book

Topic: Describe an event

Central Lesson:

Name: Art skill at a young age

Duration: 10 min for drawing pictures, 2 min check picture, 15 min writing about the picture

Step: 3

Learning Objectives: Students will be able to use their artistic skill to depict an event, and then allow another student to write a story describing their drawing.

Description: Students will need to have a paper(A4) and pencil or pen. Then let them draw a picture of an event of their choice (it can be anything) (Traffic accident, Birthday party, Khmer New Year, Pjum Ben) that they have seen before. Afterward, the students will switch the picture with another student in the class. The students will take a look at the picture they have been given for a few minutes. Then they need to start to write a story based on the picture that they saw. The story can be made up, or true if they know about it.

Additional Resources: Paper(A4), Color pencil, Pencil, Pen

P.S. This activity can be related to reading and writing

Example: On the 1st of June is the event that everyone in the world come together and having a fun time with each other. When they saw each other they will start shooting firework like lightning shooting into the sky forever. This event had started for the last 20 billion year ago, this event starts with man name Bulletin Zap, so the event name after the founder name.