WPP #9: Unit L Concept 4-8 - FCP, Combinations, and Permutations

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SP#6: Unit K Concept 10 - Writing Repeating Decimals as Rational Numbers

The viewer must pay attention to the numbers and which numbers go with what part in the formula. Also, don't forget to add the whole number to the fraction in the end. The viewer also must not get confused with geometric and arithmetic, since for geometric to find the ratio you divide the numbers. Remember to multiply by a reciprocal to cancel the fraction out

Fibonacci

Word Count: 532 words 

Golden Ratio in Human Body
In this video, I learned many interesting facts. If you divide a number by the number before it, you attain numbers very close to one another. After the thirteenth number, the number is fixed and known as the Golden Ratio which is 1.618. Leonardo da Vinci used the Golden Ratio in his designs. Also, architect Le Corbusier used the number for his designs. There are many features that you must measure to see how beautiful a person is overall, even the total width over the front teeth over the health equal to the Golden Ratio. The Golden Ratio is even found in the structure of the lung and in our DNA. The Golden Ratio is found in animals, paintings, buildings, and so much more. 

The Golden Ratio and Beauty in Architecture 
The Golden Ratio was used in ancient times. One of the Seven World Wonders, the Great Pyramid in Giza, Egypt, was formed using the Golden Ratio. Therefore, the Ancient Egyptians and Greeks had knowledge about the Golden Ratio. Renaissance artists used the Golden Ratio as well, in example of Notre Dame. The Parthenon has exterior dimensions that equal to the Golden Ratio. The United Nation building has the Golden Ratio in the width of the building compared with the height of every ten floors. 

The Golden Ratio Revisited 
The Golden Ratio is a mathematical formula made from Eucid, who is also known as the "Father of Geometry". It is an universal way of defining beauty. That is why some objects are aesthetical pleasing while other are not. The ratio is evident in the painting, "Vitruvian Man", by Leonardo da Vinci. It is also evident in Mona Lisa. It is present in book design, music, and Mother Nature. Adolf Zeising discovered the Golden Ratio in the branches along the stems of plants and veins in leave. A flower or a pineapple is appealing because of the Golden Ratio. It is present in almost everything. 

Nature by Numbers 

Fibonacci wanted to know how many rabbits would be produced in a year. He assumed that starting with January, each new month the rabbits would give birth to a new pair. He noticed a pattern that the rabbits were increasing in a sequence each month. This resulted in the Fibonacci numbers. The structure of flowers are based off the Fibonacci number. Sunflower have 33, 55, or 89 petals, which is a Golden Ratio. Organic growth is stimulated by the Fibonacci number. The Greeks believed that the rectangle had a mathematical beauty. 

Response and Reflection 

Overall, the information I learned was very interesting. I think it is amazing how these numbers determine how appealing something could be to the eye, such as things found in Mother Nature. In all honesty, I believe that Fibonacci's numbers do play a role in beauty. However,  I believe it doesn't play a major role. For something to be appealing to one's eye, color and such plays a role. It is not just about size. Also, everyone has a different preference when it comes to determining what is beautiful. The "Golden Ratio" is very interesting and valid, but only in a small role of beauty. 

Fibonacci

 Measurements of Friends:

Leslie Estrada: 
Foot to Navel: 106 cm
Navel to top of Head: 61 cm
Ratio: 106/61=1.74 cm
Navel to chin: 48 cm
chin to top of head: 17 cm
Ratio: 48/18=2.82 cm
Knee to navel: 57 cm
Foot to knee: 47 cm
Ratio: 57/47=1.21 cm
AVERAGE: 1.92 CM

Christine Nguyen
Foot to Navel: 96 cm
Navel to top of Head: 58 cm
Ratio: 96/58= 1.19 cm
Navel to chin: 44 cm
chin to top of head: 20 cm
Ratio:44/20= 1.19 cm
Knee to navel: 57 cm
Foot to knee: 48 cm
Ratio: 57/48=1.19 cm
AVERAGE: 1.35 cm

Melissa Arias
Foot to Navel: 103 cm
Navel to top of Head: 61 cm
Ratio: 103/61=1.68
Navel to chin: 45 cm
chin to top of head: 19 cm
Ratio: 45/19=2.37 cm
Knee to navel: 52 cm
Foot to knee: 50 cm
Ratio: 52/50=1.04 cm
AVERAGE: 1.69 cm

Tracey Pham

Foot to Navel: 100 cm
Navel to top of Head: 62 cm
Ratio: 100/62=1.61 cm
Navel to chin: 42 cm
chin to top of head: 20 cm
Ratio:42/20= 2.1 cm
Knee to navel: 56 cm
Foot to knee: 47 cm
Ratio: 56/47=1.19 cm
AVERAGE: 1.63 cm

Mrs. Kirch
Foot to Navel: 105 cm
Navel to top of Head: 68 cm
Ratio: 105/68=1.54 cm
Navel to chin: 49 cm
chin to top of head: 20 cm
Ratio:49/20= 2.45 cm
Knee to navel: 54 cm
Foot to knee: 48 cm
Ratio: 54/48=1.13 cm
AVERAGE: 1.71 cm

According to the beauty ratio, Tracey Pham is the most beautiful out of all five people. She was close to the "Golden Ratio" of 1.168. In my opinion, the beauty ratio does not determine how beautiful a person is. A person is beautiful by their characteristics, such as the color of their eyes, etc, not just on proportion. But, I do believe that the golden ratio is valid in that a specific measurement of a face looks more appealing on a person. But, overall, it isn't a truly valid way to define beauty, since it is based on how proportional the face is and body. 

Fibonacci Haiku: My Best Friend

Food

Delicious

Let's eat

Life is good

There is never too much

My favorite food is everything in the world

http://www.sarahbesthealth.com/wp-content/uploads/2011/05/Junk-food.jpg

SP #5: Unit J Concept 6 - Partial Fraction Decomposition with repeated factors

The reader must be careful when doing this problem because there are four equation. Also, make sure you do your math correctly or one incorrect variable can mess up your whole system. Also, make sure that you multiply the numerators and combine like terms correctly. Check your work!

SP #4 - Partial Fraction Decomposition with distinct factors

This part is called composing. We combine the fractions into a larger fraction. We then combine like terms. 

This part is called decomposition. We are given a large fraction and are trying to find the small fractions that multiplied to make it. 

Simply type the left part into the calculator and using rref you will get the answer on the right, which is your A, B, and C. 

This is what you started with when you plug A, B, and C, back together. CONGRATS. 

SV#5 - Unit J Concepts 3-4: Matrices

A viewer must pay attention to how they write their equations. Don't mistake a Z for a 2! Make you can look for equations to be simplified to make your life a little easier. A viewer must make sure to do their math correctly in the steps or your answer will be wrong and you will be very frustrated. Also, when plugging the equation in to your calculator, make sure you put the numbers in correctly or it won't match up your pair.

WPP #6: Unit I Concept 3-5: Compound Interest, Continuously Compounding Interest, Investment Application

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SV#4: Unit I Concept 2: Solving and Graphing Log Equations

The viewer needs to pay attention to the graphing the asymptote, as X creates a vertical line. Also, the viewer must acknowledge that you have to exponentiate the log in order to solve for the x-intercept. The viewer must know the different between how to find h, and that it is opposite of what it is in the equation. Lastly, the viewer needs to understand how to plug in points into the calculator and how to use the log base formula.

SP #3 Unit I Concept 1:Graphing Exponential Functions

The viewer needs to pay attention to solving the x-intercept. If you get a negative log, you have to make sure to know that you cannot take the log of something. Therefore, the x intercept is undefined and there is no x-intercept. Also you must acknowledge that the range changes all the time because it depends on the asymptote. If it the graph is below the asymptote, the  graph will go up until the asymptote. If it is above, it will start at the asymptote to infinity.

SV #3: Unit H Concept 7: Finding logs given approximations

This problem is about finding logs, given approximations. To clarify, you will be given variables that are equal to logs, that add or subtract to your solution. You will expand your clue using the properties of logs. The quotient law, product law, and power law are present in this type of equation. You will also be substituting your values (letters) given.

The viewer needs to pay attention to that sometimes, the clues given does not match up to the log you are finding. To fix this, the viewer needs to multiply the numerator and denominator continuously until both the bottom and top have factors of the given clues. The viewer also has to make sure not to confuse the quotient law with the product law. The quotient law is when you divide, your logs can subtract. The product law is that when you multiply logs, that means you can add them too.

SV #2: Unit G Concept 1-7: Graphing Rational Functions

     This student video is about finding slant, horizontal, and vertical asymptotes. You will also be finding holes and the domain. After finding these, you can graph the function. A hole is a place where the graph cannot  touch. We will also be finding limit notation and using our calculator to help us.
     When doing this problem, you must take note that when we find our holes, we need to make sure it gets plugged into the simplified equation. We also have to pay attention to when we plug in the equation to the calculator, we must use parantheses. Another crucial thing that the view needs to pay attention to is the view must not confuse how to find x intercept and y intercept. for X intercept, you set y to 0. For Y intercept, you set X to 0.

SV #1: Unit F Concept 10:Finding real and complex zeroes for a 4th Degree Polynomial

 This problem is about finding real and complex zeroes when there is a polynomial to the fourth degree. We first use Descartes Rule to find the possible number or real positive or negative zeroes. We also use the rational root theorem, p/q, to find the possible zeroes. We also use synthetic division. This video will explain how to use all these aspects to find the zeros of the fourth degree polynomial.

The viewer needs to pay special attention to Descartes Rule, when you are looking for the amount of possible negative zeroes. You have to remember that when it is an odd degree, the sign switches. The viewer also has to make sure to multiply/add/subtract correctly while doing synthetic division. The viewer has to remember that the p/q is positive AND negative. Another crucial thing that the viewer must acknowledge is distributing negatives. You must remember there could be irrational and imaginary zeroes.

SP # 2: Unit E Concept 7: Graphing polynomials, including x-intercept, y-intercept, zeroes, (with multiplicities), end behavior.

This problem is about graphing polynomials by defining how they behave at extremas, how they behave in the middle, where their highest and lowest points are, where their intercepts are, and defining their intervals. In addition, we are dealing with multiplicity of zeroes and how it defines our graph (remember 1 is through, 2 is bounce, 3 is curve?) We will be finding the x-intercept, y-intercept, determining the end behavior, finding extrema, and noting if the graph has intervals of increase or decrease with a set equation. To make a graph efficient, we must find all these aspects.

The viewer needs to pay special attention to the end behavior and how to find it. The degree and the coefficient determines the end behavior. There is even (degree) positive (coefficient), even positive, odd negative, odd positive. The viewer needs to know which direction the end behaviors go by this. Another thing that the view has to be careful on is when they factor the equation, because it is easy to make simple mistakes. Also, the viewer has to make sure they plot their graph right and where it goes through, bounce, or curve, and apply it to the graph.

WPP #4 Unit E Concept 3: Finding max/min values of quadratic applications (MAXIMIZING AREA)

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WPP #3 Unit E Concept 2: Finding Maximum and Minimum Values of Quadratic Applications (PATH OF FOOTBALL)

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SP# 1: Unit E Concept 1: Identifying x-intercepts, y-intercepts, vertex (max,min), axis of quadratics, and graphing them

This problem is about demonstrating the process of establishing a parent function equation with a standard form to begin with. The vertex, x-intercepts, y-intercepts, and axis is to be found. To make a graph the most efficient and accurate, these steps are necessary. 

The viewer needs to recognize to (x-h) in the parent function equation. The parent function equation is y=a(x-h)^2+k. To graph the x-point of the vertex, you need to know that h is opposite of what it appears to be. For example (5-2)^2. That (-2) would be 2 when you graph it. Another thing you must acknowledge is that the x-intercepts may include imaginary numbers, and when that happens you cannot graph it since it is imaginary for the x-intercepts. 

WPP #2 Unit A: Concept 7

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WPP #1 Unit A: Concept 6

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