WPP#10: Unit L Concepts 9-14 - Basic Probability, And/Or Events, & Possibility of Union/Events

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WPP #9: Unit L Concept 4-8: Fundamental Counting Principle, Combinations, and Permutations

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

Make sure to pay close attention to when plugging the summation formula and also when dividing. Also remember to reduce the fraction if it can be reduce, if not just leave as it is.

Fibonacci Beauty Ratio Reflective Essay

Golden Ratio in Human Body
In this video, I learned a lot of interesting facts. The Fibonaci number is the preceding sum of the 2 numbers. When you divide one number by a number before it. They are attain very close to one another. The number is fixed after the thirteenth series, which is known as the “Golden Ratio” 1.618. The Golden Ratio is also use by artist like Leonardo da Vinci and Architect Le Corbusier. It is even found in our teeth, heart, lung and our DNA.

Nature by Number
Fibonacci wanted to know how many rabbit would produce in a year. So he start with a pair in January. He realized a pattern 1, 2, 3, 5, 8, 13, 21,... Each number equals the two previous numbers of each series. Which is later known as the Fibonacci Series. Fibonacci Series is not only use with bunnys, but with flowers. For instance, a sunflower as a total numbers of 33, 55, or 89 petals. The Greeks believe that the rectangle held a key to beauty.

The Golden Ratio and Beauty in Architecture
The Golden Ratio was also used in Architecture. Like the Pyramid in Giza in Egypt, Parthenon in Athens, Greece, and many more. The Greeks, Romans, Egyptians, Chinese also use it in their architecture. This this shows that the Golden Ratio is used by a lot of people for designing.

The Golden Ratio Revisited

The Golden Ratio is invented by Euclid, a Greek mathematician and he is known as "The Father of Geometry. It helps define a proportion of any objects even if it was nature or man made. It was found in Leonardo da Vinci's painting like Mona Lisa and the “Vitruvian Man”. As well as in Adolf Zeising discovery and appearance. Like the arrangement of the branches, stems of plants and veins in the leaves.

Response and Reflection
From all the information I learned, I found the Golden Ratio in the Human Body is pretty amazing.
On how the Golden number 1.618 can determine who is beautiful. However, I don't believe that the Golden number can determine who is most beautiful because it is not that accurate. The are many people out there in the world that are pretty. It is just based on what the people definition of beautiful is. To me, my definition of beautiful is based on how they act and their personality not only how they look. Also based on how pure their soul are.

Fibonacci Beauty Ratio

According to my Fibonacci "Beauty Ratio" Activity, Tracey Pham is the most beautiful. She was the closest to the "Golden Ratio" of 1.168. I believe that  the beauty ratio cannot determine how beautiful the person is because Mrs. Kirch is beautiful. But the "Golden Ratio" said she is not even close. So, I believe it is not true. Everyone is beautiful in a unique way.

Fibonacci Haiku: Treasure Your Precious Moments

SP#5: Unit J Concept 6 - Partial Fraction Decomposition With Repeated Factors

You should pay close attention when plugging in the numbers and variables. Also when factoring to factor fully, or else you might mess up the problem. Good luck.

SP#4: Unit J Concept 5 - Partial Fraction Decomposition with Distinct Linear Factors

Make sure to pay close attention when solving the problem. There are a lot of tricky part that could mess you up. It is also important to make sure to plug in the right number into the calculator. Or else it would give you a different number. Good Luck :D

SV5 Unit J: Concept 3-4: Matrix

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Remember to pay close attention to what equation I plug in and how to do the back substitution. Also to make sure to distibute the sign thoroughly.

WPP #6: Unit I Concept 3-5: Compound Interest, and Investment Application Problem

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SV4 Unit I: Concept 2: Solve and Graph Logarithmic Equation

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Make sure to pay close attention to the asymptote and the Change of Base Formula. Also you should  how to  plug the equation in the calculator. You should try solving the problem on your own too.

SP3: Unit I Concept 1: Graphing exponential functions and identifying x-intercept, y-intercept, asymptote, domain, range.

Pay close attention to the domain, range, and y-intercept, why there is no y-intercept. Also you should make sure to plug in the equation in the calculator carefully. In order to find the key points, which will help you to graph the function.

SV#3: Unit H Concept 7 - Finding Logs Given Approximations

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In this video it will show you how to find logs with given approximations. There are 4 given clues that help us solve the problem. Also that there are one hidden clue. You are also required to use the power, product  and quotient to help solve.

Make sure to pay close attentions to when the number is breaking down and when expanding the log. Also that when the number is on the denominator then the sign should be a negative.

SV #2 ; Unit G Concept 1-7 - Finding all parts and graphing a rational function

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          This problem is about finding horizontal asymptotes, slant asymptote, vertical asymptote and the holes. First we must determine the equation that will help us. To tell whether it is bigger on top, same ratio, or bigger on bottom. Then we find the slant asymptote by using long division. Then we find the holes.
          However we must watch out when graphing the equation. Also to graph the holes with open open circles.

SV #1 Unit F Concept 7: Finding real and Imaginary Zeroes of a Polynomial

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1.  This problem is about finding zeroes with a polynomial and also find imaginary zeroes. First we begin by finding the possible rational zeroes. This helps us to know how many possible zeroes there are. Then we use the Descartes rule of signs to help us determine the positive and negative real zeroes. After that we use the synthetic division to help us find the zeroes.
2. However, one thing we must remember to keep sign for even power and change odd power when doing the Descartes rule of signs for negative real zeroes.

SP2: Unit E Concept 7 - Graphing a polynomial and identifying all key parts

            This problem is about factoring equation in order to find the equation. In this problem you are trying to find the x-int, y-int, zeros (with multiplicities), and end behavior. This will help you find the zeros (with multiplicities) and end behavior so you can graph it.

             Special attention is needed for graphing the equation. We must remember T=1, B=2, C=3, T stands for through, B stand for bounce, and C stand for curve. Which allows us to graph the function more accurate.

WPP #4: Unit E Concept 3: Maximizing Area

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WPP#3 Unit E Concept 2: Path of "Football"

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SP1 Unit E Concept 1: Graphing a quadratic and identifying all key parts

This problem is about identifying x-intercept, y-intercept, vertex (max/min), axis of symmetry and graphing them. In order to find the solution you should follow the steps. Which will make the answer and graph more accurate.

Special attention is needed for finding the x-intercept. You need to plug zero in the first equation and then to find the exact x-intercept. Press 2nd and find the radical then plug the number into the calculator.

WPP#2: Unit A Concept 7 - Profit, Revenue, Cost

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WPP#1: Unit A Concept 6 - Linear Models

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