WPP #10: Unit L Concepts 9-14: Basic Probability, Independent, Dependent, Mutually Exclusive etc.

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WPP #9: Unit L Concepts 4-8: FCP, Combinations, Multiple Events, Permutations etc.

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SP #6: Unit K Concept 10: Writing a repeating decimal as a rational number using geometric series

Steps and Explanations!!

1. Write out the repeating decimal with the same type of number according to its placeholder.

2. Find your first term or "a sub 1" by getting the first repeating number (in this case 127) and change it to a fraction according its placeholder.

3. Find your ratio by getting the 2nd term and divide it by 1st.

4. Once you find your first term and ratio, write the problem in summation notation, plug in formula, and add the sum. When you plug in formula, it should be an infinite geometric series.

5. When you add the sum, don't forget to add the "whole number" or the number in front of the decimal.

  The viewer should pay special attention to the repeating number in order to know how to set up the geometric series with its right placeholder. To get to the right placeholder add the zeroes before the repeating number. Make sure to know your formulas such as the geometric sequence and infinite geometric series. When adding the number in front of the decimal in the problem, make sure to show full work (common denominator etc.).

Fibonacci Beauty Ratio

Measurements of Friends:
Mia
Foot to Navel: 103 cm
Navel to top of Head: 63 cm
Ratio: 103/63= 1.635 cm
Navel to chin: 44 cm
Chin to top of head: 23 cm
Ratio: 44/23= 1.913 cm
Knee to navel: 57 cm
Foot to knee: 50 cm
Ratio: 57/50= 1.14 cm
AVERAGE: 1.563 cm

Eriq
Foot to navel: 109 cm
Navel to top to head: 65 cm
Ratio: 109/65= 1.677 cm
Navel to chin: 47 cm
Chin to top of head: 25 cm
Ratio: 47/25= 1.88 cm
Knee to navel: 58 cm
Foot to knee: 54 cm
Ratio: 58/54= 1.074 cm
AVERAGE: 1.544 cm

Sarahi
Foot to navel: 99 cm
Navel to top of head: 66 cm
Ratio: 99/66= 1.5
Navel to chin: 41 cm
Chin to top of head: 22 cm
Ratio: 41/22= 1.864 cm
Knee to navel: 50 cm
Foot to knee: 45 cm
Ratio: 50/54= .9259
AVERAGE: 1.430 cm

Kelsea
Foot to navel: 100 cm
Navel to top of head: 58 cm
Ratio: 100/58= 1.724 cm
Navel to chin: 46 cm
Chin to top of head: 21 cm
Ratio: 46/21= 2.190 cm
Knee to navel: 49 cm
Foot to knee: 49 cm
Ratio: 49/49= 1
AVERAGE: 1.638 cm

Jenny
Foot to navel: 95 cm
Navel to top of head: 56 cm
Ratio: 95/56= 1.696 cm
Navel to chin: 36 cm
Chin to top of head: 23 cm
Ratio: 36/23= 1.565 cm
Knee to navel: 47 cm
Foot to knee: 48 cm
Ratio: 47/48= .979 cm
AVERAGE: 1.413 cm

   Based on the calculations, Kelsea is the most beautiful since her average is close to the Fibonacci number or the Golden Ratio of 1.618. Her average calculations were 1.638 cm. Because she is considered the most beautiful based on the Golden Ratio, this means that her body is symmetrical and proportional. Not only her body is proportional, but also her face. When faces and bodies are in proportion, we, as human beings, recognize it as the body to be healthy and likewise, the body and face to be very appealing and attractive to the eye. However, in my perspective, I believe that to be beautiful depends on who the person really is. Yes, there are times where someone can catch your eye in a split second but by the end of the day, if that person has no sweet or great personality that attraction means nothing. To be beautiful is to have a beautiful heart. To be beautiful is to also have a kind and courageous thought; no hate.

Fibonacci Haiku: Damon Salvatore

Vampire

Diaries

Damon Salvatore

Most attractive vampire

He has beautiful eye color

He's the peanut butter to my grape jelly

http://images.wikia.com/vampirediaries/images/c/c0/Damon-Salvatore-damon-salvatore-16725155-1280-720-1-.jpg

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

Steps and Explanations!!

1. Like in Concept 5, decompose the problem and find your like terms and system.

2. The hardest part of this problems is canceling and knowing what to cancel. There's many different ways to cancel the variables but for now, try to follow my work with the whole canceling process. 

3. Once you found "A", plug it in to one of the systems and you'll also find "B". Repeat the same process with different systems plugged in to find variables "C" and "D". 

4. Once you found what your variables equal to, double check your answer with matrix and rref in your graphing calculator.

   The viewer needs to pay attention to the canceling process and understanding how and what is multiplied in order to cancel out a certain variable. As the viewer figures out that "A" is, try to keep the same denominator throughout the process (which the denominator should be 27.) Also, when using rref to check the answer, the graphing calculator will not give a fraction in the matrix but instead a decimal. The answer will still be correct if it corresponds to the fractions of A, B, C, and D.

SP #4: Unit J Concept 5: Partial Fraction decomposition with distinct factors

Steps and Explanations!!

1. Compose the problem by multiplying the common denominator to each fraction (numerator).

2. Multiply the denominator to its common denominator also.

3. After multiplying the common denominator, write out the complete factors of the numerator and denominator.

4. Decompose the problem by rewriting the numerator and write the common denominator at the bottom.

5. To decompose, use letters A, B, and C. Find its common denominator and multiply.

6. Then set it equal to the previous answer that you found (the compose part).

7. Combine like terms to the appropriate number that you set equal to (ex. 9x^2 = something that has x^2).

8. Find the "system" by crossing out the x's.

9. Rewrite the system with the matrix format and plug it in to your graphing calculator. It should have the same answer that you started with in the problem.

       The viewer needs to pay attention to the common denominator since mistakes can easily be found when multiplied incorrectly. Make sure to know the difference between "compose" and "decompose". Matrix can help the viewer know if the answer is correct. Thus, it needs to match to what the problem started with.

SV #5: Unit J Concept 3-4: Solving Three Variable Systems (Matrix)

**Sorry everyone about the video! Something went
wrong with the downloading part of the video so that's why you can't 
watch it right side up. I apologize :(

    The viewer needs to pay attention to the rows and where each equation
best fits in which row. Remember, we are trying to get zero on a specific
row and term! Also, before you actually start the problem, it'll be easier
if you factor the equation before hand. Near the end of the matrix, the
viewer should have the stairstep of 1's (in this problem at least because
it is an consistent independent system). If you want to double check your
answer, you may use your graphing calculator to make sure if your answer
is correct. In this case, the viewer should use the Gauss-Jordan elimination
system on his or her graphing calculator. Thanks for watching!

WPP #6: Unit I Concept 3-5: Interests and Investments

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SV #4: Unit I Concept 2: Graphing Logarithmic Equations

     The viewer needs to pay attention on how to use the graphing calculator to give a visual of how the graph should be able to look like. When solving for x-intercept, don't forget to exponentiate! When solving for y-intercept, don't forget to PEMDAS!Also, you can either plug in "log" or "ln" in your graphing calculator because either way, they will both come out to be the same.***I forgot to mention the domain and range in this video as you can see. When you graph log equations, your range will have no restrictions so it will also be (negative infinity, infinity). It has no restrictions because your asymptote is x=h. For the domain, you will have to refer to your graph. In this case, the graph only goes from -5 to infinity (from the asymptote to infinity). The domain in this graph will have to be (-5, infinity). Thanks for watching the video!

SP #3: Unit I Concept 1: Graphing exponential functions and identifying x-intercepts, y-intercepts, asymptotes, domain, range

    The viewer must pay close attention when solving  for the x-intercept. If the log or natural log is negative, there is no x-intercept! Also, make sure to observe the problem before you actually start. There are so many small useful tips just by looking at the problem. You will eventually keep in mind of what the graph shall look like. Figure out if the graph will go above or below (negative "a" will go below). Find the asymptote so you can determine where or not there will be an x-intercept. From there, you can easily know your domain and range even before you start the problem!

Steps and Explanations!!
1. Label your a, h, b and k. In this type of equation, your asymptote will be y=k. 2. Find your x-intercept by plugging in zero for y. You will have to take the natural log in this problem in order to cancel and simplify your answer as much as possible.  3. Find your y-intercept by plugging in zero for x. Use pemdas to solve. 4. If an exponential graph has an asymptote that is y=k, then there will be no leading restrictions on the domain. Thus, it would be negative infinity, infinity (in order pairs). 5. Determine the range simply by looking at your graph. In this case, the graph is above the asymptote. So you will have to write your range practically based on your observation of the graph. The graph began at 3 and up beyond to infinity (3, infinity).

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

  .

 In this concept, finding logs with given approximations provide the clues in order to be able to evaluate the logs in the problem. The "clues" will guide you in terms of knowing what values or letters will equal to a certain log. Using the properties of logs from the previous concept, this problem will show you how to find your answer just based on the clues that are given. This concept combines all the other previous concepts in this unit.
 The viewer needs to pay special attention to special hints. Hints such as log base b of b equal to one and log base b of one equal to zero. Make sure to break down the problem and see what kind of factors go into the numerator and the denominator of the problem. Also, if you have log base b of b to the power of x, make sure to bring the exponent down and in front of the log! This is an example of the power law. Good luck and thanks for watching the video!

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

This problem is everything about rational functions! You will learn how to find your asymptotes, holes, domain, x-intercept, and y-intercept. Each asymptote, such as the horizontal, slant, vertical, and hole, has unique rules and steps to determine the equation. Most of the different asymptotes depend on the degree of the top and bottom of the polynomial. This concept also includes the limit notation.

The viewer needs to pay special attention the vertical asymptote and hole(s) because for vertical asymptote, the denominator (or bottom) has to be set up to 0. The tricky part is the denominator. Why? Because the viewer needs to make sure that whatever is actually left in the denominator, meaning everything else is already checked if it can be canceled, can be equaled to 0. Also, it is relatively easier if you use the simplified equation for the y-intercept since there will be a hole in this problem.

SV#1: Unit F Concept 10: Given Polynomials with 4th or 5th degree

This problem is about knowing how to solve 4th or 5th degree polynomial in terms of finding the zeroes and factorization. Concept 10 goes over most of the previous concepts in Unit F. Those concepts will help us figure out on how to solve these kind of problems. This includes the p & q's, Decartes Rule of Sign, factoring, etc.

The viewer needs to pay special attention to the possible rational zeroes because it narrows down to the possibilities of what kind of zeroes the problem may have. Make sure you use the quadratic formula correctly since many people get those mixed up and confused! Simplify your answer as much as possible.

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

     This problem demonstrates the techniques of graphing a polynomial equation, which includes the end behavior, finding x & y intercepts, and zeroes (multiplicities). The graphs are very similar to Concept 4, except now we have to determined the humps or the way it should be shaped in the middle of the graph. The multiplicities will let us know if we should either go through, bounce, or curve in the graph.

   Make sure to pay close attention to the multiplicities and the end behavior. The multiplicities let us know what is going on in the middle of the graph, while the end behavior tells us what type of graph it is, whether it is an odd-positive, odd-negative, even-positive, or an even-negative graph. Also, make sure to pay attention to the y-intercept. It'll tell you how high the "hump" should go.


Steps and Explanations!! 1. Factor out the equation carefully. 2. Determine the end behavior based on the leading coefficient and degree of the original equation. Make sure to also write your notation based on the type of graph it is! 3. List out your x-intercepts based on what you just factored. Don't forget to include the multiplicities. 4. Find the y-intercept by plugging in zero or "x". 5. Graph! Make sure to use the end behavior and the x & y intercepts to graph!

WPP #4: Unit E Concept 3: Finding Maximum and Minimum Values of Quadratic Applications using calculator, interpretation of solutions

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WPP #3: Unit E Concept 2: Finding Maximum and Minimum Values of Quadratic Applications using calculator, interpretation of solutions

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SP #1: Unit E Concept 1: Identifying x-intercepts, y-intercepts, Vertex (max/min), Axis of Quadratics and Graphing

1st paragraph: This problem is about changing the standard equation to a parent function equation in order to be able to graph the quadratic. You will need to figure out your vertex, y-intercept, x-intercept, and axis of symmetry. Steps are required to convert your equation and to find your intercepts. By the end, you will use all these tools to graph your quadratic. Remember, you cannot plot imaginary answers. 2nd paragraph: To start off with full understanding, you will need to pay attention to changing your equations. You must complete the square in order to go from a standard equation to a parent function equation. Your vertex is (h,k). But remember, your "h" is the opposite to what you think it is. For instance, (x-2)^2, your "h" would 2. When you think of axis, be clear that it is the same as axis of symmetry or axis of line symmetry. When you plot your graph, it should be thoroughly and relatively easy once you got your points. Steps & Explanations!! 1. You must complete the square in order to convert the equation. Subtract 6 from both sides and complete the square by using (b/2)^2. 2. Vertex is (h,k). Remember "h" is the opposite to what you think it is! This graph is a minimum because the "a" is positive. 3. Find your y-intercept by plugging in zero for x on your standard form equation. 4. The Axis or axis of symmetry is determined by x=h. 5. Solve your x-intercepts by plugging in to your completing the square process. So you should plug it into something like "2(x+3)^2 = 12. By the end, remember to plug in all of your points that you have found onto the graph. Remember to use the axis of symmetry.

WPP #2: Unit A Concept 7

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WPP #1: Unit A Concept 6: Writing and Solving Linear Model Word Problems

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Striving to Succeed in Math Analysis: About me

Striving to Succeed in Math Analysis: About me: I love spending time with friends and family. I also love playing the guitar and now learning on how to play the piano! Of course, I have to...