Welcome to Tracey P.'s Math Analysis Blog

Sunday, December 8, 2013

SP#6: Unit K Concept 10 - Write Repeating Decimal as Rational Number Using Geometric Series

Remember to pay close attention when I'm substituting the numbers into the equation. Don't forget to add five at the end when you're done solving because there was a five in the beginning of the problem.
In the above picture, I found that "a" sub one is 0.25. However, you must convert it to a fraction which would be 25/100. "r' is 1/100 because I took the preceding term and divided it by the first.

This picture is self explanatory, after I found 25/99, I still had to add five. I multiplied five by 99 to find the common denominator and then added to find my final answer.

Sunday, November 24, 2013

Fibonacci Beauty Ratio

Measurements:
Chelsea A.:
Foot to Navel: 99 cm
Navel to top of Head: 58 cm
Ratio: 99/58=1.707 cm
Navel to chin: 39 cm
Chin to top of Head: 21 cm
Ratio: 39/21= 1.857 cm
Knee to Navel: 53 cm
Foot to Knee: 46 cm
Ratio: 53/46=1.152
Average: 1.572 cm

Christine N.:
Foot to Navel: 96 cm
Navel to top of Head: 59 cm
Ratio: 96/59=1.627 cm
Navel to Chin: 40 cm
Chin to top of Head: 22 cm
Ratio: 40/22=1.818 cm
Knee to Navel: 51cm
Foot to Knee: 48 cm
Ratio: 51/46=1.109 cm
Average: 1.518 cm

Katie W.:
Foot to Navel: 103 cm
Navel to top of Head: 63 cm
Ratio: 103/63=1.635
Navel to Chin: 44 cm
Chin to top of Head: 22 cm
Ratio: 44/22=2
Knee to Navel: 57 cm
Foot to Knee: 48 cm
Ratio: 57/48=1.188
Average: 1.608 cm


Stephanie V.:
Foot to Navel: 99 cm
Navel to top of Head: 60 cm
Ratio: 99/60=1.65 cm
Navel to Chin: 44 cm
Chin to top of Head: 22 cm
Ratio: 44/22=2 cm
Knee to Navel: 53 cm
Foot to Knee: 44 cm
Ratio: 53/44=1.205 cm
Average: 1.618 cm

Leslie N.:
Foot to Navel: 96 cm
Navel to top of Head: 63 cm
Ratio: 96/63=1.524 cm
Navel to Chin: 45 cm
Chin to top of Head: 20 cm
Ratio:45/20=2.25 cm
Knee to Navel: 53 cm
Foot to Knee: 44 cm
Ratio: 53/44=1.178 cm
Average: 1.651 cm

Based on the Beauty Ratio, Stephanie is the most beautiful because her ratio was 1.618. This also happens to be the exact number of the "Golden Ratio". I believe that a number can't decide how how beautiful someone is. Everyone is beautiful differently, whether it's their personality or intellect. In my opinion, the Beauty Ratio is valid in proving how proportionate a person is but it's not valid in proving how beautiful a person is.

Fibonacci Haiku: I Believe

Christmas
Santa
Doesn't exist
Ruined my childhood
No more presents from Santa
At least the tooth fairy is still real
http://www.celebuzz.com/photos/top-10-cutest-christmas-animals/sour-puss-2/

Saturday, November 16, 2013

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

Remember to pay close attention when adding all the like terms and remember to show all your work because it is very easy to make mistakes, especially when you have four variables.

Step 1: You first find a common denominator and multiply it to the four varaibles. Once you've done that you add up all the like terms and separate them into the common terms. Then, you can start canceling out the like terms and the results will be the system.
Step 2: Next, you take the first and second equations and add them together. Then, you can use the elimination method in the third and fourth equation, in the picture above, I eliminated D. Once you have the two equations, you use elimination on them as well and I eliminated C.
Step 3: This picture shows what I did to solve for the four variables. The picture is pretty much self-explanatory. I just solved for A first and then used the substitution method to find the other equations.
This will be your final answer in the end.





Thursday, November 14, 2013

SP#4: Unit J Concept 5 - Partial Fraction Decomposition

Be sure to pay close attention in distributing the numerator and be very careful when plugging in the numbers into the calculator. Also, remember to use the rref feature and check if the answers are correct.

Part 1: First, you would have to find the common denominator. In this case it's (x+4)(x-2)(x+1). Then, you distribute them to the numerator but remember to foil it out first. Once you have completed this step, you add up all the like terms.
Part 2: Now you have to replace the numerator with letter values. Then, you multiply by the common denominator again. This time, instead of distributing a number, you'll be distributing a letter. Next, you set the distributed product equal to the original and add up any like terms (like terms highlighted in above picture). After, you've found the like terms, you can start canceling out and the end product will be the system (as shown above).
Part 3 : The last step is to plug in the system into the calculator. Then you use the rref feature to find your answer. Once you have found what A,B, and C equals, plug them back into the original 3 fractions.



Monday, November 11, 2013

SV#5: Unit J Concept 3-4 - Solving 3-Variable Systems w/ G-J Elimination, Matrices, REF, Back-Subs., & Solve Non-square Systems

To view my video, please click here.
(This is DP#3)
Remember to pay close attention to how I'm solving the matrices and please double-check my work by doing it yourself first. This will prove beneficial because as you watch my video, you'll see that I'll tend to mess up quite a bit, but no worries because I did catch them!
Here is what the rref will look like once you've put in the numbers into the calculator:


Saturday, October 26, 2013

SV#4: Unit I Concept 2 - Graphing Logarithmic Functions & Identifying All Parts

To view my video, please click here.

During the video, please pay attention to all the steps and remember to plug in the equation into the calculator. Also, remember to put the equation as a natural log because a calculator can't find a log base five.

Thursday, October 24, 2013

SP#3: Unit I Concept 1 - Graphing Exponential Functions & Identifying All Needed Parts

In this problem, you need to make sure to check if there's an x-intercept or not. You can tell by checking if there's a negative log, if there is, then there is no x-intercept. Also, make sure to write your domain and range correctly. On an exponential graph, domain is always negative infinity to infinity.

The first step you would have to do is label your variables (a=-3, b=2, h=1, k=-2). Next, you find your y-intercept, this is basically just y=k (y=-2). Then, you find your x-intercept, and from the picture below, you can see that there can never be a negative natural log. As a result, there is no x-intercepts. The next step is to find your y-intercept. From the step-by-step work that I've shown below, the y-intercept is (0, -7/2) or it can also be written as (0, -3.5). The domain would always be negative infinity to positive infinity since it's an exponential graph. Lastly, the range would be negative infinity to negative two. It's negative infinity because the graph is below the asymptote and the negative two came from the asymptote.

Wednesday, October 16, 2013

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

To watch my video, please click on the link HERE.

This problem is about finding logs given there approximations. There are four given clues as well as a hidden clue. To solve the problem, you must use the properties of logs (Power property, quotient property, and product property). Also, you'll need to substitute those numbers with the corresponding letters  to get your final answer.

Make sure to pay close attention when factoring out the numbers because they might already be a clue. Remember to put the appropriate sign for each log, such as the plusses and minuses. The numerator will always be adding, whereas the denominator will be subtracting.

Sunday, October 6, 2013

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

To view my video, please click on the link HERE.

This video will show you how to solve for rational functions. It will show you how to find the slant asymptote, vertical asymptote(s), hole(s), domain(with interval notation), x-intercept(s), and y-intercept(s). Above all that, it will assist you in graphing the rational function as well as finding the key points necessary for the graph.

While watching this video, please pay close attention to all the steps and go along with all the instructions. For instance, plotting the rational function into the calculator yourself and working through the problems too. Also, remember to double-check that all the answers and steps are correct. (People make mistakes!)

Sunday, September 29, 2013

SV#1: Unit F Concept 10 - Finding all real and imaginary zeroes of a polynomial

To view my video, please click on the link HERE.

This video will show you how to find the zeroes and factorizations for a fourth or fifth degree polynomial. It will show you each step you would need to take to find the zeroes of a polynomial.

While watching this video, be sure to pay close attention to each steps. Also, remember to use the Descartes Rule of Signs when solving for the polynomial. Remember to double-check your answers and see if each steps are correct.



Monday, September 16, 2013

SP#2: Unit E Concept 7 - Graphing a polynomial and identifying all key parts

This picture will show you how to find the end behavior as well as the x intercepts and multiplicities. You will also learn how to tell if the graph will go "Thru", "Bounce", or "Curve". The picture shows the basic steps of how to sketch a graph based on multiplicities and x intercepts.

The first step to solve this equation is to factor out the equation. Once you have done that, the answer should be: (x-2)(x-2)(x+2)(x+1). As you can tell from the equation, it is even positive. This means that both the end points go upwards. To find the x intercepts, you put each factor equal to zero. The answers should be: (2,0) M2, (-2,0) M1, (-1,0) M1. Next, you find the y intercept is 8 because you substitute all the X's for 0's; the answer should be: (0,8). To graph it, you look at the multiplicities if it's a multiplicity of one, then it's through. If it's a multiplicity of 2, then the graph bounces and if it's a multiplicity of 3, it's curving.


Monday, September 9, 2013

SP#1: Unit E Concept 1 - Graphing a quadratic and identifying all key parts


This problem is showing how to find x-intercepts, y-intercepts, and the vertex (Maximum/minimum).
~Completing the Square~
In this problem, I first added 8 to the other side of the equation. Then,I took out a four and put it outside of the parenthesis. I then divided by 4. After,I square rooted everything and subtracted 2 to the other side. Because the equation is positive, it will be a minimum. The axis of symmetry will be at -2. To find y-int, you substitute 0 in for x, and find that it's -8.