SP #6: Unit K Concept 10: Writing a repeating decimal as a rational number using geometric series (no calculator)

The viewer should pay special attention to writing the correct formula (infinite geometric series formula) for the summation notation and when plugging in your values to the formula. Evaluating the sum will be the trickiest because you do not have a calculator to plug the values into so be careful with your division.

WPP #8: Unit K Concept 11

WPP #7: Unit K Concept 11

Fibonacci Beauty Ratio Blog Post

Friend's Name:    

Kimberly H.  

 Foot to navel: 100 cm       Navel to top of Head: 60 cm        Ratio: 100/60 = 1.677  

Navel to chin: 45 cm         Chin to top of Head: 20.5            Ratio: 2.195

 Knee to navel: 54 cm        Foot to knee: 46.5                             Ratio: 1.161

                      
Average: 1.677

Isaac A.      

   Foot to navel: 113 cm       Navel to top of Head: 66 cm        Ratio: 113/66= 1.883 

              Navel to chin: 43.5 cm         Chin to top of Head: 22 cm   Ratio: 43.5/22= 1.477

 Knee to navel: 58.5 cm        Foot to knee: 51                             Ratio: 58.5/51= 1.147

 Average: 1.502

Marisol R.     

 Foot to navel: 92 cm       Navel to top of Head: 58 cm        Ratio: 92/58= 1.586                        

 Navel to chin: 44cm         Chin to top of Head:   43         Ratio: 44/43= 1.023

 Knee to navel: 44.5 cm        Foot to knee:    54.5                           Ratio: 44.5/54.5= 1.147

Average: 1.252

William D.    

 Foot to navel: 107 cm       Navel to top of Head: 118 cm        Ratio: 107/118= .907

 Navel to chin: 47 cm         Chin to top of Head: 21            Ratio: 47/21= 2.238                 

 Knee to navel: 57 cm        Foot to knee: 46.5                              Ratio: 57/46.5= 1.226

Average: 1.457

Chelsea A.  

Foot to navel: 98 cm  Navel to top of Head: 56 cm        Ratio: 98/56= 1.750

                  Navel to chin: 39 cm         Chin to top of Head: 20                  Ratio: 39/20= 1.95          

        Knee to navel: 51.5 cm      Foot to knee: 47                       Ratio: 51.5/ 47= 1.096

Average: 1.597

 According to the Golden Ratio, Kimberly is most mathematically beautiful with an average of 1.677 cm. The rest of my friends results were based on measurements made based on their body parts. Using a meter stick we measured each part carefully in centimeters. In my opinion, the Beauty Ratio is a great way to see the world in a different perspective by basing it off measurements from Fibonacci. The Beauty Ratio is a reliable source of measuring the accuracy in architecture, art and human life.

Fibbonaci Haiku: The Happiest Place on Earth

Disneyland

Nostalgic

Walt Disney's

Joy and inspiration

The Happiest Place on Earth  

 

 

"..enter the world of yesterday, today and fantasy". 

https://secure.parksandresorts.wdpromedia.com/resize/mwImage/1/630/354/90/wdpromedia.disney.go.com/media/wdpro-assets/dlr/parks-and-tickets/attractions/disneyland/sleeping-beauty-castle-walkthrough/sleeping-beauty-castle-walkthrough-holiday-00.jpg?25102013104611

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

The viewer must pay special attention when distributing the common denominator to each numerator and denominator because if you make mistakes there you won't be able to get your correct answer. Also pay attention when combining like terms because adding and subtracting wrong will give you incorrect answers to your steps and final answer, as well.

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

The viewer must pay special attention to distributing your common denominator and combining like terms to get the correct system in the end. Be sure to plug in your row's terms into the rref feature in your calculator to check your answer. Your answer should match up your original fraction's numerator.

SV 5 Unit J Concept 3-4 - Solving three-variable systems with Gaussian E...

Pay special attention when subtracting your rows because you might end up with an incorrect difference. If you put an incorrect answer you cannot solve for the system correctly. Also, pay attention to what type of system you end up with. Since we ended up with an inconsistent system, we have no solution.

WPP#6: Unit I Concept 3-5- Investment application

SV4 Unit I: Concept 2: Graphing logarithmic equations

     Pay attention to your equation used when plugging it into your y equals screen. Be sure to use the change of base formula to convert your equation and then plug it in into the y equals screen. Also, make sure you exponentiate your log and to the other side when solving for your y-intercept.

SP3 Unit I: Graphing exponential functions and identifying x-intercept, y-intercept, asymptotes, domain, range

 Identify all parts of the equation (a,b,h, and k) and know how they affect your graph. So understand that "a" shows that the graph will be below the asymptote and "b" shows that the asymptote is at -2. The viewer needs to pay special attention to the x-intercept. You cannot take the log of a negative number. Thus, it is undefined and you have no x-intercept. Make sure you input your equation correctly into your y= screen. Use your table to plug in the x-values that will give you a more accurate sketch of the graph and obtain the values for your key points. Remember "The EXPONENTIAL YaK Died."- exponential graphs have an asymptote of y=k, leading to no restrictions on the domain. For the range, go from the lowest most negative point up to the asymptote, -2.
    

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

     Pay attention to factoring the fraction's numerator and denominator down correctly making sure they are your clues given. After you have factored your numerator and denominator  condense your clues into one log, multiplying each clue on the top and bottom. Expand your log using your clues using the properties of logs and make sure each number has one log in the problem. Be sure you bring down the power over to seven. Substitute all the values, or letter, given from your expanded problem.*Please excuse my pauses from 3:39 to 3:50*

SV#2 Unit G Concepts 1-7- Graphing a Rational Function

The problem shows you how to graph a rational function when the degree is bigger on top and one bigger than the bottom degree, meaning that it has no horizontal asymptote and it has a slant asymptote. In this problem, you perform long division in order to get your slant asymptote equation in slope-intercept form that gives you your first two points for the graph. Cross off any common factors from your factored equation and your remaining factor's zero is your VA equation. Plot any holes from the equation, any crossed off common factors equal to zero then for your y-value you must plug in your x-value into the simplified equation, not the factored. We found the domain of the equation: the x-value of my vertical asymptote. The x-intercepts are found by plugging zero for y using the factored equation, canceling the denominator, then setting the numerator's factors equal to zero. For the y-intercept plugging in 0 for all of the x's and solving  factor the numerator and denominator of the function  Be sure to graph all of the pieces on the graph: sketch asymptotes (slant/vertical), plot any holes, plot x-intercept and y-intercept and tracing any other needed points for the graph.

Pay attention when factoring your numerator and denominator, making sure it's not incorrect otherwise you will not graph the rational function right. Remember that we do not include our remainder from long division into our slant asymptote equation, you must plug in the x-value into the simplified equation to get the y-value meaning you do not use your factored equation. Make sure you put parenthesis around your correct rational function when inputting in your calculator tracing to get other values. Be sure to sketch your graph correctly, not to cross through the vertical asymptote.

SV#1 Unit: F Concept: 10: Given polynomial of 4th or 5th degree, find all zeroes (real of complex zeroes)

This video demonstrates an example problem on finding zeroes of a polynomial of 4th degree. We list out all possible real/rational zeroes (p's and q's). Then we use Descarte's Rule of Signs to find out how many possible positive and negative real zeroes there will be. We use the Factor Theorem and start trying to find remainders of zero (zero heroes) using a number from the p/q list. Continue to find zero heroes until your reduce your polynomial to a quadratic. Once you have a quadratic, factor it using the quadratic formula.

Remember to take out a GCF from your quadratic before using the values inside the parenthesis into your quadratic equation. Break down your square root (if you can) and in your remaining factors you should distribute the GCF if there are any fractions.

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

This problem is about graphing polynomials using its x-intercept, y-intercept, zeroes (with multiplicities), and end behavior. Factoring the equation will help you find the zeroes that will help you graph the points of the equation on the graph. It's end behavior allows you to know the direction of the arrows and then you graph the y-intercept.

Pay special attention to the multiplicity of the zeroes so you know how to act around the x-axis! A multiplicity of 1(T) will go straight through the graph, 2 (B) will bounce off the graph; does not cross the x-axis, and 3 (C) will curve through the graph.

WPP#4: Unit E Concept 3 - Maximizing Area

WPP#3: Unit E Concept 2 - Path of Football (or other object)

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

In this problem, in order to graph the equation more easily we complete the square in standard form to put it in parent function form: a(x-h)^2+k. Our graph includes 4 points: the vertex, y-intercept, axis and x-intercepts.

Pay attention to the max and min of the vertex so in our case it is min because the "a" in the equation is positive. Note that when solving for your x-intercepts you may end up with two,one or none (imaginary) x-intercepts so when you have your x-intercept, plug it into a calculator you have your exact and approximate x-intercepts.

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

WPP #1: Unit A Concept 6- Linear Models