RWA #1: Unit M Concept 5: Ellipses

1). An ellipse is the set of all points such that the sum of the distance from two points known as the foci is a constant. (http://www.lessonpaths.com/learn/i/unit-m-conic-section-applets/ellipse-drawn-from-definition-geogebra-dynamic-worksheet)

http://www.mathwarehouse.com/ellipse/equation-of-ellipse.php

2). Representing an Ellipse Graphically: An ellipse consists of a central point known as the center, 2 vertices connected with the major axis, and 2 co-vertices connected with the minor axis. The distance from the vertex to the center is known as 'a' and the distance from the co-vertex to the center is known as 'b'.

https://people.richland.edu/james/lecture/m116/conics/conics.html

Ellipses also have 2 points known as the foci. As demonstrated in the picture to the left, The sum of the distance from these two points (d1 + d2) is always a constant (2a). This is essentially what makes an ellipse. Also, the distance from the focus to the center is known as c..

http://coachjpocconics.weebly.com/ellipses.html

Algebraically:  As the picture suggests, there are two different ellipses with their corresponding equations which differ slightly with the placement of 'a' and 'b'. If 'a' (the bigger value) is under the y term, then the ellipse will be a vertical/ skinny ellipse and if it is under the x term, then the ellipse will be horizontal/ fat. 'H' and 'k' represent the x and y coordinates of the center.

Important: It is significant to know the eccentricity regarding an ellipse. Eccentricity is how round a conic is, 0 being perfectly round. An ellipse's eccentricity is greater than  0 but less than 1. This could be written as  e = 0 < x < 1. This is because an ellipse isn't perfectly round like a circle (whose eccentricity is 0) and yet it is more round than a parabola (whose eccentricity is 1). Eccentricity could be found by dividing 'c' by 'a' (c/a).

3). Real World Application: Elliptical Training Machinery
Elliptical gym equipment, such as elliptical runners/climbers are very useful when trying to avoid joint injury in a workout. Basically, the elliptical motion which is usually amplified with the use of handle bars or a motor drive, limits the impact on the joints that is very common with running. This article outlines this use for ellipses as well as a few other uses: http://www.ehow.com/info_8522010_real-life-uses-ellipses.html
...And this is a guy with a cool accent who will transmit elliptical knowledge to your brain in a brief 2 minutes:

4). URLs cited : Pictures from the top-down:
http://www.mathwarehouse.com/ellipse/equation-of-ellipse.php

https://people.richland.edu/james/lecture/m116/conics/conics.html

http://coachjpocconics.weebly.com/ellipses.html

Youtube video link: https://www.youtube.com/watch?v=AVrUEAiw5gA

WPP # 10: Unit L Concepts 9-14: Probability

Create your own Playlist on LessonPaths!

WPP #9: Unit L Concepts 4-8: FCP, Cominations, Combos with multiple events, Permutations, and Distiguishable Permutations

Create your own Playlist on MentorMob!

Sp #6: Unit k concept 10: writing a repeated decimal as a rational number using geometric series

One must pay attention to a few things. Firstly, one should read the steps  and explanations written in blue ink in order to understand the work. Secondly, pay attention to the formulas for it is easy to miss a key part of them.

Fibonnaci Haiku: Working Out

Workout
Squats
Swaggity swag
Dat protein tho
Do you even lift bro?
Got so much muscle, you don't even know

http://us.123rf.com/400wm/400/400/texelart/texelart1112/texelart111200011/11559808-athlete-lifting-weights.jpg

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

One must pay special attention to several things to get this. First off, one must be careful to not make any mistakes, for they could be fatal. Also pay attention to the factors; needless to say, those are important (understatement of the day). Also, pay attention to my writing, I shamefully admit that I do not own the most remarkable penmanship (also the first picture was incorrectly took and the result was a hard to read, vertical image). As the great writer Sophocles once quoted, "My bad, dawg."

SV #5: Unit J Concepts 3-4: Solving three- variable systems with Gaussian Elimination and Solving non-square systems (matrices)

It is very important to pay special attention to several key elements of this awesome video. First off, it is very important to pay attention to each step individually so as to understand what is being done. Second, it is important to use the correct row for each step. Also, be certain that all your work is done properly, for matrices are very complicated.