Tracksters

High school track: 24 placers earn 108 points, allocated as follows; 7points for first(f) , 4 for second(s) , and 1 for third(t) . School's second placers total it's first and third placers.
This string of data can be arranged into three equations:
{7f + 4s + t= 108}
{f + s + t= 24}
{-f + s - t= 0} simplified by the inverse of addition, subtraction, from  {f + t= s}
From these equations, a matrix arises:     [7  4  1  108]
                                                              [1  1  1  24]
                                                              [-1  1  -1  0]
Which, using the reduced-row-echelon-form function yields: 8 first placers, 12 second placers, and 4 third placers.      {8 + 4= 12}      12*4 + (7*8) + 4= 108

"The night will last, forever!" ~ Nightmare Moon

"The Men who Wear the Star"

Good evening everypony, this week I bring unto you a logic puzzle of a man's ancestors and their military ranks. (Evan plus his four paternal ancestors)
1: "Martin is the grandson of the man who retired with one-star."
2: "Jacob is not Randolph's son." 
3: "Nathaniel had two more stars than Evan's great-grandfather
4: "Either Jacob or Martin had three-stars"
 From clue three, Evan's great-grandfather can have no more than two-stars, and Nathaniel (Nate) must have either three or four. However Nate is not Martin or Jacob, so he must have 4-stars and Evan's great grandfather must have two.
 From clue 1, Martin must be Evan's grandfather because the position of great-grandfather is filled with a two-star holder.
 Jacob and Randolph cannot be next to each other and so must be the father and G grandfather, or 2G grandfather, but this puzzle is unsolvable for that very reason. Nate must be the father because that is the position lacking a star and a name but that forces a violation of clue 2.

"Making sense, hah. What fun is there in making sense?" ~ Discord.

Linear Functions

In the story problem, a shoe factory has certain parameters for two types of soccer shoes.
1) each pair goes through a two-step process
2) Outdoor shoes (X) take 2hrs in 1st step: 1hr in the 2nd, yielding 20$
3) Indoor shoes (Y) take 1hr in step 1: 3hrs in step 2, yielding 15$
4) 40hrs are available for step 1
5) 60hrs available for step 2
Knowing this, the maximum number of either shoe that can be created is 20 pairs [40/2, 60/3] {X<= 20, Y<=20}   {X>=0,  Y>=0}    F(X,Y)= 20X+15Y
With this, the feasible region is a square defined at the points: (0,0); (0,20); (20,0); and (20,20)
Max F= (20,20); [20*20+(15*20)]=  700$

"Dumb fabric." ~Sweetie Belle

Week 2

*The solutions of inequalities are all points that satisfy the conditions either above or below the line, dependent upon the nature of the inequality. However, with an inequality system, the solution is the area of overlay betwixt the two(+) inequalities.
*{Y<4
  {X>-4 Solutions include: (-3.99,3.99)_(-3.99,-infinite)_(infinite,3.99)_(infinite,-infinite) and all area within that.

The Basics of Linear Equations

1:Linear equations are the mathematical means of expressing a constant change, be it growth, speed, decay, or the like.
(y=mx+b (y= slope times x plus y-intercept.))

2:Linear equations. are graphically marked by a straight line with a slope that intersects the y, and x-axes.

3:The function of a linear eqn. is a straight, slanted line much like: / or \. However, the absolute function, [x], is a straight line parallel to the x-axis, perpendicular to the y-axis: _  



"~Yay." -Fluttershy

Egocentricism

  My name is Brian Johnson and I have an interest in mathematics. I plan to pursue an accounting degree because I have had pseudo-experience with accounting due to a chemistry class. I found money management to be easy and fun and, quoting my 'subordinate' accountant: "Numbers don't cause drama. It's just, here's what we have to spend, if we can't afford it, you can deal without it. Sorry but that's how it goes."

  In addition to math, I enjoy quality music, and that, for the most part means music from before the 21st century. Sorry pop fans, three chords and computer modulation is not quality. Not to say that electronic music can't be good, it's just, there is a difference between sound-experimentalism, the House genre, and Auto-tune.

  Say what you will towards a 17 year-old male, but I am a fan of the current iteration of My Little Pony, "Friendship is Magic" (which is the fourth generation of Hasbro's perennial pony programme.) What attracted me to the ponies was the attention to detail by the animators, the surprisingly complex stories, the little references that the 'target' audience would not get, and the highly-creative community-base of fellow young (mostly) males called bronies (bro+pony=brony.)
 

-Luna Nobis Custodit  Luna keeps us.