Fibonacci Haiku: Piano

http://www.manuel-music.com/wp-content/uploads/2013/05/Piano-keys.jpg

           

"Piano"

Soft

Loud

Tonic

Piano

Terminology

Wonderful Instrument It Is !

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

First separate it into three separate factors and then find the common denominator. Multiply the common denominator to the top and bottom. Combine like terms and set it as a system. Then with a calculator plug it the same way as if you're plugging in a matrix. The answer from that should be your equation.







     The trickiest part of this problem is probably when you multiply the common denominator to the top and bottom because C only needs one and it's (x-1). Also when you combine like terms, it can be easy to make a silly mistake there.

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

 Pic 1: I have this equation 4/x+3 + 9/x+2 + 3/x-4 and the first thing you want to do is find the common denominator. When you find it multiply it to the top and bottom. Then you add them up together and it's all over  (x+3) (x+2) ( x-4). Next you combine like terms for the top. And at the end you 16x^2 - 2x - 122.

 Pic 2: First separate the factors and put the letters A, B, and C. Then we get the least common denominator for the three fractions by multiplying each part by what missing. Next you group all the like terms and set the coefficients of the numerator equal to the like term letters on the right side. And on the left side the numerator of the composed equation.

 Pic 3: You plug this in the calculator by pressing 2nd matrix and go to "EDIT" and plug this in. Then you 2nd quit and go back to 2nd matrix and you go to "MATH" and go down to "rref" and press enter. Go back to 2nd matrix and press enter to "[A]". Next you just press enter.

P

Pic 4: You will get 4, 9, and 3 and those are the same number that are in the first picture.












One thing you want to look out for in my problem is to check each step carefully. If one number is added or subtracted wrong is can affect the whole thing.

SV#5: Unit J Concept 3-4: Solving Three-Variable Systems With Gaussian Elimination

One thing that you should look for is knowing which Rows to use when your solving for a 0. For the first 0 you can use Row 1 or 2, and when it the second 0 you must use Row 1. On the last zero you also must use Row 2.