Fibonacci Haiku: Break

Break.

Rest.

A week.

Peaceful times.

Thanksgiving dinner.

There is always room for dessert.

Making precious memories with friends and family.

Procrastinating and cramming all your homework in on Sunday night with some regret. 

http://fc01.deviantart.net/fs71/f/2011/154/4/3/pokemon_rgb_by_mk3mty-d3hz832.png

SP#5: Unit J Concept 6:Partial Fraction Decomposition with Repeated Factors

 <- This is your problem

1. Set up the partial fraction decomposition problem

- set the numerator to A, B, C, etc.
- multiply the numerators with the LCD
- combine the like terms
- set up the system by making an equation for each of the like terms and getting rid of the x's

 1. Add the first two variable equations from your system to get Equation #1.
2. Use elimination to add the remaining two problems from the system to get Equation #2.
3. Add Equation #1 & Equation #2 using elimination to get Equation #3.
4. Use elimination to add Equation #3 with one of the equations from the system. Solve for A.
5. Plug A into one of the equations from the system. Solve for B.
6. Plug B into  the system. Solve for C.
7. Plug C into the system. Solve for D.

Plug A, B, C, & D into the original set up for partial fraction decomposition.













In this concept, pay special attention to how I set up the partial fraction decomposition problem. Also, examine how concepts 5 and 6 are different because this concept deals with repeated factors. Finally, take special care not to mess up in eliminating or substituting. Good luck!

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

 Part 1 - Composing

- find the LCD & multiply to the numerator
- combine the like terms

 Part 2 - Setting up the partial fraction decomposition problem

- set the numerator to A, B, C, etc.
- multiply the numerators with the LCD
- combine the like terms
- set up the system by making an equation for each of the like terms and getting rid of the x's








Plug the system into your calculator- rref to check work

The answers should be the numerators of the equation you started with in part 1.



In this concept, you need to pay special attention to how we set up the problem for distinct factors. Moreover, be careful when you combine the like terms because it is very easy to make a mistake. Finally, pay attention to how I set up the system and plugged it into the calculator.  Good luck!!

SV#5: Unit J Concept 3-4: Solving three-variable systems with Gaussian Elimination

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

In this video, you should pay special attention to how I check my answers using rref on my calculator. Also, pay attention to which 0's I found first and how I got my staircase 1's. I also forgot to mention in the video that when you are looking for the first 0 in Row 3, Term 1, you will use either Row 1 or Row 2 to help you; you must use Row 1 to find the 2nd 0 in Row 2, Term 1; and you must use Row 2 to find the last 0 in Row 3, Term 2.  Good luck!