Fibonacci Haiku: Happiness or Success

Happiness

Success

Which one?

Success equals happiness

Or does happiness equal success?

Have a smile on your face every day

 

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SP #5: Unit J Concept 6 - Partial Fraction Decomposition with Fractions

 

The viewer must pay special attention to setting up the equations, and that they distribute carefully and properly. It is important to remember to set the coefficients of the numerator equal to the term letters of the right side (if there is no number for the term, make sure to add in "0" in the front). Because of our answers being fractions, we cannot use the "rref" function on our calculator.

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

 
For part 1, make sure to pay special attention to multiplying out the numerator. Make sure to carefully distribute, this including negatives, otherwise one mistake could change your whole answer.

 

For part 2, the viewer should be careful when writing the equations. It is important to copy correctly and not forget any negative signs.

For part 2 (wasn't enough room), it is also crucial the viewer remembers to cancel out the x's.

For part 3, plug in the coefficients into the calculator. It is crucial you plug in the right numbers or else you will get the wrong answer. It is important to recheck what you plugged in.
                    
For part 4, follow the necessary steps to find the ordered triple. The viewer should be able to follow the steps as stated in the image. The fourth column provides the ordered triple, making them the numerators of the original equation found in part 1.

SV #5: Unit J Concepts 3-4 - Solving Three-Variable Systems

 The viewer must pay attention to interchanging (arranging) the system before using the boxes to find the "zero triangle" and the "stair-step one line", which would make the process of solving the matrix easier. They also need to pay close attention to multiplying a row by a constant and adding/subtracting it to another row correctly, otherwise it could mess up the whole matrix. The view must know when solving, row 3 goes with row 2, and row 2 goes with row 1.