Fibonacci Haiku: Stars

Stars

Dream

All alone

Yet inside dreams

The brightness of the stars
Invites me and you to dance with them

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Movie: 5 Centimeters Per Second

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

        First of all, we must remember that what distinguishes these types of problems from other ones is that they have repeated factors. Basically, all you do is count up, which means, as you separate the initial fraction, you repeat the factors, but with their exponent increasing incrementally by 1. It sounds confusing, but if you had saw an example, you'd get it right away. As always, with these types of lengthy problems, you must remember to calculate carefully, as one mistake could ruin you. Oh, and you can't use calculators for many of these problems, since most of the answers come out as decimals, which we are not permitted to utilize, unless they are definite (don't go on forever). Fin.

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

        There are several crucial things that one must remember in order to fully get through this struggle and emerge victorious. First of all, one must pay close attention to the calculations that they do in their head, because it's really easy to mess up. And if you mess up once during the problem, you'll have to go back and redo the entire thing from that point onward. Second of all, you have to remember to transfer the correct sign (+/-), and also utilize them correctly, for the next step. One mistake could mess up your entire problem. Lastly, if you're not utilizing a calculator to derive RREF (Reduced Row Echelon Form), you have to remember to utilize your elementary row operations without mistake, for one mistake could, again, cost you the entire answer, ergo, a whole lot of time. That is all.

SV #5: Unit J Concept 3 - Gaussian Elimination

        The first and foremost important thing to remember to do, is distinguish which rows and numbers you need to work on, and which rows you may use in order to eliminate the numbers. It's really the entire backbone of this concept. Another important thing to remember to do is to calculate correctly, for if you mess up even once, you will proceed to arrive at a wrong answer. Lastly, you should check your answers with a calculator, if an answer sheet is not readily available. That is all.

WPP #6: Unit I Concepts 3-5 - Compound Interest

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SV #4: Unit I Concept 2 - Graphing Logarithmic Equations

        Some important things that need to be noted whilst completing problems of this particular field of study, are: remembering how these types of problems share the same structure, remembering how you find the asymptotes for logarithmic equations, and remembering the domain/range of logarithmic equations. First of all, the parent type function for these problems  is log base b of (x minus h) plus k. Second of all, the asymptotes for logarithmic equations will always be x = h, and you can remember this specific rule with the phrase "The Log's Xylophone was Happy and Rich", where you derive x = h from "Xylophone was Happy". Lastly, the domain of logarithmic equations will always be restricted (unless there's no h value), and their ranges will never be restricted. This can also be remembered by the previously noted phrase, and is extracted from "Rich", in which the r proclaims that the range is to never be restricted. The end.

SP #3: Unit I Concept 1 - Graphing Exponential Equations

        Alright, so some important things to remember when finding the components of exponential equations, and afterwards, graphing it, include: making sure that you have extracted the a, b, h, and k values correctly, making sure that you've got the right type of asymptote for the such equations, and remembering how to tell whether or not the equation will have an x-intercept or not. Basically, you just adhere to the parent graph closely (adapted for the exponential equations) to make sense of said values. The exponential yak died will tell you that exponential equations have the asymptotes of y = k. It will also tell you that the domain is never restricted, which is why y-intercepts will always be present in these equations. Lastly, you can easily tell whether or not an equation has an x-intercept by seeing whether or not the equation crosses the x-axis, which would only occur when the horizontal asymptote is not blocking the way to the axis.