Fibonacci Haiku: Ariana Grande

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Ariana Grande

I love tweeting

Ariana Grande followed me yesterday 

I was so happy when I saw it 

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SP #5: Unit J Concept 6- Partial Fractions Decompostion with repeated factors

In this problem i did an example of partial fraction decompostion with repeated factors. It is pretty much the same as SP #4 but this time it has repeated factors. After i found the systems i plug in into a matrices box. I used the rref feature in my calculator to find my answer. I checked it by plugging my answer back in to see if it came out the same. The trickest part of this concept is that you have to remember what to do when there is repeated factors. For repeated factos you MUST count up the powers and include the factors as many times as the exponent. Other than that this problem was very similar the concpet 5. You follow all the same stpes except we add that repeated factor step. Thank you for reading!

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

In this student problem, I had to make up my own example of a partial fraction decomposition with distinct factor. I first had to compose my problem I made. Then i had to decompose it but now with replacing the top with letters according to the amount of facotrs i have on the bottom. Then i had to get a least common denominator for the three fractions by multiplying each part by what is missing. After i grouped them together and set it equal to the numerator that we first started with. Lastly we solve the equations by using matrices and the rref feature in our calculator and plus it back in. The most trickiest part about these types of problems is having so many variables. You can get confused with all of them so keep count on how many you are suppose to have. Another thing that was tricky is knowing how to use matrices because all these problems are related. One thing i found interesting was the rref feature gives us the answer so we know our work is correct. Other than that it was really simple. Thank you for watching! *Sorry i forgot to set it equal to the numinator in the 2nd picture :(

SV #5: Unit J Concepts 3-4- Solving three-variable systems with Guass-Jordan elimination/ matrices/ row-echlon form/ back-subsitution

In this video I explain DP problem number 3. I explained how to solve a three-variable system with Guassian Elimination and how to check your answer with the rref feature in your calculator. The trickest part in these types of matrix problems is being able to know what row to use. To make my life easier I just use the row on top so I won't get confused. It is really hard when you start mixing up the rows because you will get confused. Another thing that is difficult about these types of problems is making sure you know how to use your matrix feature. This feature is really helpful when checking your answers so if you do not know about it, you should. Other than that matrices are pretty simple if you do Mrs. Kirch's 4 step way of doing. One more thing, ALWAYS ALWAYS ALWAYS show your work. You need to show all your work so if you mess up, you will know where to go back and change something. Thank you for watching.

WPP #6: Unit I Concepts 3-5- Finding compound interest, continuously compounding interest, and investment application problems.

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SV #4: Unit I Concept 2- Graphing logarithmic functions and identifying all parts

In this video, I explained a problem about graphing logarithmic functions. I had to find the x-intercepts, y-intercepts, asymptote, domain, range, 4 key points on the graph, and then the final graph. The hardest part of this problem will have to be finding the y-intercept. I would say this was the trickets part because you have to remember to use the change of base formula. If you do not use it, then there is no way you can find the y-intercept. Another part that was pretty tricky would have to be x-intercept. I would say this was tricky because you have to remember to expotentiate both sides when trying to get rid of the log. Other than that, it was pretty easy. Thank you for watching!

SP #3: Unit I Concept 1- Graphing exponetial functions and identifying x-intercept, y-intercept, asymptotes, domain and range

In this student problem I made my own example of a graphing exponential equation. The first step in these types of problems is finding your a, h, b, and k. 'a' tells you if the graph is above or below the asymptote by the sign. If it is postive then it is above and if it is negative then it is below. B tells you what side, right or left, the graph is. If the absolute value of b is less then one (fraction) then it goes on the right side. If the absolute value of b is greater than 1 then it is on the left side of the asymptote. You find h by setting the exponent equal to zero and this shifts the graph left and right but for this example the key points do the shift. 'k' tells you if the asymptote moves up or down. If it is positive then it moves up units but if it is negative it moves down. You find the key points by adding four numbers to the 3rd key point. You find the asymptote by just looking at k because y=k. You find the x-intercepts by plugging in zero for y and for the y-intercepts you plug in 0 for x. The domain for these probelms will always be (-inf, inf) because an exponential graph has an asymptote of y=k, leading to no restrictions to the domain. The range depends on the asymptote. Lastly for the graph, you just plot in the key points and the intercepts.

The trickets part of these types of problems is probably finding the x-intercept. It was the trickets part for me because you need to make sure you divide by ln correctly and do all your intermediate steps correctly as well. Another tricky part of this problem will have to be the graphing. You need to make sure you do not cross the asymptote, plot each point you find correctly, and go in the right direction.