WPP #10: Unit L Concepts 9-14: Proabablitiy Mixes

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WPP #9: Unit L Concepts 4-8: FCP, Combinations, and Permutations.

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SP#6: Unit K Concept 10: Infinite Geometric Series with Repeating Decimals

 

This problem is all about how to find the infinite geometric series of repeating decimals (those pesky decimals that never end). It is really quite simple and fun. It is easy breezy and not too difficult. You can do it! Do not fear the repeating decimals.
     There are a few things that you must pay attention to. It is That you do not worry about any numbers to the left of the decimal point until the very end. Secondly is that you need to make sure you include the right amount of zeros. Third is that you make sure that when dividing a fraction by a fraction you multiply the numerator and the denominator by the reciprocal of the denominator. The rest is fairly simple. Do not fear you can do this.

Fibonacci Beauty Ratio

My most beautiful friend was Sandibel at a 1.616cm (1.618 is the Golden Ratio). She was the closest one to the Golden Ratio. Everyone else was not that far off though. The Golden Ratio is used to determine how beautiful you are. This could have occurred because of many things. She might really be my most beautiful friend or it could have been helped a little by the shoes she was wearing or quick measurements by me. Many things could have gone wrong, but according to what was measured in class Sandibel is my most beautiful friend, but that does not mean that everyone else is ugly. The other measurements simply did not measure up to Fibonacci. They were off by parts of a centimeter; they were all extremely close.

I do not believe that this is a valid measurement. Many things can go wrong when you are measuring someone. The measurements could be imprecise or changed due to what you are wearing. Different people measure differently. I simply cannot trust this ratio. I do not believe that I measure the best or the most precise. The Golden Ratio may or may not be true, but in this test run I do not believe that it is completely accurate or valid (sorry you guys). It is very interesting though.

Vanessa	Foot to Naval: 97 cm	Naval to Top Head: 68 cm	Ratio: 97cm/68cm= 1.426 cm	(1.426cm+ 2.15cm+ 1.178cm)/3=   1.585 cm
	Navel to Chin: 43 cm	Chin to Top Head: 20 cm	Ratio: 43cm/20cm= 2.15 cm
	Knee to Naval: 53 cm	Foot to Knee: 45 cm	Ratio: 53cm/45cm= 1.178 cm

Ana	Foot to Naval: 106 cm	Naval to Top Head: 64 cm	Ratio: 106cm/64cm= 1.656 cm	(1.656cm+ 2.095cm+ 1.057cm)/3= 1.596 cm
	Navel to Chin: 44 cm	Chin to Top Head: 21 cm	Ratio: 44cm/21cm= 2.095 cm
	Knee to Naval: 56 cm	Foot to Knee:53 cm	Ratio: 56cm/53cm= 1.057 cm

 

Gisella	Foot to Naval: 103 cm	Naval to Top Head: 62 cm	Ratio: 103cm/62cm= 1.661 cm	(1.661cm+ 2.25cm+ 1.14cm)/3= 1.684 cm
	Navel to Chin: 45 cm	Chin to Top Head: 20 cm	Ratio: 45cm/20cm= 2.25 cm
	Knee to Naval: 57 cm	Foot to Knee: 50 cm	Ratio: 57cm/50cm= 1.14 cm

 

Jorge	Foot to Naval: 112 cm	Naval to Top Head: 73 cm	Ratio: 112cm/73cm= 1.534 cm	(1.534cm+ 2.273cm+ 1.16cm)/3= 1.656 cm
	Navel to Chin: 50 cm	Chin to Top Head: 22 cm	Ratio: 50cm/22cm= 2.273 cm
	Knee to Naval: 58 cm	Foot to Knee: 50 cm	Ratio: 58cm/50cm= 1.16 cm

 

Sandibel	Foot to Naval: 89 cm	Naval to Top Head: 60 cm	Ratio: 89cm/60cm= 1.483 cm	(1.483 cm+ 2.25cm+ 1.116cm)/3= 1.616 cm
	Navel to Chin: 45 cm	Chin to Top Head: 20 cm	Ratio: 45cm/20cm= 2.25 cm
	Knee to Naval: 48 cm	Foot to Knee: 43 cm	Ratio: 48cm/43cm= 1.116 cm

Fibonacci Haiku: The Mexican Potato

"The Mexican Potato"

 

Vanessa

 

Lame

 

My Sister

 

Tad Bit Crazy

 

A Lame Yet Cute Potato

 

She Is My Mexican Who Loves Wearing Sombreros

 

 

 



http://cookiedudes.files.wordpress.com/2013/05/15122101-illustration-of-a-potato-mascot-wearing-a-mexican-hat.jpg



 

 

 

SP#5: Unit J Concept 6: Partial Decomposition (repetitive)

This problem is all about repetitive partial decomposition. That means that in the denominator there is polynomial that is to the power greater than one. That means that you have to count up that many times and have that many of the polynomials in your break down. It involves a lot of steps and patience.
Be careful for this problem has a lot of twists and turns. There are a lot of steps that involve multiplying and dividing so that means that you cannot forget any of the negatives or positive that come from that. Make sure to combine right and count up properly. Do not miss any steps at all. Be careful of what is going on and follow through completely. Be sure you back substitute and eliminate properly. Good luck.

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

This is all about how you compose and decompose a fraction when the terms are all individual and different, when there are no repetitions. It is something that you will need to know when you take calculus next year (the fun stuff). It is not too hard to understand, just be careful.

In this problem type there are a lot of areas where you can make a mistake so keep your eyes peeled. The first is make sure you do not drop or add any negatives. The second is you have to be careful when you are distributing your numbers and foiling that you make no mistakes. Decomposing can get tricky so make sure to take your time so that you do not mess anything up. Make sure you combine the right terms at the right times and type the coefficients into your calculator correctly. Have fun and be safe.

 

 

SV#5: Unit J Concepts 3-4: Matrices

This video will be going over one of the Dr. Prescription problems in the SSS Packet for these two concepts. It is going to be either consistent independent, inconsistent, or consistent dependent. It is simple to do, just follow the steps that you know and everything will be fine and dandy. Get ready for one great ride.

While watching this video and working it out, make sure to keep an eye out for any of the clues to lead you to what the answer to this matrix will be. If it is a consistent independent then it will have all three rows follow row echelon form. If it is inconsistent then there will be two rows where the variable will have two answers or there will be three zeros for the terms and an answer after which creates a false statement. Then if it pure zeros across the board then it is going to be a consistent dependent. This means that you will have to plug in an arbitrary value and solve. Thank you for watching and be careful.

WPP #6: Unit I Cocepts 3-5- Compounding and applications.

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SV#4: Unit I Concept 2: Logarthmic equations

        This video is all about how to solve for the logarithmic equation. It is a step by step walk through of the problem. It is not the best video I know, however it does get the job done. It is useful and helps you get through the problem. There are pictures below for clarification if needed.
        There are some tricks to the problem. Do not let the h confuse you. Remember that you have to switch the sign that it gives you when finding your asymptote. Then when solving for your x-intercept do not forget to put the proper parenthesis so that you do not get the wrong answer. Then for your y-intercept do not forget that when exponentiating it is putting the base as the new bas on both sides. Use caution when graphing and enjoy. Thank you for watching. (Sorry the video is labeled wrong...)

clarification

 

SP#3: Unit I Concept 1: Finding parts and graphing exponential equations.

Steps!
1) Find your a, b, h, and k (remember that your a is first, then b, then h is either added to or subtracted from x, and k is the constant that is added or subtracted to the equation).
2) Write your asymptote. Remember the asymptote is y=k (a horizontal asymptote).
3) Then you find your x-intercept by plugging 0 in for y and solving like a regular equation for x (reminder: you will not always have an x-intercept).
4) Find your y-intercept by plugging 0 in for x and solve the equation.
6) Write your domain.
7) Write your range down ( depends on location of graph).
8) Use h as your third key point and choose two below that and one above it then use your table application to find the other point.
9) Graph it by first putting your asymptote as a dotted line, then your intercepts, and finally your key points. Then connect them appropriately and do not forget your arrows.

 

   This problem is all the steps on how to solve for exponential equations. It is an example of one without an x-intercept and it shows each step for ease. It is a walk through on how to get these types of problems done. It is all about the exponential equations and involving other ideas from other concepts. Enjoy.

 

     There are a few things that you need to pay close attention to. One is remember that the h is the opposite of what is seen in the equation. Also with exponential equations your domain will always be negative infinity to infinity. The range is different though. Remember if it is below the graph then it will be negative infinity to the asymptote and if it is above the graph then it will be the asymptote to infinity. It is easy to mess up on the little intermediate steps of solving for the intercepts so be careful and take your time. Also it is very easy to misinterpret things and end up with the wrong answer so take your time and check using the table and graph feature on your calculator. Remember there is no x-intercept because the asymptote is -2 and since the graph is below the asymptote (a is negative) then it will never cross the x-axis. Also mathematically if you wanted to verify the answer is an unreal answer meaning there is no x-intercept. Enjoy!      

WPP#3: Unit E Concept 2 - Path of Football (or other object)

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SV#3: Unit H Concept 7: Log Approximations

The video is all about log approximations. It is a treasure hunt that is full of joy. You are expanding a problem from one log to many. It is really quite simple. It is a lot of fun and I hope you enjoy it.
 You must be careful though. This is not as easy as it seems. Make sure that your signs match up. If you are using a product use an addition sign to connect the logs. If it is a quotient then make sure to connect the logs using a subtraction sign. Those are your lines on the map that guide you to the x, the final approximation. Be careful and have fun.
Thank you for watching and I am sorry for the few mistakes and stuffy speech, I am at tad bit sick. Flu season, but really enjoy lovelies.

SV#2: Unit G Concepts 1-7 - Finding all parts and graphing a rational function

      This video is all about the different types of asymptotes. It is an explanation of how to find the horizontal or slant asymptote, the vertical asymptote(s), and the possible holes. Then from there you can find your domain(D.I.V.A.H.) and your x and y intercepts (set the opposites to zero). After that you can create your graph. Remember to find your other points in each of the sections that are cut off by the asymptotes. There is a ton of things to do, but it really is not that hard once you get the hang of it.
     Hey dears, you do have to be careful though. When finding the x-intercept remember you do not use the holes; remember to use your simplified equation. Also just be careful with every step that you do because it is very easy to make a small mistake any where. Remember all the chants because it will help you get through it all. Just take your time and use caution when solving these problems.
     Thank you all for watching my video. I hope you enjoyed and I am sorry for any stutters and blurs. Below is a picture if you need a reference.

These are the asymptotes and the hole.


This is the domain, intercepts, and the graph.

SV#1: Unit F Concept 10 - Finding all real and imaginary zeroes of a polynomial

This is a video that depicts a problem that is not factorable like other concepts. This is a problem that involves imaginary along with real zeros. It takes everything that has been learned in the previous concepts and sandwiches it into one nice video. It explains everything step by step and helps you understand what is happening. It is a video about a problem with some imaginary friends that need to be found.

You have to pay attention to every single step that you are taking. If you mess up once then you are going to mess up the whole problem. Each step is a guideline for the next one. Be careful not to mix up the degrees or any of the positives and negatives. Do not forget to switch the signs when going from zeros to factors. It is very important that you take your time and really do each step with care and patience. It is a long amount of time for a single problem, but in the end it is really worth it. Be careful and enjoy.

SP#2: Unit E Concept 7 - Graphing a polynomial and identifying all key parts

Step by step: 1) Factor out the x.
2) Factor the rest of the equation.
3) List the end behavior (learned in concept 4)
4) List the x-intercepts (the zeroes) with their multiplicities (concept 6).
5) Find the y-intercept.
6) If possible find the extremas (the min and max) and then list in intervals of increase and decrease.
7) Plot all available points onto the graph, indicate your end behavior and then draw the graph following all graphing rules.

 

 

       This is an example of a factorable polynomial being graphed with all the appropriate parts. There are five steps that will always be there. Those are factoring the equation, end behavior, x-intercepts, y-intercept, and plotting/graphing them all. The parts that will sometimes be there are those of the extremas and the intervals of increase and decrease. This problem is to show you what these kind of problems look like and also what they consist of. They are multistep equations that involve your full attention. They are exciting problems that really review everything that we have been learning and introducing us to future concepts. They are great problems.

     This problem is not easy peasy though. You cannot breeze through these problems. You really have to pay attention to the end behaviors and the zeroes. The end behavior is based off of the highest degree and the leading coefficient in the standard equation. This one happens to be an even (the degree) positive (the leading coefficient). That means it will go up on both the left and right of the graph. Other equations will see different end behaviors though. Make sure your end behaviors are going in the correct direction and do not make up intercepts to keep in line with your end behaviors. The second is the zeroes. You have to make sure to put their multiplicities. That tells you how they will appear on the graph. If it is a single multiplicity then it will go straight through the x-axis, if it is a multiplicity of two then it will bounce on the x-axis, and if it is a multiplicity of three then it curves through the x-axis. These intercepts are the only times the graph will cross the x-axis. It will never go past a solid line with no intercept. Those are really the only tricky parts.

WPP#4: Unit E Concept 3 - Maximizing Area

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SP#1: Unit E Concept 1 - Graphing a quadratic and identifying all key parts

This is the whole problem. The work, the graph and the parent function along with the answers to create the graph.

This is the picture to show the steps and the graph to show you what the function becomes. You begin with your standard function. Then you add two to both sides of the equation. After that you take out the leading coefficient which is in this case -4. Make sure you have that on both sides of your equation to keep in line with the math rule, whatever you do to one side you must do to the other. Then you take your b. -3, and divide it by 2, giving you -3/2. Then you square your answer giving you 9/4. Add 9/4 to both sides within your parenthesis. Now you should have -4(x^2-3x+9/4)=2-4(9/4). After that you reduce your quadratic on the left and solve on the right. You should be left with the answer -4(x-3/2)^2=-7. Once you have that, you add 7 to both sides and get your parent function equation (also known as graphing equation) which is f(x)=-4(x-3/2)^2+7. From here you get your vertex (h,k) and that is (3/2,7) reduced is (1.5,7). Then you get your axis from that, which is the x-value so your x-intercept is 1.5. After that you go back to the equation right before the addition of the seven and find your x-intercepts by solving for x. You divide both sides by -4 then take the square root of both sides and finally add 3/2 to both sides. That makes your x-intercepts, with the 3/2 reduced, (1.5+√7/2,0) and (1.5-√7/2,0). To approximate that plug them both into your calculator and round to the nearest hundredths/thousandths place. Your x-intercepts become (2.82,0) and (.177,0). Then you find your y-intercept and to do that you plug zero into the x in the standard form and you get your answer of (0,-2). [The blue highlights are the parent function, the orange is your non-reduced and reduced x-intercepts, green is your vertex, pink dashes are your axis, and the purple is your y-intercept.] Then you plot each point, draw your dashed axis and connect the dots. Do not forget to reflect your y-intercept across the axis.

This is just the answers put into the key and color coded onto the graph for a nice visual. Your vertex in this equation is a maximum due to the negative a.

WPP#2: Unit A Concept 7 - Profit, Revenue, Cost

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WPP#1: Unit A Concept 6 - Linear Models

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