WPP # 10: Unit L Concept 9-14 - Probability

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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: Repeating decimal as a rational number

First you should write the decimals in a pattern, like the one that I did below the original problem. Ignore the 2 until the end. We get our "a" sub "1" by the first decimal which is 96/100, and our ratio is 1/100. Using summation notation and the geometric infinite formula we can start plugging in. The summation notation will also use the geometric sequence formula and you already have the ratio and the"a" sub "1". Next will be the infinite geometric series and just plug in (96/100) / 1-(1/100). You subtract the 1 to 1/100 and get 99/100. With (96/100) / (99/100), use the reciprocal of 99/100 and multiply it to the numerator and denominator. Now you should have 96/99, and this is were you include the 2 from the beginning. Add 2 to 96/99 and your answer will be 294/99 but reduced will be 98/33.

  Well for this problem your need to pay attention to the reciprocal part. It can be confusing and it's easy to make a mistake here. Also the part when you add 2 to 96/99 because you have to reduce and it can get tricky if you do it wrong.

Fibonacci Haiku: Piano

http://www.manuel-music.com/wp-content/uploads/2013/05/Piano-keys.jpg

           

"Piano"

Soft

Loud

Tonic

Piano

Terminology

Wonderful Instrument It Is !

SP# 5: Unit J Concept 6: Partial Fraction Decomposition with repeated factors

First separate it into three separate factors and then find the common denominator. Multiply the common denominator to the top and bottom. Combine like terms and set it as a system. Then with a calculator plug it the same way as if you're plugging in a matrix. The answer from that should be your equation.







     The trickiest part of this problem is probably when you multiply the common denominator to the top and bottom because C only needs one and it's (x-1). Also when you combine like terms, it can be easy to make a silly mistake there.

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

 Pic 1: I have this equation 4/x+3 + 9/x+2 + 3/x-4 and the first thing you want to do is find the common denominator. When you find it multiply it to the top and bottom. Then you add them up together and it's all over  (x+3) (x+2) ( x-4). Next you combine like terms for the top. And at the end you 16x^2 - 2x - 122.

 Pic 2: First separate the factors and put the letters A, B, and C. Then we get the least common denominator for the three fractions by multiplying each part by what missing. Next you group all the like terms and set the coefficients of the numerator equal to the like term letters on the right side. And on the left side the numerator of the composed equation.

 Pic 3: You plug this in the calculator by pressing 2nd matrix and go to "EDIT" and plug this in. Then you 2nd quit and go back to 2nd matrix and you go to "MATH" and go down to "rref" and press enter. Go back to 2nd matrix and press enter to "[A]". Next you just press enter.

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Pic 4: You will get 4, 9, and 3 and those are the same number that are in the first picture.












One thing you want to look out for in my problem is to check each step carefully. If one number is added or subtracted wrong is can affect the whole thing.

SV#5: Unit J Concept 3-4: Solving Three-Variable Systems With Gaussian Elimination

One thing that you should look for is knowing which Rows to use when your solving for a 0. For the first 0 you can use Row 1 or 2, and when it the second 0 you must use Row 1. On the last zero you also must use Row 2.

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

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SV#4: Unit I Concept2: Graphing Logarithmic Functions

One thing your going to want to look out for in my equation and probably most equation like this, is that when you plug it in the equation, use the change of base formula. It will make things easier and get the most accuate graph. If you change to the table you can also find key points.

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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SP#3: Unit I Concept 1: Graphing Exponential Functions

Equation: You can see that -4 is A, 2 is B, 3 is H and it comes from (x-3) which is the exponent of 2, and -1 for K.
Key Points: I've used the -2, 1, 2, and 3 for the x-intercepts. To get the y-intercept you need to plug in equation I've given you into your calculator. But you'll need to use the change of base formula to get the right points.
Asymptote: To get the asymptote is pretty simple, it's just the number in K's place. In mine it will be -1.
X-intercept: To find X you will need to replace Y with 0 and then add 1 to both sides. Next divide -4 to both side and you should have -1/4 = 2^(x-3). Last you'll put LN to both sides to get ride of the 2. But in this case there is no x-intercept because LN can not be a negative number.
Y-intercept: First you'll have to replace X with 0 and the exponent for 2 will be -3. 2 with it's new exponent will now be 1/8. If you multiply the -4 to 1/8 you'll get -1/2. Add -1 to -1/2 and your answer should be -3/2. And your y-intercept should be (0,-3/20.
Domain and Range: The domain will be infinite for the x and y because it goes left and right. The range will be negative infinity for the x and -1 in the y because of the asymptote on -1.

In my problem the parts you need to pay special attention to are the x and y-intercepts. X because of the -4 and the fact that we can't have negative LOGs. Also Y due to the fact that there are fractions and it'll get with that.

SV#3: Unit H Concept 7: Finding Logs Given Approximations

     Well one thing you should look out for in this problem is knowing that there is a free clue. Some problem problems might not even use them but mine does. Also when it's already in exponential form, the LOGs that have exponents, their exponents should be moved to the front of the LOG so it can be the leading coefficient.

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

     This problem is about finding three different asymptotes; horizontal, slant, and vertical.To have a horizontal there can't be a slant, but in my problem there is a slant but no horizontal. It does have a vertical when we foil out the numerator and the denominator and (x+7) cancels because it's found in both. So this problem also has a holes. But once we have all of those we find the domain, x-intercepts, and y-intercept. Then whats left is the graphing.
     In my problem one thing you'll have to pay close attention to the hole points. They can be tricky because you may never know where they go. On my it's pretty hard to tell where the hole goes. 

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

    This problem is from concept 10, and in this problem we are basically find it's zeroes. But in order to find them we must find the p's and q's and the possible positive and negative real zeroes. Then we use synthetic and probably the quadratic formula. Well to really sum up, if you know how to do concept 6 then your good.
    The part I suggest you should pay attention to is when your finding the two zero heroes. 1 and -1 will not always work so your going to use the rest of the p's and q's and it would get tricky. I suggest you use the fractions first when whole numbers, it would be a bit easier.

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

Factoring: First factor the equation fully. Then we can take out x^2 from the original equation. We an distribute x^2+3x+2 even more to (x+2) (x+1).

End Behavior: By looking at the leading coefficient and the exponent,we know that it is an even positive.

X-intercept: With the variables, we know that there should be 4 zero multiplicities because the leading exponent is 4. Since 0 has the multiplicity of 2 then the line bounces off of its point. -2 and -1 have the multiplicity of 1 then the line goes threw them.
Y-intercepts: We replace the x's with 0 and multiply it with it's coefficient. Since it equals 0, then the y-intercept it 0.

This problem is about finding multiplicities and graphing it's points. While we do that we are also identifying all of it's parts as we go along. Then we graph the polynomial according to it's points.

To understand this concept, the viewer must first look at the leading coefficient and the exponent to see how many zero multiplicities there are and how the graph is suppose to look like. When they are done factoring the polynomial, they must see if the number of zero multiplicities are the same as the leading exponent.

WPP #4: Unit E Concept 3 - Maximizing Area

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WPP#3: Unit E Concept 2 - Path of Football

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

SP# 1: Unit E Concept 1: Identifying x and y intercept, vertex, axis of quad. and graphing them.

• Subtract 9 to both sides 
• factor the left side and find the missing number which is 4
• then divide 3 to both sides
• square root both sides
• then subtract 2 to both sides

   In this problem we identify the x-intercept, y-intercept, vertex, axis of quadratics, and we graph them. We first need to find the parent function before we do anything else like graphing.
   The part that you should pay more attention to is when your solving for the x-intercept. Mine came out as whole numbers and that's easy because it doesn't need any more points. If is was a negative when it's imaginary, if it's not and it has a square root then it came be solved.