RWA#1: Unit M Concept 4-6 Conic Sections in real life

Hyperbola 

Definition: a set of all point such that the difference in the distance from two point is constant.  

Algebraically: The equation is (x-h)^2 over a^2 minus (y-k)^2 over b^2 equals to 1.You can tell if the hyperbola is open left/right if x comes first. It will open up/down if y comes first in the equation. Also, the needs to be in standard form to make it easier to classify the hyperbola. The equation needs to be subtracted for it to be a hyperbola. Otherwise, it will be an ellipse.

Graphically: By looking at the hyperbola the x and the y affects how the graph will shape. It will shape the graph left/right, up/down. There will be a focus on one side and the vertex on the other side of the graph. The "C" will go through the focus while the transverse axis connect the two vertices together.The "a" and the "b" will affect where the two vertices and co vertices will be placed/ how much it will move on the graph.

Key: To start the equation needs to be in standard from which is (x-h)^2 over a^2 minus (y-k)^2 over b^2 equals to 1. The center could be find by taking the opposite of h and k from the standard form. From there, you can determine if it is up/down if y comes first and left/right if x comes first. To find "a" you take the square root of a^2. Similarly, you can find "b" by taking the square roots of b^2.  Plot the center and count number of "a" from the center and "b" from the center to find the vertices and co vertices. The numbers that dominates in the ordered pairs will be the transverse axis and conjugate axis.You can use a^2+b^2=C^2 to find c. As for the eccentricity, you take C divided by A to get the answer. The two foci will be (x,y+-eccentricity). "The 'foci' of an hyperbola are 'inside of each branch and each focuses is located some fixed distance c from the center."  (credit) Finally, to find the asymptote, you find the m slope by taking a/b or b/a depending on the direction of the branches. After finding the slope, plug in to y=mx+b .

Real World Application:

Hyperbola can be applied to the real world. For example, it could be the shape of your lamp, where it will cast a hyperbolic shape on your wall. It can also be found in many things such as Dulles Airports, sonic boom, cooling tower of nuclear reactors, stone in lake, etc. 

Reference:
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WPP#10: Unit L Concepts 9-14 - Bsic Probabilities of Independent and or events

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WPP#9: Unit L Concept 4-8 - CAlculating Possibilities with Combinations and Permutations

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Unit K Concept 10: Writing repeating decimal as a rational

In this concept, student will learn about rational number. Students will be able to write the repeating decimal as a rational number without using a calculator. To solve for it, you need to use the sum of infinite geometric series. Students need to find the firs term and the common ratio. To get the common ratio. To find the common ratio, you take the number divided by the preceding number. Finally you plug into the formula and evaluate.

One thing that students need to be careful about it listing out the number. It will give you a completely different number if it is not listed right. Also students should be careful about subtracting the whole number by the fraction.

Fibonacci Haiku: Winter is Coming

Cold
Cold
Rainy day
Water drip drop
Wrap in my comfy blanket
Hot chocolate melt and infused in my mouth

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SP #4: Unit J Concept 4: Partial Function Decomposition

In this problems, student will learn to use their algebra skills to solve this problem. Students will find the common denominator and multiply both the numerator and denominator by what it is missing and solve for it by decomposing it. 

What students need to be careful about when solving for this is foiling all the equations. One mistake will need to a different answer to the problem. Also students should use their calculator to check their work at the end.

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

In this concept, students will be separating the fractions, in other word, decompose the fraction in order to solve for the variable. This concept is similar to concept 4, in which students need to find the common denominator and multiply the top and bottom by what it is missing and then solve for it by combining like terms and use elimination. However, in this concept, there is a repeated factors.

Students need to be carefu about the repeated factors. The repeated factors need to be listed up to a power. Example: the repeated factors is (x+3)^3 is written as (x+3)(x+3)(x+3)^3. Also students needs to be careful when foiling because of the negative signs. It can change your whole answer.