CONICS

CONICS(part1)
 hi everyone, this is Rajvir. I will be going over the basic of Conics we had learned in class.


In unit 6, the conic sections there are 4 main conic sections. 
Circle
Parabola
Ellipse
Hyperbola


First class, we learned about Circles on a coordinate plane. A circle is the set of all points in a plane, each of which is at a fixed distance from a given point. 


Area of a Circle: πr^2


Circumference of a Circle: 2πr


Standard form:

 Read H, K values as opposite. 


Centre: (0, 0)
Radius= √r^2 =r















Centre: (h,k)
Radius: √r^2=r


General form for a circle 




Example 1 

since this conics is a circle and it is in the standard form the center will be a (0,0) 

In this case we are given the h, k values for the center, which is read as opposite. 

Example 2




First : We recognize that this a circle. 
Second : complete the square

Third: Graph 

PARABOLAS 


Next we learned about the Parabolas on a Coordinate Plane.


There are 3 different shapes 

There 2 different types of parabolas


Vertical

Horizontal 



















EXAMPLE 1 

EXAMPLE 2

Hope this was helpful!!!!

 

By-Rajvir

Conditional Probability

Hey whats up guys, it's Darian again and i'm here to tell you about conditional probability.

When the problem has two conditions you use the equation.

Now that that's outta the way, time to get into some questions

Example 1

Example 2

Example 3

Closer look at part b

 Thats it for today, I know it wasnt super in depth, but it shows the basics of what you will need to know to understand the concept of conditional probability.

 

 KITTENS, THEIR SO FLUFFY!



Denny here, just a quick recap of what we learned yesterday.

Hey guys its Darian, I know its been a while but I finally did it :P.

Today we learned about Circular Permutations and as you can guess by the name, They involve Circles, Thats it thats the blog, circles are awesome.

Just kidding, now really a circular permutation does not have a first or last. The position in the circle are relative to the other objects of this circle. Therefore, all of the permutations that we deal with will be placed around the placement of the first thing placed. (Too many placements).

The number of permutations of n objects in a circle is (n-1)! you minus one because someone always has to be seated first so the following arrangements of people around a circle are more so based apon the people who are not seated first and the places they will sit.

Ex.1 We have a table that can sit 12 people and in turn there are 12 people who are going to sit down, they can sit wherever they feel like, How many ways can these 12 people sit.

Now a question like this is probably one of the easiest questions we will have, all you do is use the formula.

                           number of permutations=(n-1)!
                           number of permutations=(12-1)!=11!
                           number of permutations= 39,916,800


Now circular permutations are not always so simple, We can have restrictions on our circular permutations questions such as, two people have to sit together, two people must not sit together,the people at the table must alternate,etc.


Ex.2  How many ways can 4 friends (Tony,Steve,Bruce,Thor) be seated together around a circular table, if Jackie refuses to sit near any of them and there are 4 people already at the table and the table sits 12.

Well first you would draw a diagram

                        
Then we would use the equation nPr to calculate the total amount of placements for Jackie

nPr       n=5        r=1

             5P1= 5

Now to calculate the the amount of permutations for the 4 other people and because there is 6 places left to sit and they can sit in any of them, calculating the amount of permutations is easy all you do is use the dashed method.



        And now you count the 4 friends as 4! and put and equation together to find the total number of permutations


Which would be :    4!x5x360= 43 200


You may have questions in which you have to make multiple dashed line methods and add them together this is one of them.

Ex.3

How many 8 digit numbers greater than 56,000,000 can be formed using the numbers 4,4,4,5,5,6,7,and 8

To solve this equation you must make 2 dashed line methods and add their answers.

and

you then add the two numbers you get from these methods which are 360 and 1260 and add them to get your final answer which is 1620.


And finally a common exam question is a question about keys and how many different permutations can be made with the keys, this may seem straight forward but there is a trick because the keys are double sides and they are the same on both sides you must divide the answer you get using the circular permutations equation by 2!.

Ex.4
How many different key rings can be made of 12 different color coded keys.

You start out using the Circular Permutations equation which is pretty straight forward

             (n-1)=?!
             (12-1)=11!
             11!=39,916,800

            Now Divide this answer by 2! and you get your final answer

            39,916,800 ÷ 2! = 19,958,400

Thats it, Thanks for reading, I hope you enjoyed this scribe and learned something from it, If you didnt follow everything I scribed, uhmmmm Ask Mr.P he can probably tell you :P.

Thanks for reading and now heres a squirrel.

Solving Exponential Equations by AC

Solving Exponential Equations Video

Monday, April 10, 2012

 Hey guys, it's Luke. 

Today we did some Logarithmic Theorems

and also familiarize these two:
-Pattern: logaa^x = x
-Alternate Pattern: a^loga^x = x

Also we started learning about Laws Of Logarithms
This is done by expanding
Division Law: Subtract
Multiplication: Addition
Exponent Law: Exponent become coefficient "logaM^n = NlogaM"


We also did Logarithmic Expansion Steps, where we follow the steps carefully and do it step by step. Or else you're back to square one or you get the wrong answer..

1. Roots become fractional exponents.
2. Division Law- Division becomes subtraction.
3. Multiplication Law -Multiplication becomes addition.
4. Exponent Law - Exponents become coefficients (Move to the front)

Like for this example: 



Yeap, It's that equation is pretty long and also confusing.. Butc ouple of points to remember.

• Always use brackets (or else you are likely to get messed up)
• On the Multiplication Law always identify which one is multiplied for example: "log5z^3 = 3log5 + 3logz" No.. the correct answer is "log5 + 3logz" since "log 5 . z^3"
• Remember Roots become fractional exponents.

Familiarize this then you're good to go (: or you can just stare at it and cry..
.. Anyways have a good night~!

Denny Stepic here! Just going to recap what we learned last class + one more thing.

Solving Exponential Equations

1. Make the bases on each side equal
2. Cancel same bases
3. Solve the remaining exponent equations.

Ex: 2^x = 32
   
      2^x =  2⁵
   
       x  = 5

Exponent Rules:

Logarithmic Functions 

Find the inverse of  f(x) = a^x using this four step method:

1. Replace f(x) with y
2. Reverse the roles of x and y
3. Solve for y in terms of x
4. Replace y with  f ^-1(x)

Ex: Find the inverse of  y = 3x + 2

x = 3y + 2

x - 2 = 3y

y = x - 2 / 3

 f ^-1(x) = x - 2 / 3
_________________________________________________________________________________

_{Note: If no number is shown beside log we assume it is 10.}

This is called the "seven" rule.

Ex:  log₁₀(1000) = 3
10^3 = 1000 

   **********************  UNRELATED MATH JOKE BELOW **********************