so in class today we went over some of last nights homework, and some of the homework on periodic functions a couple days before we learned sequences. the unit periodic functions, well lets say I'm the brightest in that unit. i still don't get the whole concept. so I'm going to try and explain how to answer one of the questions we did for homework.

EXAMPLE

Jud was working with a sinusoidal data, but lost all of it except for two points. A maximum point was (3, 13) and a minimum point next to it was (7, 1). Write a sinusoidal equation that matches Jud's data.

This is the sine formula

f(x) = AsinB( x - C ) + D

What does this formula mean?

"check Lamael's most recent post to find out what it means"

To help you write a sinusoidal equation, the best way is to draw what information that has been given to you.

In this question the maximum point is (3,13) and the minimum is (7,1)

what does this mean? remember in grade like 9, when the the first number would tell us the point on the X- axis and the second would be on the Y -axis? well this is exactly that.

this is how your drawing should look like.

After your done that, you figure out what the sinusoidal axis is. Sinusoidal axis equals the average and that average equals out to be your D in the sine formula.

the sinusoidal axis usually lays on the y -axis creating a straight line in between the minimum and maximum point.

In this case the minimum point is 1 and the maximum is 13. Add those two numbers up and divide by 2 and you get the sinusoidal axis which is equal to 7.

So now we got the sinusoidal axis. having that we can figure out the amplitude or A in the sine formula. The amplitude is the distance from sinusoidal axis to a maximum or minimum point.

In this case, we would subtract our sinusoidal axis from a minimum or maximum point. Here, our sinusoidal axis is 7 so we subtract that from our maximum which is 13 and get a difference of 6 which is equal to our A in our sine formula.

This is how our graph looks like now.

Why does the graph look like this your wondering? remember were dealing with periodic things, so it always goes up and down at a steady pace. like a bug on a wheel.

where did the 11 come from? well on the x - axis the points are going up by 4 so you add another 4 to 7 and you get 11.

the two variables were missing now is B and C.

Lets find B. B in our sine formula is NOT the period it determines the period according to this formula.

PERIOD = 2Pi/B OR B = 2Pi/PERIOD

The period is the difference between two maximum points. In this graph the maximum points are always at 13. At point 3 on the X - Axis the graph is at its maximum point and as you keep going down the line on the X - axis to find the next maximum point you find it to be 11. The difference between 3 and 11 is 8. So our period is 8. we then plug our period into our period formula to figure out what the variable B is.

B = 2Pi/PERIOD

Then.. B= 2Pi/8

Reduced.. B = Pi/4

The last variable were missing is C. C is called the phase shift, or horizontal shift on the graph. in this case, there was no horizontal shift so we leave C as 1.

So our sinusoidal equation looks like this..

f(x) = AsinB( x - C ) + D

f(x) = 6sin(Pi/4(x-1)) + 7

Hopefully my scribe has helped some people. Doing this scribe has helped me understand the unit a little better.

PERIODIC FUNCTIONS TEST TMRW! STUDY STUDY STUDY!!!

next scribe is..
Amanda

Developing Expert voices

March 16, 2009

Rupert has either milk or cocoa to drink for breakfast with either oatmeal or pancakes. if he drinks milk, then the probability that he is having pancakes with the milk is 2/3. the probability that he drinks cocoa is 1/5. the probability that he drinks cocoa is 1/5. if he drinks cocoa, then probability of him having pancakes is 6/7.
a) show the sample space of probabilities using a tree diagram or an other method of your choice.

b) find the probability that Rupert will have oatmeal with cocoa tomorrow morning.

May 14, 2009

Lucy Brown wants to buy a condo, but does not know how much money she should spend based on her income. She earns $44 000 per year, and has saved $9000 for a down payment. the propery taxes for the condo she likes are $1500 per year, and the heatig costs average $90 per month. the condo/strata fees are $18 per month, the bank will give her a 250 year mortgage at an interest rate of 7.5%. what is the maximum price she can afford for a condo, based on spending no more than 32% of her gross income on household and accommodation expenses?

Timeline

May 20 - Consult with the group and decide which units were going to do our projects on.
May 22 - Make sure that everyone has slowly progessed on their projects and help eachother out on what their missing.
May 25 - Another group meeting, making sure everyone has got something done.
May 30 - Start putting bits an peices of our project together.
June 3 - Complete Project
June 4 -6 - Put the finishing touches on the project
June 7 - Hand in completed assignment

REFLECTION!

Well the unit we were on was on vectors. I didn't really understand it at first. We had to review some of our trigonometry knowledge from years before. After the review I started to understand what we were being asked for. Since the program Trisolve2 was introduced to us, I started to understand more about the unit and help me figure out the sides and angle more. I found this unit to be a really short unit.

REFLECTION!

Statistics, well what can I say about statistics. It was a pretty long unit and it was hard to get a grasp of everything. But I read over the slides and got some help from some of my fellow classmates. I started to understand what was being asked and which functions I needed to use and which bits and pieces of information that was missing. I understand the majority of the functions and which each does now, the only thing I'm not to sure on is making a histogram. Tomorrow is the test, Good luck to everyone :D

Today in class Mr.K started off by putting us into groups. We went over the homework that was assigned to us the night before. The answers to the questions are posted on todays slides, March 12th.


The new lesson we learned today was COMBINATIONS ( the "choose" formula). The formula is as follows:





"n" is the number of objects availabl to be arranged

"r" is the number of objects tht are being arranged




EXAMPLES:















You would read this as 10 "choose" 5 equals 10 divided by 5 factorial multiplied by 5 factorial.


By choosing 5 people to make a team which equals 5!, that means there is remainder of 5 other people from the 10.



The answer to this question is : 252

Another example:

This you would read as 15 "choose" 3 equals 15 divided by 3 factorial multiplied by 12 factorial.

This shows that you would choose 3 people(3!) out of the 15 people (15!) given which leaves you with 12 people (12!) left.

The answer is: 455

Tomorrow is Pi day. So don't forget to bring your pies. Also remember to find a cool math joke to share with the class.

The scriber I choose is:

MAC

Today in class, Mr.K put us into groups to go over our homework. Our homework was on Transition Matrices. We went over the homework and did some more review questions on Transitions Matrices.

Mr. K gave us an example of a Transition Matrix.

Example

Suppose that the population of a small island is classified into three distinct groups, children, teenagers and adults and that each year :

• Children are born at a portion of 6% of the adult population , 1% of the children die



• 10% of the children become teenagers , 5% of the teenagers die



• 14% of the teenagers become adults , 7% of the adults die

This year, Youngville's population is 25 000. 5000 children, 18 000 teenagers and 2000 adults.

A) Write a row matrix that currently represents the population of Youngville.

The question is asking to right down the state matrix, a state matrix shows the information that that is currently given as a constant. Which is the population of Youngsville. We would label the matrix "S" which tells us that it is the state matrix.

A = Adults

T = Teenagers

C = Children

We would usually write the matrix in alphabetical order but in this case we would write it going oldest to youngest showing the population of the city more clearly.

B) Write a 3 x 3 transition matrix that shows how the population is changing over time.

To answer this question we would need to find out how the population changes.

The following matrix is labeled "T" which stands for "transition matrix."

Confusing? Well hopefully my explanation works. Adults can't turn back into teenagers so that's why there is a zero in the A,T position. 6% of the portion of adults become kids because adults make kids, and 1% of the children die, leaving 93% of the adults stay adults.

6% + 1% = 7%

100% - 7% = 93%

Teenagers can't go back into children so T,C becomes zero. 14% become adults, and 5% of the teenagers die, leaving 81% of the teenagers still teenagers.

14% + 5% = 19%

100% - 19% = 81%

Children can't just be adults right away so C,A becomes zero. 10% of the children become teenagers and 1% of the children die. Leaving 89% of the children stay children.

10% + 1% = 11%

100% - 11% = 89%

So that's how I understood the example Mr.K gave us. Hopefully this helped people understand it more.

IMPORTANT NOTE: Mr. K and the class decided that tomorrow will be another review class and that the pretest was moved to Tuesday as there is no school on Monday, Louis Riel day. The unit test will take place on the Friday of that week which is the 20th of February. Wednesday and Thursday we will be starting on our new unit.

The next scriber I choose is....

Mac