Periodic Functions

Whoa!! I almost forgot I was the scribe for today. Anyways...here it is..In class , we worked on a periodic function problem as groups of 3 or 4. It took us a while to figure out this problem so we had spies from each group to see what the other groups had done. Here is a recap on the problem.

A tsunami(commonly called a "tidal wave" because its effect is rapid change in tide) is a fast-moving ocean wave caused by an underwater earthquake. The water first goes down form its normal level, then rises an equal distance above its normal level, and finally return ti its normal level. The period is about 15 minutes. Suppose that a tsunami with an amplitude of 10 metres approaches the pier at Honolulu, where the normal depth of the water is 9 metres.

For this problem we first need to construct a graph and fill in "DABC".

This is how we start our graph. It stated that the normal depth of the water if 9 metres therefore it is the average value of function(sinusoidal axis). It is where our graph will start. We then add 10 metres to the sinusoidal axis since the amplitude is 10. It tell us how far to go from the sinusoidal axis. This will give us the maximum(19 metres). We then find the minimum by subtracting 10 from 9(-1).



We can now construct the graph.

The graph first goes down since it is stated in the information that the water first goes down from its normal depth. This wave has an amplitude of 10(as stated earlier) therefore the wave goes down its minimum depth which is -1. It also says that it then goes back to its normal depth at the same equal time. Therefore we divide the whole period(which is 15 ) into 4 parts because it first goes down then up, then up again and finally down.

We can now find "DABC"

A= -10 ( amplitude. it is negative because the first movement of the wave is down)

B=2(pi)/15 ( determines the period , we place 15 because a period is every 15 mins)

C=0 (since the wave started at 0 minutes and at the sinusoidal axis, there is no horizontal shift)

D= 9 ( this tells us that the whole graph will move 9 metres up, it is the sinusoidal axis)

Now we can put these informations into an equation.


The amplitude
2 Pi(3.14) / 15 = o.42
The vertical shift\

A) Assuming that the depth of the wave varies sinusoidally with time as the tsunami passes, predict the depth of the water at the following times after the tsunami first reaches the pier.

i) 2 minutes ii) 4 minutes iii) 12 minutes

For this problem, we could just insert these times into the equation in place of x to determine the depth of the water. For example, this is the equation for 2 minutes:

We do the same for the rest, place the minutes in place of x.

B) According to your model, what will be the minimum depth of the water? How do you interpret this answer in terms of what will happen in the real world?

We can see the lowest depth of the water by looking at our graph. It is -1 since it is the lowest the wave can go. In the real world this is kind of confusing. How can the lowest depth be -1 , this would mean it digs under see bottom. Therefore we state it as , for lenght of time the wave is at its lowest, we can see the bottom.

C) The wavelenght of the water is the distance a crest of the wave travels in one period. It is also equal to the distance between two adjacent crests. If a tsunami travels at 800 kilometers per hour, what is the wavelenght?

For this question. it is stated that the the wave is traveling 800 km/h. In our graph, one period of the wave is 15 minutes. We found the answer for this question by cross multiply.

THE NEXT SCRIBE IS CHRIS A.!!!!

B.O.B

Its that time of the month again. Im pretty sure our class has a good understanding of this unit on Periodic functions. This unit was pretty easy I guess. Its just a matter of knowing which goes where and the word that helps us in "DABC"(dabic). Wait a moment, was'nt Mr K asking us if we were ready for this test. I never got the chance to ask if our test is really tomorow....Anyways good luck!!

B.O.B

Its our test today and i don't know if im ready. Maybe, maybe not. Our personal finance unit was interesting. We learned many thing about saving money to buying houses. I seriously did not know the things connected with buying a house before. What can i say, this unit was pretty interesting. It also got me thinking about what Mr K always mentioned to us about saving our money now and becoming a millionaire in the future. I hope this test is easy because its worth like 1000! marks whoa..Well, good luck everyone!

BOB

..I know its late to do this BOB since we just finished our test..lol..,but I think I still need to have one for when Mr K. looks at our posts. This unit on vectors wasn't as hard as our past units. This was actually a fun unit. Dont you guys think so. Measuring and figuring out angles and sides kept us all awake...especially KYLE..lol just joking.

Scribe August,23,07

My apologies for those who were'nt in class yesterday for posting my scribe late, my network connection was acting up again. Well here it is. Yesterday we started our class with a suprise quiz. Heres a recap on the quiz.

These were the five ways in which a vectors direction can be stated. Some of us had a little bit trouble with this because we got confused. The confusion was having a degree with either "west of south" or "south of west", because those two are different directions.

For this question, we had to use exact measurement since it is asking for a scale drawing. we use our calculator if it asks to calculate the vectors.

*Remember* Dont forget to indicate a scale. It represents your measurement.

Part A is drawn that way because it states that it is East 15 degrees. Therefore we place the protractor upside down with the zero line on the horizontal line of the "T" scale( I forgot what it was called lol). We then measure the down from zero since it is also stated that it is South.

Part B is similar to part a except the direction is not given instead we were given a bearing.

We then start to measure the angle by starting at North working your way around the protractor until it is 300 degrees.

These questions were new to us. I think this was the first time we were given questions lke these.The first question we just added the vectors since they are both east meaning pointing the same direction. Speaking of direction, the second question is different. The answer is 1 meter west because a vector is going 3 meters east and another one at 4 meters west. Unlike the first one we added the same direction, for this one we subtract.

In the afternoon period, we had another quiz. This quiz was more on problem solving.

On this question we moved one vector to make this question easier. By moving the vector we can easily construct the resultant vector making it easier to find missing angles by looking for the "Z". When we have three information about the triangle, we then use our program in our calculator called Trisolve and punch in these information. By doing this, the calculator solves the rest of the missing info about the triangle.

probability

jarb
Originally uploaded by jhay-ar.

BOB

When Mr. k told us that the next unit was going to be on Probabilities, I was like "OH MAN".... I knew that this unit was going to be hard. I didn't really get this unit right away. I had trouble with the equations used to solve problems. I didn't which one was the one for a particular question. The questions were also kind of hard to understand sometimes. It almost seems like its a tricky question. Today's class cleared the blurr in my head. I can now use the right equations to solve problems, thanks group2!!. The people in my group help me understand the problems I had, now only if i can go back in time to when we had the quiz. Other people wrote that the pre-test will help them on the test on Thursday, well..same goes for me. Good luck!!...Oh yeah..anyone know our next unit...

PROBABILITY and Pi"e"

Today was the last day of our second unit, Probability. In the beginning of class, Mr. K reminded us about Pi Day which is on March 14. This lead to discussing about the party on that day. PARTY!!!!!. Everyone is then going to bring their own pies to share to the whole class....oh...and milk.

Later on, we continued our questions and we left off yesterday. Here are the reviews with some explanations

question: The probabilty that Tony will move to Winnipeg is 2/9, and the probability he will marry Angelina if he moves to Winnipeg is 9/20. The probability that he will marry Angelina if he does not move to Winnipeg is 1/20. Draw a tree diagramm to show all outcomes.

That is how we can construct a diagram with information from the question.

the next question is...

=What is the probability that Tony will move to winnipeg and marry Angelina.

BOB

My first reaction to matrix was that it was going to be an easy subject since it looked and sounded simple, but I was wrong. To be able to figure out these matrices, must know what your doing and focus on it since you wont get lost without knowing it. The way these matrices are added, subtracted or times, i mean "multiplied", is not like normal addition or subtraction. You must know which ones go together and you must also satisfiy the rows and columns. In the beginning i had trouble with this part, but as the participation of the class increased, i started to understand bit by bit. So it really goes to show that "Learning is a conversation"

Transition Matrix

In the beginning of todays class, we had a review on last weeks lesson about multiplying matrices. Transition matrix was then introduced to us. Transition matrices involves probabilities and percentages. It describes change and can be symbolized with "[T]" To be able to work with these matrix, the columns and rows must have the same information.

This example I'm about to give is from the first transition matrices worksheet Mr K handed out. We had a hard time understanding example 2, which was the sports one, so ill re-cap on that one..

EXAMPLE 2, SPORTS
The annual Oxford-Cambridge boat race, has been rowed regularly since 1839. Using the data from 1839 up to1982, there were 57 Oxford wins and 67 Cambridge wins. If the relationship between the results of a given year and the results of the previous year are considered, the following table can be constructed.



**



**-This means that Oxford got 35 games won after another (two games won in a row) and 22 wins without a two game in a row streak ... This goes the same for Cambridge.

To be able to work with this matrix, we need to convert to a percentage then to a decimal. I'm sure we all know how to convert these into decimals. the result should be.










Question: If Oxford wins this year, what is the probability they will win next year? in two years? in three three years?

Answer: to solve this question we need to have a transition matrix and a state matrix.

The transition matrix is :










This matrix represents the change. for example, there is a 61% chance that Oxford will have a two game winning streak.


The state matrix is simply stated "how it begins". For example, in the question it stated that Oxford won this year

Therefore we put a 1 under the column of Oxford in a 1x1 matrix which the rows represent the win. There is a zero under Cambridge because this represents the first year and they lost the first year.


We then multiply the transition matrix and the state matrix to get the probability of each team.
It goes:

2









The Transition matrix has an exponent of two which will give us the result for a second year percentage. We all know by now how to multiply matrices. That is the next step. the result is:











This means that in the next year. Both teams will have the same chance of winning between themselves.


.




.i hope this is much better than my other post.. :)