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Monday, May 29, 2006 

SCRIBE: Goodbye Periodic Functions, Hello Sequences!

Hi everyone. I have good news and more good news. Today we finished Periodic Functions. Good?! I don't know about you guys, but I'm a bit relieved -_-' And finally, we're on our last unit: Sequences. So after this unit, we have the exam, aaand then we're DONE!! Hope that was a bit motivating...

Before I talk about what we did in class today, I just wanted to remind everyone that the Wiki assignment has been extended to the end of the week: Friday, June 2nd (midnight at the latest). Mr. K just wanted to say that you shouldn't be afraid to edit someone else's work because any previous work is saved in the history..which shouldn't be hard for Mr. K to find. But to make sure he knows whose work is whose, then you should remember to sign in with your name. Another reminder: For the constructive modification, you cannot edit your own work!!

So today we had two classes. For third period, We did a Group Problem.

Group Problem - Periodic Functions 5 // Tsunami
A tsunami (commonly called a "tidal wave" because its effect is like a rapid change in tide) is a fast-moving ocean wave caused by an underwater earthquake. The water first goes down from its normal level, then rises an equal distance above its normal level, and finally returns to 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.

Before continuing with the question, it's best to sketch a diagram/graph:


From the sketch and information from the question you can figure out the equation:

A = 10, B = 2π/15, C = 0, and D = +9

And the equation would then be: y = -10 sin ( [ 2π/15 ] x ) + 9

* Parameter A is NEGATIVE because "the water first goes down from its normal level.." which can also be seen from the sketch.

(a) Assuming that the depth of the water 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.

This can be found by plugging in the equation into y= , graphing the equation, and to find each time you would go to: 2nd CALC > [value] and plug in the time asked. (I also rounded to two decimal places).

i. 2 minutes ii. 4 minutes iii. 12 minutes
1.57m -0.95m 18.51m



(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?

To find the minimum, you'd go to 2nd CALC > [minimum], left-bound, right-bound, guess anywhere and from there you should get the value: -1. So this means that the "lowest" depth of the water would have no actual wave. Technically /mathematically the height is -1 but you can't go beyond zero because there's no where to go. All that's left in reality is the ocean bed.

(c) The "wavelength" of a wave 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 kilometres per hour, what is its wavelength?

800km/hr = 800km/60min ; you can figure it out like that.

OR

800km/60min = x km/15min

The answer is : x = 200km



After the group problem we had a tiny introduction into Sequences:

The numbers in grey are the 'nth' terms. The blue two's under the arrows is the common difference between the black and red numbers in the sequence. Surprisingly there is an equation that you can extract from the sequence. You can imagine that x=n , m(slope)=2, b(intercept)=4, and y=value. And so:

y = mx+b equals y = 2n+4

*Not every sequence has a common difference.

Here are the three other sequences that we didn't get a chance to look at. I'm not sure if my answers are right, but I'll post them anyway:

b) 1, 2, 4, 8, 16, 32

c) 2, 3, 5, 8, 12, 17, 23, 30, 38

d) 4, 2, 1, 1/2, 1/4, 1/8, 1/16

For fifth period, we did our test on Periodic Functions. So that means no homework tonight, just Wiki if you haven't already finished it.

And of course, before I forget: tomorrow's scribe will be C-A-I-T-L-I-N =)




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