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Sunday, June 11, 2006

end of the course-afternoon

So today there are two scribes. Marquin for the morning and me for the afternoon. This afternoon we FINALLY finished the course. This afternoon we wrapped up the last unit and also did a exam rehearsal for the Circular Functions unit .

So here's the notes...

Sigma Notation: A shorthand way to write a series.
example



is the capital sigma (from greek alphabet); means "sum"

- supbscript n=1 means "start with n=1 and evaluate 2n-3"

- superscript 4 means "keep evaluating (2n-3) for successive integral values of n, stop when n=4; then add all the terms."

- (2n-3) is the implicit definition of the sequence

Geometric Series: the sum, to the nth term, of the terms in a geometric series given by:

- Sn is the sum of the first n terms in a geometric sequence

- n is the rank of the nth term

- t1 is the first term

- r is the common ratio

Infinite Geometric Series

- when >1, the infinite sum of a geometric series grows without bound _ it DIVERGES

- when <1,>CONVERGES

END OF COURSE

the next thing we did was the exam rehearsal for ciruclar functions.

1) Through how many radians does the minute hand of a clock turn in 24 minutes.

A) 0.2 pi

B) 0.4 pi

C) 0.6 pi

D) 0.8 pi

2) If cos theta = -3/4 and tan theta <0.>

A) -4/5

B) -root 7 / 4

C) 4 root 7 / 7

D) root 7 / 4

solution:

3) If y= 2 cos(1/2X) - 3, what is the minimum value of y?

-5

solution: since the graph lies on -3 and the amplitude is two the minimum value is -5. (-3) - 2 = -5

4) if theta=arcos(- root2 / 2), find the value(s) of tan theta?

tan= sin / cos

= -1

5) The tide at a boat dock can be modeled by the equation d(t) =-2cos(pi/6T)+8

a) How deep is the water at high tide? low tide?

since the amplitude is 2 you have to add 2 to 8 to get the high tide and subtract 2 from 8 to get the low tide.

low tide: 8-2=6

high tide: 8+2=10

b)How lond is it between one high tide and the next?

period=2pi/B

pi / 6 = 2 / period

12 = period

c) For how many hours, between t=0 and t=12 is the tide at least 7 feet deep?

7 = -2 cos pi/6T + 8

-1 = -2cos pi/6T

1/2=cos(pi/6T)

theta=pi/6T

1/2=cos theta

since cos 1/2 is equal to pi/3 and 5pi/3 on the unit circle, we plug it in for cos theta

theta = pi/3

pi/6T = pi/3

T=2

theta = 5pi/3

pi/6T = 5pi/3

T=10

now you find the difference of 10 and 2...

10-2=8 hrs

The tide will be at a dept of atleast 7 ft deep for 8 hrs.

That marks the end of my scribe. Don't mind if i say it again but i just love saying it.. THIS MARKS THE END OF THE COURSE.. haha.. anyways i don't know whole will be scribe tommorow since there was two scribes today. whose gonna pick? me or marquin? we'll just see tommorow..




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1 Comments:

At 6/13/2006 7:56 PM, Blogger Mr. H said...

A great post. Good use of colour and illustrations to demonstrate different knowledge. You belong in the Hall Of Fame

 

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