SCRIBE POST Sofia Navas and Cristina Franco

SCRIBE POST

Like every day in 11ª Pre-Calculus class, we start off by the P.O.D (problem of the day). Today’s P.O.D was on a topic we already learned but which was helpful as a review for our upcoming final exam.\

P.O.D 6/7

Solve the equation for all θ є [0,360º] 3sec q-9 = 1.

First to solve, we have to isolate θ, so we subtract 9 from both sides, and then we divide each side by 3 and finally get the inverse of sec on both sides.



This album is powered by BubbleShare - Add to my blog



Now we have to find all 1st revolution angles, we know that the angles are located in the first and fourth quadrant because it a positive angle. So we ºsubtract 72.54º from 360º.

360º-72.54º ≈ 287.46º so,

q ≈ 72.54º, 287.46º


REMEMBER TO STUDY QUIZ TOMORROW!!
TOPICS:

-SIGMA NOTATION
-INFINITE SERIES
-LIMITS

11A’S FINAL PLAN:

-Mr. Alcantara will post a final exam study list to the block for those of you interested.

-The post will have an assignment on the back for those students who will not have time to do a second block.


Yesterday we ended off in a sigma notation problem, today we picked up were we left yesterday and solved it.

Express the series in Sigma notation and then use
Sigma properties to find the sum:

3•2+3•3+3•4+3•5 …+3•18

To solve the problem we first have to identify what type of series is. We can tell is an arithmetic series because 3 is always being multiplied by a number that increases by 1.
Now we have to find the number of terms we have to add. So,



This album is powered by BubbleShare - Add to my blog



Last Property of Sum:

n
Σ c where c is a constant ( not dependent on n)
n=1

ex:
n
Σ 4 = 4+4+4+4+4 = 5•4= 20
n=1 ( add 4, 5 times )



PROBLEMS:
16
• Find Σ 3k-10
n=1

First evaluate the problem, what is it saying? Their sayings add 3k-10, 16 times. To make it easier we have the properties of sum to solve this problem. Divide the proble in two parts and solve for each.




This album is powered by BubbleShare - Add to my blog




PRACTICE PROBLEMS AND SOLUTIONS:


1. Find the sum using sigma notation 1•3+3•5+5•7 +... 99•101




This album is powered by BubbleShare - Add to my blog




2. ∞ n-1
Σ 7• 2/3
k=1



This album is powered by BubbleShare - Add to my blog





Lucho and Mr. Janke run a race. Lucho runs 1.5 times as fast as Mr. Janke. If Mr. Janke has an 8m head start, how fast will Mr. Janke run before Lucho catches him?

* Lucho speed is 3/2 Mr. Janke's->

* Lucho covers 3/2 the distance that Mr. Janke covers in the same time->

* Mr. Janke covers 2/3 the distance that Lucho covers in the same time->

* By the time Lucho makes up the 8m, Mr. Janke will have gone 2/3(8m)->

* The lead that Lucho has to make up will be 2/3 less each time.



Lucho runs:



Mr. Janke runs 24-8=16m




This album is powered by BubbleShare - Add to my blog




4. Find and Justify lim sn , where tn 10(3/2)
n->∞




This album is powered by BubbleShare - Add to my blog




5. Find the sum: 2•4+6•8+10•12+...+398•400
1 2 3 ?




This album is powered by BubbleShare - Add to my blog






6. Express the series in sigma notation and then use sigma properties to find the sum:

200+192+184+...-64



Arithmetic or Geometric?

d=-8


This album is powered by BubbleShare - Add to my blog




NO HOMEWORK ! BUT STUDY HARD FOR FINAL EXAMS AND EXAM TOMORROW !....