Applied Math 40S

The Adventure Continues ...

2006-06-29T15:52:00.000-05:00

Our adventures in blogging continue....

Watch for 3 new blogs going live September 6, 2006 ...

Pre-Cal 30S (Fall '06) (Grade 11)
Pre-Cal 40S (Fall '06) (Grade 12)
AP Calculus AB 2006-07 (Grade 12)

So Long ...

2006-06-28T18:23:00.000-05:00

We had our graduation exercises today. A gentle push into the world for all of you. I hope you're leaving with the keys to your future in your hand.

I'm so glad we've had this time together,

Just to have a laugh or learn some math,

Seems we've just got started and before you know it,

Comes the time we have to say, "So Long!"

So long everybody! Watch this space in the fall for pointers to new blogs for each of my classes.

Farewell, Auf Wiedersehen, Adieu, and all those good bye things. ;-)

Student Survey Results

2006-06-18T23:08:00.000-05:00

We did a little survey in class the day after we recorded our podcapsule. The results are below; 17 students participated. So, without any further ado, here are the results of our class' survey. Please share your thoughts by commenting (anonymously if you wish) below .....

Classroom Environment
The questions in this section were ranked using this 5 point scale:

Strongly Disagree	Disagree	Neutral	Agree	Strongly Agree
1	2	3	4	5

The bold numbers after each item are the average ratings given by the entire class.

1. The teacher was enthusiastic about teaching the course. 4.88

2. The teacher made students feel welcome in seeking help in/outside of class. 4.65

3. My interest in math has increased because of this course. 3.76

4. Students were encouraged to ask questions and were given meaningful answers. 4.53

5. The teacher enhanced the class through the use of humour. 4.47

6. Course materials were well understood and explained clearly by the teacher. 4.47

7. Graded materials fairly represented student understanding and effort. 4.24

8. The teacher showed a genuine interest in individual students. 4.12

9. I have learned something that I consider valuable. 4.29

10. The teacher normally came to class well prepared. 4.59

Overall Impression of the Course
The questions in this section were ranked using this 5 point scale:

Very Poor	Poor	Average	Good	Very Good
1	2	3	4	5

1. Compared with other high school courses I have taken, I would say this course was: 4.65

2. Compared with other high school teachers I have had, I would say this teacher is: 4.65

3. As an overall rating, I would say this teacher is: 4.53

Course Characteristics
The questions in this section were ranked using this 5 point scale:

Very Easy	Easy	Average	Difficult	Very Difficult
1	2	3	4	5

1. Course difficulty, compared to other high school courses: 3.35

2. Course workload, compared to other high school courses: 3.31
(This question answered by 16 students.)

3. Hours per week required outside of class:
(This question answered by 16 students.)

0 to 2	2 to 3	3 to 5	5 to 7	over 7
25%	44%	12%	19%	0%

4. Expected grade in the course:
(This question answered by 14 students.)

F	D	C	B	A
0%	29%	29%	36%	7%

Specific Feedback
What was your best learning experience in this course?

Pre-tests
Vectors
Probability
Design & Measurement
Real life applications of math (2)
Almost everything

Online tools
All but Statistics
Stories about the Greeks and infinity
Scribes (3)
Blogging (4)
Wiki assignment

"Say it six times"
Group work (2)
Learning to use graphing calculator
Using the internet for learning
How teachers love teaching

What was your worst learning experience in this course?

Statistics
The exam
Using the iMac lab for the Personal Finance unit

None (4)
Not getting tests back quickly

Fear of asking questions
Homework quizzes
Personal Finance (2)

What changes would you suggest to improve the way this course is taught?

More stories and extra topics (2)
Blog
Math dictionaries
More Projects

None (3)
Give notes on using the graphing calculator
Give tests back quickly (4)

Give regular grade updates
More jokes
More wiki work
Teach Personal Finance using only the graphing calculator

It's interesting to compare the items that were considered both the worst and best learning experiences. Also, take a look at the list of worst learning experiences compared to suggestions for next year. Help me do a better job next year by commenting on what you see here ....

Message in a Podcast: Our Podcapsule

2006-06-16T00:12:00.000-05:00

The students in our class wrote their final exam on Wednesday June 14; they ended their high school mathematics careers. We made a podcast to celebrate! We left ourselves a "podcapsule" instead of a "time capsule." We left our future selves a message; hopefully it will help us improve our learning.

Here is our Podcapsule (5 minutes, 52 seconds). Please leave any questions, concerns, complaints, compliments, confusions, uncertainties, anxieties or other inquiries in the comments to this post.

You can also leave us an audio message if you wish. ;-) (You'll need a microphone.)

This isn't our last post yet -- I've got at least two more I want to get out before the end.

SCRIBE!!!

2006-06-13T22:42:00.000-05:00

HELLO EVERYONE! This is Jessica, I haven't been the scribe in a while so I decided to volunteer again! This morning we had our first part of our exam and hopefully everyone did well!! Tomorrow morning we have our second part of our exam, everyone don't forget we need two pencils, an eraser and a geometry set. BE READY! In class today a couple of us recorded our podcapsule and the rest of us continued making our notes on our sheets.

Thats all for today! GOOD LUCK EVERYONE ON THE EXAM TOMORROW!

2006-06-13T19:26:00.000-05:00

The password to the wiki is rwgtktea.

.. Just in case anyone was unclear.

Scribe ; The Day Before Provs!

2006-06-12T18:55:00.000-05:00

Hellooo everyone. Unbelievably I am scribe, once again -_-' But that's fine, not much to report anyway. But here is something very, very important: As everyone should know by now, tomorrow is the start of the Provincials! Everyone should be infront of the Imac Lab @ 8:45 am, due to the fact that pen should be on paper by 9:00 am. MAC LAB, 8:45 am. That also goes for the continuation of exams on Wednesday. So today for first period, we were handed one yellow sheet of paper on which we were able to write anything that we thought could help us for the exams. We could have written on the sheet, back to back if we wanted. The thing is, seeing as how we have 'tools' such as our blog and thinkfree and everything else we've been taught during the course, we'll legitimately be able to access these websites for the exam as well. So for second period, a Wiki was created in which we started to put the information from our dictionaries. I believe it was Cait who initiated this, I'm not entirely sure actually..But there we have it, our very own Wiki! So hopefully, everyone contributes a little bit so that we have good notes to refer to incase we need to for the exam.

Goodluck to everyone. Study well. It was great being in this class =)

UNITS

2006-06-12T18:04:00.000-05:00

Matrix Modelling - feb
Probability - feb/mar
Variability and Statistical Analysis - mar/apr
Vectors - apr
Personal Finance -may
Applications of Perodic Functions - may
Sequences -may/ june
Design and Measurement-june

Scribe Post for Friday, June 9

2006-06-11T20:16:00.000-05:00

We had one class for math on friday and everyone got to choose which units to review for the exams.

Nobody chose to review Matricies and Sequences. So we are to review these units: Design & Measurement, Statistics, Probability, Personal Finance, Vectors, and Periodic Functions.

Today we did a worksheet on design & measurement.

(a) COST OF FLOOR COVERING: (show all work.) (1 mark)
Vinyl flooring is sold in 6-foot widths. The area under the tub will not be covered and the flooring is to be installed in one piece. What length of flooring do you need to buy?

10 - 2.5 = 7.5 ft

(b) PAINT COSTS: (show all work) (5 marks)
The walls are 8 feet high and the dimensions of the door are 30 inches by 78 inches. The walls require 2 coats of paint. The second coat will require 2/3 as much paint as the first coat. The area behind the tub and vanity do not need to be painted.

* Calculate the area of the walls to be painted.

Walls:
10 * 8 * 2 = 160 square ft
6 * 8 * 2 = 96 square ft
160 + 96 = 256 square ft

Area behind bath tub: 2 * 2.5 * 2 + (6*2) = 22 square ft
Area behind sink vanity: 3 * 3 = 9 square ft
Door: 2.5 * 6.5 = 16.25 square ft
Total: 22 + 9 + 16.25 = 47.25 square ft

Area to be painted: 256 - 47.25 = 208.75 square ft

A 4L can of paint covers 120 square ft at a cost of $42.99. A one litre can of paint covers 30 square ft at a cost of $14.99.

* What combination of cans of paint do you need to buy in order to minimize the coast? What is your final cost?

With both coats of paint: 208.75 * 1(2/3) = 347.92 square ft

347.92 / 30 square ft = 11.59 L or 12 L

Cheapes combination of cans:
Three 4L cans
3 * $42.99 = $128.97

(c) BASEBOARD COSTS: (show all work) (2 marks)
The baseboards are sold in 8-foot lengths at a cost of $5.36 each. Determine the number of 8-foot baseboards needed and calculate the total cost of the baseboards. State any assumptions you have made.

Assumption: Baseboards are around the tub and vanity
6 ft + 7.5 ft + 7.5 ft + 3.5 ft + 4 ft = 28.5 ft
Cost: 28.5 / 8 = 3.56 lengths --> 4 lengths * $5.36 = $21.44

OR

Assumption: No baseboard in front of the tub or vanity
7.5 ft + 4.5 ft + 3.5 ft = 15.5 ft / 8 = 2 lengths
2 * $5.36 = 10.72 + 0.75 + 0.75 = $12.22

(d) BUDGET:
You have a $300.00 budget for the entire bathroom project. How much money will you have left for the floor covering after you have considered the paint, baseboards, GST and PST?

Paint: $128.97
Baseboards: $21.44
SUB-TOTAL: 128.97 + 21.44 = $150.41 * 1.14 = $171.47

Amount left for flooring: $300.00 - $171.47 = $128.53

That was all the work we did and the NEXT SCRIBE is...

STEPH

One steals on my hammer, the other one is skating

2006-06-08T20:53:00.000-05:00

Hello all... Today I had the honor bestoded upon my of being the scribe... joy...
well its not like we did too much *rolls eyes* just finished two subjects, and got some closure on a couple questions, like the Ice Rink one, apparently people paint the ENTIRE surface of their ice rinks, hmmm...

First off
^2 = squared, ^3 = cubed... etc.

Sequences - If I Had A Hammer

Three nails, each 6 cm long, are hammered into a board until the head of the nail is flush with the surface of the board.

Note: To be flush, the head of the nail must not be more than 0.10 cm above the board's surface.

Nail 1 Moves 0.90 cm into the board with each hit of the hammer

Nail 2 Moves 0.90 cm into the board with the first hit of the hammer.
After each successive hit, the visible part of the nail is 80% of its previous
height.

Nail 3 Moves 0.90 cm into the board wiht the first hit of the hammer.
After each successive hit, the nail moves 0.30 cm less than it moved
previously.

Task A.
How may hits of the hammer will it take to drive each nail into the board? Support your answer for each nail.

(My answer)
Nail 1: uMin = 1
u(n-1)-0.9
u(nMin) = 6

7 Hits @ -0.3 cm

Nail 2: uMin = 1
0.8u(n-1)
u(nMin) = 5.1

19 Hits @ 0.09187 cm

Nail 3: Stops at the height of 4.2 cm

Task B
Which of these three situations is least likly to occur and why?

(My answer)
Nail 3 is least likely to occur

Task c
Create a new scenario where a 10 cm nail is hammered until it becomes flush with a board using from 19 to 21 hits (inclusively). The nail cannot move more than 1.5 cm on the first hit.
Support your answer.

(My answer)
nMin = 0
u(n) = u(n-1)-0.5 cm
u(uMin) = {10}

So that was that... lets move on....

---------------------------------------------------------------------------------------------
Samantha's Ice Rink
Samantha wants to have an ice rink built in her backyard. In order to do this, she must:

Hire someone wiht landscaping equipment to level her back yard. This costs $2.50 per square metre.
Flood the ice with enough water to form ice to a depth of 12 centimeters. As water freezes, the volume of ice formes is about 1.1 times the volume of the water. The price of the water is $2.10 per 1000 liters. Note: 1 m^3 = 1000 liters
paint the ice with ice paint that costs $8.99 per litre. One litre covers eight square meters.
allow $65 for miscellaneous materials she need to buy.
pay PST and GST , both at 7 percent, for all materials, and only 7 percent GST for labour (having their yard landscaped).
pay her children for flooding the rink. Water flows through the garden hose at 20 litres per minute, and the children insist on receiving $3.50 per hour for flooding. Samantha pays no PST or GST on this expense.

Samantha has a budget of $400 to build this rink. Determine the maximum-size rink she can build for that amount. What would be a suitable shape of rink to design? What are the dimensions of the shape you suggest?

ok... that took forever, now the answers:
because everything can be split to fractions of the whole except for the paint, so we used the amount of area that the paint can can cover as the base number for the price quotes and then just divide the anoumt of money by the base price... you'll understand afer its all written down

Land scaping $2.50/m^2 + GST
Water $2.10/1000L = $2.10/m^3 + PST &GST
Paint $8.99/8m^2 + PST & GST
Misc $65 {assuming the taxes are included]
Flooding $3.50/h 1200L/h

For 8m^2
Landscaping 8 X 2.50 + Tx = $21.40
Water 0.8727 X 2.10 + Tx = $2.09
Paint $10.25
Misc $65
Flooding $2.55
Total..............$36.29 per unit

For water:
12 cm = 0.12 m
Vice = 8(0.12)
= 0.96m^3

Amount of water to make 12 cm of ice
1.1w = Vice
1.1w = 0.96
w = 0.96/1.1
w= 0.8727 m^3

How many liters is that?
1000L/1m^3 = XL/0.8727m^3
X = 272.7L

How many hours will that take to fill?
872.7/1200 = 0.72725 hr or 42 minutes and 36 seconds (I belive)

So all said and done how big can we go?
well $400 - $65 = $335
335/36.29 = 9.28

or 9.28 meters by 8 meters, but because we cant buy partial cans of paint, well have to go with 9m X 8m with this budget

-----------------------------------------------------------------------------------------------
Ok... the next question is from a while back, about 2 weeks I think

A water tank is a sphere with a diameter of 3.6m. Estimate the volume of water in the tank if the depth of the water is 24 cm.

Vcone is cone of water
Vcone = Pir^2L/3
=(Pi(0.8979)^2(0.24)/3)1.1
= 0.2228m^3

Well thats it for today, and that on took forever :)
thanks for reading
Shane

Next Scribe is......... Andrew

Create a Scribers Guide to Scribing

2006-06-08T10:34:00.000-05:00

Two days ago I received this email from a teacher friend of mine, Mr. Harbeck.

I would like to congratulate you[r classes]. Every scribe post I read is like taking part in your class. The students take tremendous pride in creating their posts and are all scribing at Hall of Fame levels. It would be interesting for them to reflect on their scribing and come up with a criteria for making the Hall of Fame. They know how much effort they put into their posts and what is worthy or not. As an outsider teaching 13 year olds who have no choice but to be in my class I do not see the devotion these scribes put forth every day. Everyone takes a turn and does a great job.

I would be curious if you did a "bob" on reflecting about scribe posts. The first to the last. What made a difference from the beginning of the course to the end. My topic was a dry etc one...this is how I spiced it up.

Could they create a scribers guide to scribing?

This is a talented bunch of students. Use them while you still have them. The Next bunch could be even better.

So here it is folks. You've more or less created this art form, now you can write the book on it. In the comments to this post answer these questions:

How do you go about writing a scribe post? Do you do anything differently in class when it is your turn to scribe? If so, can you describe what you do differently in class when you are scribe?

What makes a scribe post worthy of entry into The Scribe Post Hall Of Fame? Specifically, what should be included in the post for it to achieve this recognition?

Compare the first scribe post you wrote to the most recent one. What, if anything, did you do differently?

Your replies, and those of my other classes, will be collated and posted on a special page in The Scribe Post Hall Of Fame. Do yourselves proud. The world is watching; teach them how it's done. ;-)

SCRIBE,SCRIBE,EBIRCS,EBIRCS

2006-06-07T22:48:00.000-05:00

Hey all, it is i todays scribe NIKKI!! Yeah today we didnt dooo tooo much all we did was had a quiz and were assigned questions, i will be posting the questions from the Quiz and tellin u about wat we will be doing tomorrow k KOOL :)!!!!

QUIZ 1 on Sequences and Series

1.Write the first 3 terms of the sequences generated by each of the following functions:

(a) f(x)=4x-3 (b) g(x)=2X3^x
4(x-3)=1 2X3^x=6
8(x-3)=5 2X3^2=18
12(x-3)=9 2X3^3=54
1,5,9 is the answer 6,18,54 is the answer

2.Write the function that generates each of the following sequences:

(a) 1,-2,4,-8,16... (b) 10,5,2.5,1.25...
Tn=T1-2^(n-1) Tn=T1(1/2)^(n-1)

3.Consider the following sequence: 3,6,12,24...

(a) Find the 8th term of the sequence.
n Min= 1 The 8th Term is 384
u(n)=u(n-1)*2
u(nMin)={3}

(b) Find the Nth term of the seqence.
Tn= T1(n-1)*2

4.An army is marching in a triangular array: 1 soldier in the first row, 3 in the second row, 5 in the third row, 7 in the fourth row. etc.

(a) If each soldier requires 4 feet of space in a row, how long is the 53rd row?
nMin=1 The 53rd row is 105
u(n)=u(n-1)+2 To get the length of the 53rd row u take 105 and multiply it by 4.
u(nMin)={3} 105*4=420 Ft.

(b) What is the total number of soldiers in rows 22 through 87?
nMin=1 u(1,87)-->L1
u(n)=u(n-1)+2 sum(L1,22,87)
u(nMin)={3} =7128

I hope all of my answers were correct cause i didnt do too wellon the Quiz :)!!! BUt yeah thats wat we did for the Quiz it wasnt long but it was spur of the moment!!!!

Now for homework we have to do Pg.295 #1-7!!!!!!!!!
For tomorrows class we will be taking up Design and Measurment cause we never really learned it in class n thats for tomorrow!!!!
A few tips for the Exam:
1) Make sure you lay out your exam in the outmost detail, like dont forget a degree sign or anything like that because those can cause u to lose critical marks on the exam!!!!
2) For our exam on the 13th it will be on Design and Measurment and on Sequences!!!1
3) Dont forget to read all your homework and study paper at least 6 times through because your going to need all your work to be engraved into your memory!!!!!
4) STUDY STUDY STUDY STUDY STUDY STUDY!!!!!!!!!!!

Well thats all for now i hope you take these tips into consideration and dont forget exams are only next week so take this weekend to prepare!!!!!!!

ps sorry for the late scribe post :)

Next Srcibe will BEEEEE!: SHANE

Scribe: Sequences

2006-06-06T20:42:00.000-05:00

Sorry guys my scribe will not be up till tommorow because im not sure if my answers are right. SORRY for those who are waiting. Ill post the scribe as soon as i can tommorow promise. :b

Fractals

2006-06-05T23:13:00.000-05:00

hi everyone,
This scribe is for Monday, june/05/06. We had only one class and the subject that was taught is about fractals.
We started off with the following diagram.

Fractal:A mathematically generated pattern that is reproducible at any magnification or reduction.

In this diagram the green square is twice as big as the blue one. And the blue one is twice as big as fuchsia and so on........ .

The question is wether these triangles ever pass the edges of the paper.

Answer: If we go to infinity it will cross the paper.

And a sequence is created by the following formula.

(n-1)

tn=t1(r)

(n-1)

tn=8(1/2)

Area

64+32+16+8+2+1/2

It is a geometric sequence they have common difference. Some times the first number in this case 64 does not fit the sequence so we start with second number 32.

u(1,100)store in (L1)

HOME WORK IS ON THE BLOG

Next scribe: Nikki (if not avaiblable then shane)

Fractal Homework

2006-06-05T13:30:00.000-05:00

Draw the following fractals. Be sure to save your drawings and bring them to class tomorrow. Draw them centered, one fractal per page.

(1) Draw a rectangle that measures 12 cm by 8 cm, and shade the inside of the rectangle. Construct the midpoints of each side of the rectangle, and then draw a quadrilateral by joining these points. Shade the quadrilateral white. Now continue the process by finding the midpoints of the quadrilateral, drawing the rectangle, and shading it the same colour as the first rectangle. Draw six generations. (The initial rectangle is the first generation.)

(2) Create a fractal that begins with a large square 20 cm on each side. Each pattern requires that the square be divided into four equally sized squares, that the bottom-left square be shaded, and the process continues in the upper-right square. Repeat the process four times.

(3) Create a fractal where a square is inscribed in a circle. The diameter of the original circle is 16 cm. Shade the area between the circle and the square. Inscribe a circle inside the resulting square, and then inscribe a new square inside that circle, and shade the area between the new circle and square. Repeat this process three times.

Fractal Homework

2006-06-05T13:15:00.000-05:00

THURSDAY JUNE 1ST CLASS

2006-06-02T10:27:00.000-05:00

Two weeks before the exam. This is how today’s class began. Mr. K discussed how the exam is going to take place, that we going to do two question in the mac lab. And correct me if I am wrong. He also said the question are based on "design and measurement" and "Sequences". If you missed today’s class, then you missed Mr. K dripping Words of Wisdom. I am going to share little of his dripping words of wisdom. He said " You can't just walk out of the class if you wanted to. To walk out of the class, you have to walk half the distance from the exit (door), then again half of that, then half of that. Etc.... it also got something to do with sequences. The second thing was an ordinary man and his donkey. mmm. I think I better keep the rest to myself. i have shared enough. To get more of Mr. K dripping words of wisdom comment on the blog page, or if you are Mr. K student ask him in class tomorrow. Ok lets get business started. The notes are as follows:

Sequences & Series

Sequence: an ordered list of numbers that follow a certain pattern (or rule).

Series: the sum of numbers in a sequence to particular term in the sequence.

Example: Given the sequence: 3, 6, 12, 24, 48, ............

the series S5 denotes the sum of the first 5 terms:

S1=3 thus we have the series:
s2= 3+6= 9 3,9,21,45,93...
s3=3+6+12=21
s4=3+6+12+24=45
s5=3+6+12+24+48=93

in general, Sn denotes the sum of the first n terms.

Arithmetic Sequence:

i) Recursive Definition: an ordered list of numbers. Generated by continuously add a value.
(the common difference). to a given first term.
ii) Implicit Definition: an ordered list of numbers in the list is generated by a linear equation.

Common Difference: (d) i) the number that is repeatedly added to successive terms in an arithmetic sequences.
ii) From the implicit definition it is the slope of the linear function.

To find the n^th term in an arithmetic sequence.

tn= t1 + ( n - 1 ) d tn is the n^th term
t1 is the first term.
n is the rank of the n^th term.
d is the Common difference.

Geometric Sequence:

i) Recursive Definition: an ordered list of numbers generated by continuously multiplying a given first term by a particular value (common ratio)

ii) Implicit Definition: an ordered list of numbers where each number in the list is generated by an exponential function.

Common Ratio: (r) i) the number that is repeatedly multiplied to successive terms in a given sequence.

Geometric Sequence:

ii) from the implicit definition it is the base of the exponential function.

to find the n^th term in a geometric sequence.

tn= t1 (r) ^(n-1) tn is the n^th term
t1 is the first term
n is the Rank of the n^th term.
r is the (common ratio).

just don't forget that you can't have a series without a sequence.

Convergence and Divergence

When |r| > 1 the sum of an infinite geometric series Diverges. i.e. grows without bound.

When |r| <>

** Reminder that after the exams we do have classes, and we also going to do a pod cast. Basically it is kinda interview, don’t get scared. it not another exam. Mr. K is going to ask us couple of question, actually two questions to discuss. 1. What is something you would wish you would do better.
2. What thing would remind you of this class, that’s going to help you in future, studies i.e. university, and finally any closing comment.

Scribe

2006-05-31T22:22:00.000-05:00

All right, so I guess it's up to me to break the tie of hall of famers in a row. It's never a good idea to leave this sort of stuff up to me. :P

The first thing we did in this morning's class was hover around Mr. K's computer and look at our sexy wiki. Remember guys, our constructive modification + significant contribution are due this ~~Friday~~MONDAY. Mr. K gave us a bit of an extension (again!) because he's a really cool teacher. [/suckup] Seriously, thanks Mr. K.

Then we got onto sequences. Mr. K wrote two examples on the board for us to solve.

We got to use our calculators today, I am not sure if they were used the other day. With that said, make sure the calculator is in sequence mode!

-All you have to do is press mode and arrow over to seq. Then yeah, hit enter.

Question the first:

My cat is sick. His name is Little John and he has a cold. The vet has given him some medicine. Each day he gets a pill with 35 mg of medicine. His body eliminates 25% of the medicine each day and then he gets another pill.

a. How much medicine will be in his body in 5 days?
b. Will the amount of medicine in his body stabilize? How many days will it take and how much medicine will be in his body?

Answers:

a. After 5 days, there will be 106.77 mg of medicine.
-In the second column, the reason you multiply by .75 is because Little John's body eliminates only 25% of the medicine, leaving the other 75% in his body. Then, when he has another pill (35 mg), it's added with the medicine still in his body.

-.75 represents what you multiply U by, U being the term. N is the column. I believe so, anyway. Also, to get to that screen all you have to do is press Y=.

-I really like this, because you can go up as many terms as you'd like and then store them into one of the lists. 1 represents the first term, and 50 is the term I chose to go up to. I would assume you guys know all about this, as we did it quite a bit with periodic functions. The only difference is that we have it in sequence mode and we put the u. Ohh, to get the U it's 2nd mode 7.

b. The medicine does stabilize after 36 days, at 140 mg.

-This represents the first week of medication.

-This is where it stabilizes. Hurray! :D

- This is the graphed data, as you can see, it stabilizes

Question the second:

A small forest pf 4000 trees is under a new forestry plan. Each year 20% of the trees will be harvested and 1000 new trees are planted.

a. Will the forest ever disappear?
b. Will the forest size ever stabilize? If so, how many years and with how many trees?

Answers:

-.80 is what you multiply by the first term, as 20% is being cut down, leaving the other 80% in tact. 1000 is what we'd add on to what we're left with after the first year. 4000 is what we started with, as it's stated in the question.

-See the difference? The "ipart" means that we won't have answers with decimals. We can't have part of a tree.

a. As long as they're replanting, the forest won't disappear. In fact, the amount of trees inceases before it stabilizes.

b. The forest size does stabilize at 27 years with 4996

This afternoon:

We worked in our textbooks this afternoon, starting on page 264. I'll go over the first three questions, as I think that's where the majority of the class was by the end of class. I could be wrong, but too bad. :P

Une:
1. Use a calculator to generate the following sequences and find the indicated term.
a) 5, 7, 9, 11 ...; the 14th term

nMin=0
u(n)=u(first term)(n-1)+2 (The sequence goes up by 2)
u(nMin)={5} (Our sequence starts at 5)

-To get the 14th term you go to the home screen, u 2nd function, 7. Then (14) ... You could do (1, 14) ... but the first way is faster. Oh yes, and the answer is 31.

b) 5, 15, 45, 135, ...; the 12th term

nMin=0
u(n)=u(first term)(n-1)*3(multiplying by 3)
u(nMin)={5}(Again, our sequence begins at 5)

- The answer is 885735. To get the answer you do the same thing you'd do for the first problem, except instead of 14 it'd be 12. I'll spare you the play by play from here on. ;)

c)3.7, 2.3, 0.9, -.5, ...; the 15th term

nMin=0
u(n)=u(n-1)-1.4
u(nMin)={3.7}

- The answer is -15.9

d) 2.4, 3.6, 5.4, 8.1, ...; the 9th term

nMin=0
u(n)=u(n-1)*1.5
u(nMin)={2.4}

- The answer is 61.51

e) 12, 3, .75, .1875, ...; the 10th term

nMin=0
u(n)=u(n-1)/4
u(nMin)={12}

- The answer is .000046

Deux:
A salesperson at a car dealership receives a base salary of $275 per week, plus $50 for every car sold. Each week, the salesperson sells one more car then the previous week. In his first week, he sold one car.

a. Create a graph to show the salesperson's earnings each week.
b. Use your graph to determine the week in which earnings will exeed $1000, if the pattern continues.

-This table is simple enough, all you do is add the base salary to the money made for each car sold. Week 15 is when more than $1000 is made.

c. solve the problem using another method.

nMin=0
u(n)=u(n-1)+50
u(nMin)={275}

-Quit to the home screen.
u(1,15)
{325 375 425 475 525 575 625 675 725 775 825 875 925 975 1025}

Trois:
A colony contains 100 ants at the start of May. Suppose the population doubles every month and no insects die.
a. How many insects are there at the beginning of July?
I did this in my head. May-July is a span of 2 months. There will be 200 at the beginning of June, and therefore 400 at the beginning of July.
b. How many insects are there at the beginning of September?
Again, did this in my head. July-September is again, a span of two months. We had 400 insects at the beginning of July, therefore by August we would have 800. This means that by the beginning of September we'd have 1600 insects.
If you wanted to, you could do 100x2⁴. That would give us 1600 as well.

Two terms to keep in mind are:
Arithmetic Sequence:
There is a common difference between terms. For example; 3.7, 2.3, .9, -.5. The common difference is -1.4 as you're taking -1.4 from the one term to get the next, or adding 1.4 to get one term from the previous.
Geometric Sequence:
There is a common ratio between terms.
For example; 2, 4, 8, 16. The common ratio is 2, as you're multiplying by 2 to get the next term, or dividing by 2 to get the previous term.

And finally:
Our homework is finishing up Checking Your Skills on pages 264 through 265.

The scribe for tomorrow is: Mr. M. Sherif~~sucker~~!

Scribe Post - 05/30/06

2006-05-30T15:52:00.000-05:00

Sequences
The Scribe Post - May 30, 2006

- We only have one class today, since Caitlin wasn't in our class, Stephanie decided that I should go instead but anyways. Here is what we did.......

Mr. K directly putted up 4 Sequences while the announcers are speaking. He asked.

Find the next three Terms.....

4, 7, 10, 13, ?, ?, ?

3, 6, 12, 24, ?, ?, ?

32, 16, 8, 4, ?, ?, ?

2, 3, 5, 8,12, ?, ?, ?

The Answers.....

4, 7, 10, 13, 16, 19, 22

3, 6, 12, 24, 48, 96, 192
32, 16, 8, 4, 2, 1, 1/2
2, 3, 5, 8, 12, 17, 23, 30

How did we find out?

It is actually easy to find out, what is the next number of these values, IF YOU HAVE COMMON SENSE; we're not actually talking common sense in here, but I would like to say we're talking about math and here how it goes.

We see in 4, 7, 10, 13, 16, 19, 22 this values have all the same differences, and the difference between this numbers is THREE ( 3 ). It is easy to see that 3 is the difference, there is also another way to do it.

One of the way we can solve the number is by 3 (The Differences) multiply by the numbers right up the value and add 1.

The right equation for this Sequence is tn = n3 + 1 This is the RULE.

If you would to find out what is the next term without finding the TERM BEFORE THAT, this is what we called the RECURSIVE DEFINITION. The other definition for that is ..... Do the same thing to get the next answer is the ReCursive Definition.

For EXAMPLE, if you would like to find the 7th term without finding out what is the 5th, and the 6th terms. The equation for that is........

We need to put in the First term then we add the Number of Columns then minus 1 from it since there is only 6 in between and in between that's the differences and the Difference for this value is 3.

TO SOLVE THE EQUATION BY FINDING THE TERM 7...this is how is goes.

T7 = 4 + (7-1) 3

--- = 4 + (6) 3

--- = 4 + 18

--- = 22

( The SEQUENCE THAT HAVE A COMMON DIFFRENCE IS WHAT WE CALLED ARITHMETIC, and one example is right above*)

FOR THE NEXT SEQUENCE.

3, 6, 12, 24, 48, 96, 192

(This sequence is what we called GEOMETRIC, by having COMMON RATIOS in all the values*)

This is how we solve the equation, by finding the term without looking for the number before that value.

Tn = the term you are looking for

T1 = the first term

r = the ratio

n-1= the number of columns minus 1

T7 = 3 (2)^7-1

T7 = 3 (2)^6

T7 = 3 (64)

T7 = 192

The last two Sequence are also GEOMETRIC, because they don't have a common differences.

Then later on that period Mr. K told us about the Implicit and Explicit.

Implicit is a cuirrent inside suggestion

Explicit is a high current outside.

There is one more way we can find it, the LAST ONE IS IN OUR CALCULATOR. First we need to check if our mode is in SEQUENCE, so CLICK MODE, Go to the 4th row then choose SEQ.Then we enter our information in our Y= screen, and then we need to check our window for a better view.

To generate:

Go Second Quit

Enter in your calculator:

u by 2nd, 7 the bracets (First Term, and the up to what term would you like to see)

Then we store it in our L1.

MR.K also SAID THAT ADD UP SEQUENCES IS CALLED SERIES.

I don't know if I'm doing good at this scribe post this time, damn I shouldn't have wait for a day to fix this up now my memory is kind of loosing it.

SCRIBE: Goodbye Periodic Functions, Hello Sequences!

2006-05-29T17:13:00.000-05:00

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 =)

Ma blogging and ma unblogging(periodic functions)

2006-05-29T10:36:00.000-05:00

This unit so far has given me a big headache, the problem with this unit is that it makes sense when the teacher is doing a question but later when i am trying it its hard to find a way to solve these kind of questions specially the problem ones. Almost every one so far is saying that the unit went easily and i agree with them but still i have difficulties in understanding the word problems. I hope someone would listen to me and agree to postpone the test.

CHEERRSSSS

B.O.B. - Periodic Functions

2006-05-29T01:19:00.000-05:00

This unit was fairly easy. From converting degrees to radians and vice versa, to knowing the sinusoidal function. Like always, problem solving is the toughest part in this unit since it can be very confusing if you don't read the question carefully. What's also sort of confusing is figuring out the horizontal shift on the sinusoidal axis. Hopefully I'll do okay on the test. That is, unless I somehow blank out. But I'm sure everyone else will do okay on the test.

BOB

2006-05-29T00:21:00.000-05:00

almost forgot! ha, well test is already tomorrow, and so far, this units been okay...it was easy in the beginning. like converting degrees into radians and radians into degrees, i understood that. i also understood how to look at a graph and find the y= equation from it. also i understood how to graph with the given equation. i thought that was okay, then when it came to the applying it to problems. i understood them when we did them in class, but trying the homework was kinda tricky. kind of different, but i did enjoyin figuiring out the problems in our group activities. welps, its late...good lucky everyone!

-CORRIE

BOB

2006-05-29T00:11:00.000-05:00

Aight, all i have really got to say about this unit is that its basically all calculator functions. I found the unit pretty easy. I aslo found that the unit went by super quick. Thats probably because it did. The only problem that I think i may have a slight problem with drawing the graphs. I understand it pretty well but some times i make stupid mistakes. If I avoid those mistakes I think I will do pretty well on the test.

Cya,

3D Tic-Tac-Sunday!

2006-05-28T22:22:00.000-05:00

Better late than never. ;-)

I missed the Sunday Funday post last week and I really don't want to make that a habit so this week I'm posting two versions of this week's game ... 3D Tic-Tac-Toe. Here are the instructions for the game pictured on the left (may take a little while to load) ...

The object of 3D Tic Tac Toe is to get four in a row horizontally, vertically or diagonally on one plane or across all four planes.

You are Red, the Computer is Blue. In the first game, you go first. In subsequent games, the loser goes first. If the game ends in a tie, whoever went first will do so again.

The moves of the game are notated on the right. Moves that threaten a win are noted with an *. The Computer plays a strong, but not unbeatable game. Good luck!!!

These are the instructions for the game on the right ...

This game is basically a 3D tic-tac-toe, except that the rules have been changed to keep the first player from winning all the time. Here you have to form two rows that meet at a right angle (in the shape of an "L").

Have Fun!!

BOB

2006-05-28T22:19:00.000-05:00

the periodic functions unit for me was half review and half learning. there were some things in the unit that i already knew how to do because i've done it before in other classes. and the new things that i learned were mostly calculator functions. hopefully i do well on this test. make up for my last test. goodluck to everyone else tomorrow.

In Depth Analysis of the Friday class. Applied Math 40s

2006-05-28T12:30:00.000-05:00

I hope u guys didn't have any problem with thinkfree online beta. also if you can't get the files on there, after u go to NEW DOCS. try the search box. on top of the screen (right) side. search as: contruction1, contruction2, Contruction 3, Contruction4. and Friday.doc. or scroll down the page and look for my name, as Mr. K say: theres many ways to skin a cat, but don't skin a cat, cau'z thats cruel. back to business.

ok. first you have to calculate the Area of driveway, you can do that as follows:

Option 1: devide into triangle & trapezoid

Area 1 of driveway ( Rectangle)

Area: 98' by 18'----- 98*18=1692ft^2

Area 2 of driveway ( trapezoid)

((16+21)4)/2=74ft^2

OR you can devide into rectangles and triangle:

Rectangles:
A: 73'*18'= 1314'

B: 5'*18'= 90'

C: 22'*16'= 352'

Triangles:

D: (4*5)/2=10'

Total Area of driveway= 1766ft^2

Concrete & Gravel ( first method)

Then use the area to calculate volumes & cost. change inches into ft. 12''=1 ft

Example : 12''---- 12/12= 1 ft.

For first method as follows: For second method as follows:

Gravel : 1 ft Limestone: 1.00ft Lime stone: 1.00ft

concrete:0 .33ft sand: 0.29ft sand: 0.29ft

concrete: 1.33ft

paving stone: 1.50ft

To calculate volume changed ft. into cubic ft. then cubic ft. into cubic yard to calculate cost.

First method volumes & Cost: Gravel= 1766*(12/12)= 1766ft^3/27 = 65.41 yd^3

Concrete=1766(4/12)= 588.67ft^3/27= 21.80 yd^3

Volume excavation= gravel + concrete= -------------------------------------= 87.21 yd^3

Gravel = 65.41 yd^3 ( $12.00/yd^3) = $784.92

Concrete= 21.80 yd^3 ($130.00/yd^3) = $2834.00

Excavation= 87.21yd^3($60.00/yd^3) = $5232.60

Subtotal:----------------------------------------------------------------------= $8851.52

Taxes: concrete and gravel= $2834+$784.92= $3618.92*14% =$ 506.65

Excavation $5332.60 * 7% ----------------------------------------- =$ 366.28

* Cu'z, only GST is calculated for excavation

Total Taxes= $ 872.93

Total cost= subtotal plus taxes------------------ Total Cost= $ 9724.45

Paving Stones (Second Method)

Second method Volume & Cost: Paving Stone = 1766*(2.5/12)= 367.92ft^3/27= 13.62 yd^3

Lime Stone = 1766*(12/12)= 1766ft^3/27 = 65.41 yd^3

Sand= 1766*(3.5/12)= 515.08ft^3/27 = 19.08 yd^3

Volume Excavation= volume lime stone + volume paving stone + volume sand = 98.11 yd^3

Paving Stone= 13.62 yd^3 change into ft^2 = $4730.85

Lime Stone= 65.41 yd^3($15.00/yd^3) = $981.15

sand= 19.08 yd^3 ($14.00/yd^3) = $76.32

Excavation= 98.11 yd^3($60.00/yd^3) = $5886.60

Subtotal= $11314.92

Taxes: (cost sand + lime stone + paving stone) * 14%--------------------------- =$ 759.97

(Excavation * 7%)------------------------------------------------------ = $412.06

Total Taxes= $1172.03

Total cost= subtotal plus taxes Total Cost= $12486.94

*** Therefore paving stones cost more by---------------------- $1286.94-9724.45= $2762.50

That's All Folks. have good weekend next scribe i will pick in class on monday.

NOTICE

2006-05-28T09:32:00.000-05:00

i have tried to upload the files, it keep saying error uploading. which sucks. but no problem. i saved the file on thinkfree. which is the best ever online office on earth. it works. really it works. so go to www.thinkfree.com and click on NEW DOCS. then the files class is all there. i did spreedsheet part. click on Contruction1, Contructions2, Contruction3, Contruction4. and if you need to Get the questions part Click on Friday.doc, which will explain what went on friday class. i will try to do on paper explaining how all the method we used to get those answers. brb.boys and girls, or should i say ladies and gentlemen.

Friday's Post DMCI Applied Math 40s.

2006-05-27T16:10:00.000-05:00

I am trying here to post the scribe. but i am having trouble uploading files. from paint and microsoft word, it is a long scribe, so it will take a while.

Bob on Periodic Functions

2006-05-26T09:38:00.000-05:00

On this chapter. we worked with formulas to solve problems. the main formulas that we have to know is DABC. which Y=AsinB(X-C)+D. the problems where easy to at the beginning as we only had to change degrees in radians, and vise versa. but when we get to solving real problems using DABC. things where little hard. but hope the test won't be that hard. thats all folks.

B.O.B(Ivy 05/25/06)

2006-05-25T23:06:00.000-05:00

The Periodic Function Unit (B.O.B)

hmmm....This unit for me at first was easy..but when we got to this problems now I'm in trouble...I didn't find A,B,and D hard to get but C is. About C first I was cool with it, by doing the sketch by looking at the formula y=AsinB(x-C)+D and by converting formula to sketch it was cool. I also like doing the converting Radians to Degrees and the other way. I really do need to review, like whoa...~~for the last units we have, I never did study and I ended up failing the tests, and I really do feel bad about it~~, one thing is I also keep hustling, and just let my studies go for a passing mark, oh whatever.. but yeah, need to focus this is the last time I'm going to study math.. ahehehehe. Oh. Yeah..~~I also feel bad about missing the last class this afternoon~~

Scribe: Periodic Functions Problems

2006-05-25T17:13:00.000-05:00

Today we had 2 periods and we were supposed to have a pre-test and we had but not the actual pre-test instead we answered 2 problems as our pre-test. So whoever missed the class here are your pre-test.

We did two problems and here is the first one:

LIFT OFF!!!

When a spaceship is fired into orbit from a site such as Cape Kennedy (which is not on the EQUATOR), it goes into an orbit that takes it alternately NORTH and SOUTH of the equator. Its DISTANCE FROM THE EQUATOR is approximately a SINUSOIDAL FUNCTION of time. Suppose that a spaceship is fired into orbit from Cape Kennedy. 10 min. after it leaves the Cape, it reaches its farthest distance NORTH of the equtor, 4000 km. HALF A CYCLE later it reaches its farthest distance SOUTH of the equator (on the other side of the Earth) also 4000 km. The spaceship COMPLETES an orbit once EVERY 90 min. (completes a cirlce around the world).

Let 'y' Be the number of kilometres the spaceship is north of the equator (consider distance south of the equator to be negative). Let 't' be the number of minutes that have elapsed since liftoff.

Tip: When trying to answer this kind of question try to write what you are given.

- 4000 km. (max and min) NORTH and SOUTH (this is the "A" )
- 10 min., from CAPE, it reached the farthest NORTH
- 90 min. to COMPLETE A CYCLE (this is the "B")
- HALF A CYCLE (90/2 = 45) it reached the farthest SOUTH (it took 45 min. to reach SOUTH from NORTH)
- EQUATOR as the SINUSOIDAL AXIS (this is the "D")

A.) Sketch a complete cycle of the graph of y versus t, and write the sinusoidal equation expressing y in terms of t.

This is how I got the C: (refer to the graph)
In 10 min. the spaceship reach the farthest NORTH and 45 min. to reach the farthest SOUTH from NORTH.
10 + 45 = 55 (half circle)
the middle number between 55 and 10 is 32.5
10 + 55 = 65 then 65/2 = 32.5 (quarter Circle)
now since I know the quarter circle
32.5 - 10 = 22.5
10 - 22.5 = -12.5 (C)

A = 4000 (max and min range)
B = 2(3.14)/90 (Period) (3.14 = pie)
C = x - -12.5 (Starting point)
D = 0 (Sinusoidal axis)

y = 4000sin((2*3.14/90)(x - -12.5))+0

window: Xmin=-20 Xmax=100 Xscl=10 Ymin=-5000 Ymax=5000 Yscl=1000

B.)Use your equation to predict the distance of the spaceship from the equator when:

Since we didnt talked about this in class here is what I came up.

Solution:(use calculator Ti-83)
Put in the equation "y = 4000sin((2*3.14/90)(x - -12.5))+0)" on "Y="; then "GRAPH"; then "2nd FUNCTION" "TRACE"(CALC); then choose "VALUE"; then plug in whatever the number is asked.
window: Xmin=-20 Xmax=100 Xscl=10 Ymin=-5000 Ymax=5000 Yscl=1000

i.) 25 min
ans.= 2000 km.

ii.) 41 min.
ans.= -2236.77 km. ( - = going south)

iii.) 24 hours. (adjust Xmax window setting = 1500)
24 x 60(min.) = 1440 min.
ans. 3064.17 km.

C.) Calculate the distance Cape Kennedy is from the Equator by solving for Y when t = 0

Solution: same as what I did in B.
Plug in 8 as your x value
ans. 3064.17km

Here is the second problem now:

EAST COAST HARBOUR

On May 3rd, the DEPTH of the water in an east coast harbour will vary over time as described by the equation:
"y = 2.3sin0.506(x+3.1)+2.8"
where x represents the time (hours), and y represents the depth (metres) of the water.
The time at x = 0 is midnight of May 2nd, and x = 12 is noon of May 3rd.

Since we are given the equation already:
A.) What are the minimum and maximum depths of water in the harbor?
D + A = MAX
2.8 + 2.3 = 5.1

D - A = MIN
2.8 - 2.3 = .5

B.)What is the average depth of the water in the harbour?

- you can refer to the SINUSODAL AXIS = 2.8
- or use this way (max + min)/2 (5.1 + .5)/2 = 2.8

C.)How much time is there between two high tides

Write the equation "y = 2.3sin0.506(x+3.1)+2.8" in "Y="; then "GRAPH"; then "2nd FUNCTION" "TRACE"(CALC); then choose "MAXIMUM";
Then "left bound and right bound and guess"; The X coordinate is the time
x = 12.4217 since there are no decimal hour: .42 X 60 = 25

window settings: Xmin=-2 Xmax=(30 or 50) Xscl=6 Ymin=-1 Ymax=6 Yscl=6

ans. 12:25 p.m. 12 hours and 25 minutes (from 0 hours)

D.) What is the depth of the water at 8:00 AM?

With the same equation; press "GRAPH"; then "2nd FUNCTION" "TRACE"(CALC); then choose "VALUE"; then plug in 8 for x
ans. 1.377

E.) At what time in the afternoon is the water at it's lowest? How deep is the water at this time? (This is the time that little Ziggi likes to go kayaking in the harbour because there are no large boats moving at this time.)

With the same equation; put the .5 (lowest) in Y2(or in any Y); then "GRAPH"; then "2nd FUNCTION" "TRACE"(CALC); then choose "INTERSECTION"; it'll will give you the x coordinate which is
ans. 6.21 ; .21 X 60 = 6:12 am, 6:12 pm. etc...

D.)A commercial boat requires at least three metres of water to more around the harbour. Describe how you would determine when it is safe for the boat to operate in the harbor.

With the same equation; put a the 3 (required level) in Y2(or in any Y); then "GRAPH"; then "2nd FUNCTION" "TRACE"(CALC); then choose "INTERSECTION"; it'll give you Y coordinates. In able for the boat to operate he should ONLY operate in hours in the blue line.

So that all folks. Sorry my scribe is too long. Anyways gotta sleep and Mohamed you are the scribe for tommorow.

B-O-B ; Periodic Functions

2006-05-24T19:50:00.000-05:00

So here's my blogging on blogging for Periodic Functions. I remember this unit from last semester but I never did like it. Although I'm somewhat comfortable with the concept..I don't think I feel too strongly about the word problems. I can figure out parameter D, A, and B. But C always seems to stump me at times. Figuring out parameter C is probably my only problem right now. Hopefully someone can show me before Friday?!

SCRIBE

2006-05-24T17:19:00.000-05:00

Today we only have one period, the unit is done and we are going to have a pre-test on thursday and our unit test would be on friday ... but before anything else here is what happened on our class today.. We did couple of problems regarding on applying periodic functions on a data collected..

*Problem Solving
---> Based on the data collected over the last 30 years, the average high temperature for regina are shown.

Part I
A. sketch the graph
B. find the equation for the data by approximating values for each parameter
A,B,C and D
C. Use your function to calculate the temp. on
Apr. 15th (using calculator)
Part II.
A. Find the equation of the data(using table of
values)
B. Use your equation to calculate the temp. on
Apr. 15th
C. Why is the value different from the one
above?

Part I

A.

Equation: Y = 18.65 sin[2ii/ 12(x-3.75)] +7.65
B.) A = 18.65
.....B = 2ii / 12
.....C = 3.75
.....D = 7.65

C.) Using the 2nd calc.-->VALUE button in the Ti83 calculator we found the temp on April 15(4.5) is 14.78 degrees celsius.

Part II

A. using these values from the list: press STAT>CALC ^ SINREG enter 2nd L1, 2nd L2,Y2, press VARS> Y-VARS 1 Function enter Y2
Equation: 19.6 sin (.48X - 1.82) + 7.33
B. Using 2nd CAlC Value X= 4.5 the temp. for Aprill 15 == 14.78 degrees celsius

Group Work Problem

*Cottage owner Brad measures the depth of the water in his dock 10 times during the course of one day. The water keeps changing because of the tides. The times are based on the 24-hour clock, and written in decimal form (i.e 5:45AM is 5.75 hours) The charts shows the times and the water depths A. Sketch a rough graph and write the appropriate equation for the values indicated.B. Use the calculator to find the equation of the values.
......Store the TIME and DEPTH values in L1 and L2. Then press STAT > CALC ^ SinReg Enter...SinReg L1,L2,Y2...then the equation is .................Y = 0.814 sin(X - 0.862) + 3.25

C. What is the depth of the water at 23:00 hours(11pm)?
......Graph the equation in the calculator then press 2nd CALC, Value 0f X = 23 Enter
......depth at 23 hours is 3.125 meters
D. What is the median depth of the water?
16 m + 5.75 m / 2 = 10 .88m

next scribe is jesse

* unit's almost done.

2006-05-23T20:04:00.000-05:00

Well, I have just looked over everything that I have to include into this scribe post for today and well....theres alot! So bare with me, sorry if its late, if i missed anything, or did anything wrong, cause i'm still learning myself. First off, we started the week off with 2 classes.

In the first class we went over a equation that we worked on last week.

So the equation was y=-3sin4(sinx-π/8)-2
On the graph here I have shown the y=sinx.

So when drawing out this equation you'd want to first look at D and A of our equation. D and A of our y=AsinB(x-C)+D formula. Thats shown in red, above.

From our equation we see that D is -2, and D is our sinusoidal axis, that is were it shows if the graph shifts either up or down x units. -2 means, that our graph shifts down 2 units. ( as shown above).

Now we look at our A, which is our amplitude , it shows us how far away the max. and the min. are from the sinusoidal axis. From our equation our A is -3. With the negative (-) sign in front of the 3, this means that our graph starts from the minimum. So you go down 3 units. That shows the distance from the minimum to the axis.

The next thing we look at is B, and in our equation this is 4 . So, now we need to look for the period, to do this we taken the formula 2π/B.
period=2π/B
=2π/4
=π/2 <- makes one wave.

So now, that we've got D, A, and B down, C is left. C is just where we have to shift our graph left or right on the sinusoidal axis. It shows that our C is -π/8. So we take our graph and shift it right π/8 units.

So thats, that. After that he had assigned us two problems to do at the spot. One, we were given the equation and we had to graph that. Then the second problem, we had a graph, which we had to find the functions, A, B, C, and D. And also, write the equation out for that graph. I'm not going to bother putting them up on here, because theres so much more I have to do, but if anyone does want to see the two equations, just leave a comment or something to let me know, and i'll make sure to post them up.

-----------------------------------------------------------------------------------------------

2ND CLASS

So if anyone missed class this afternoon, we wrote some more in our dictionaries. Here it is.

Applications of Periodic - an example

A ferris wheel has a radius of 25 meters. It;s center is 26 meters above the ground. it rotates once every 50 seconds. SUppose you get on at the bottom at t=0.

a) graph your height above the ground during the first 2 minutes of the ride.
b) write an equation for the graph, showing heigh as a function of time.
c) find how high above the ground you are at:
i) 10 seconds ii) 20 seconds iiii) 60 seconds
d) find two times when you are 50 meters above the ground.

THE SOLUTION:
A) Draw a picture of the situation and then sketch the graph. It is also helpful to figure out the value of each parameter A, B, C, D.

1 m. above ground (min. height)

diameter is 50 m.

max. height is 51 m.

y = A sin B(x-C)+D
A=51-26=25 (radius)
B= 2π/50 [2π/period]
C=12.5 [starting point moved right 12.5, see graph]
D= 26
y=25sin[2π/50(x-12.5)]+2

The he just told us, if we wanted to find out for 2 minutes. We would just continue on with our graph, with the pattern. Yeah gets?!

------------------------------------------------------------------------------------------------

Then after our dictionaries, we got into groups and started to do an activity.

Pebble Round and Round
As tiy stio tiyr car at a traffic light, a pebble becomes wedged between the tire treads. As you start to drive, the pebble remains stuck in the tire tread, and the distance of the pebble from the pavement varies sinusoidally with the distance you drive. The period is, of course, the circumference of the wheel, and tghe wheel has a diameter of 24 inches.

(a) Sketch a graph of this function.

(b) Write the sinusoidal equation of this function.

y=12sin(2π/75.398)(x-12.50)+26

How we got this.
Circumference = 2πr
=75.398 or 24π
D= 12
A=12
B=2π/period
=2π/75.398
C=18.8495 or 6π

(c) Caculate the distance the pebble is from the pavement after you have driven 15 inches; 100 inches; 200 inches.

So you enter the equation y=12sin((2π/75.398)(x-18.8495))+12 into [y=] in your calculator.
Then you would now have to go to your homescreen so [2nd][MODE]. From there hit the [VARS] -> Y-VARS [Functions][1: Y1]

Once Y1 is on your homescreen, put in brackets (15)
Y1(15) = -9.30
Then, with (100)
Y1(100)=-1.04
Then, (200)
but it has to be (200)(12), dont know why?! Got lost there!

EEK! Kay, I don't know if im doing this last part right, Mr. K was in such a rush I couldnt really get it, something like that? Not sure. Sorry!

-----------------------------------------------------------------------------------------------

So, that was pretty much our day back from the long, long weekend! I hope you guys get this, its not the best, not 'hall of fame' material. It's okay, I just want this over and done with. So, PATRICK, your next scribe okay, make it a good one! =)

- CORRIE

LONG HOLIDAY SCRIBE POST

2006-05-19T23:12:00.000-05:00

( THE ABOVE DATA GOES IN TO YOUR DICTIONARIES)

The follwing questions were assigned as class work but i couldnot Solve any due to time shortage. For blood donors i will Put those quesions on.

Sketch Graph for Each of the Following Equation

a) Y=2Sin X-1 b) y= Sin(2X)+1 C)y=3Sin2(X-Pii/4)

HomeWork (238)

Try Questions(1,2,3,5,6,8)

And a reminder to Muxxi and Ivy:

Muxxi= Coffee

Ivy = Auocado

Corrie is Tomorrow's scribe( In case she is abscent Ivy will be the next scribe)

HAvE PATIECNE

2006-05-18T23:18:00.000-05:00

The Scribe post will be on Soon(Sat-Sun). For those of you who went for blood donation here is a brief description of what we did in class. we just copied down some notes in our dic. and did a few questions on how to graph equations. So have patience until the scribe post is on.Yup

SCRIBE!!!!

2006-05-17T19:47:00.000-05:00

Well then today was a one day class and the first thing we did were some quick DICTIONARY notes which were as follows:

Periodic Functions

Period: The "period" of a periodic function is a measure of how often the function repeats the same values.
For example: The period of the sin function. Y=sinX, is 2 pi.

Periodic: A function is periodic if it keeps repeating the same values.
Eg. Heartbeats on an EKG monitor.

Degree: A unit of measurment for angles. There are 360 degrees in a circle.

Radian: Another ("more natural") unit of measurment for angles. There are 2 PI radians in a circle.
Note: The radian arises from the fact that if you "wrap" the radius of any circle around its circumfrence, it will fit exactly 2 PI times.

Converting Degrees and Radians

A is an angle in degrees.
R is an angle in radians.

EXAMPLE 1: Convert 27 degrees to radians.

<<<(Note to everyone the 180 degrees cross each other out.)

EXAMPLE 2: Convert 7 PI/10 Radians to Degrees.

The Big massive circle that consists of 360 degrees is right here wit all ur angles and stuff (even tho steph already made one here it is again):

And now for my final magic trick i will be showing u a few of our basic SIN functions have fun with these and yeah have a good night!!!!!!!!! :)

Your basic SIN(x) function looks like the following picture:

You can get this image by setting your calculator to RADIANS instead of DEGREES. You go to your Y= screen the put in Y=sin(X) and u will get this beautiful image and it is the same thing as the other 4 i will show u so just watch and learn :)

Now we have the SIN(x)+2 function which looks like this:

The formula for this is: Y=sin(X) and then under this one u put Y=sin(X)+2.

Now the 2sin(x) function is as follows:

The formula for this is: Y=sin(X) and then 2sin(X)

The lighter line is 2 times bigger then the thick line.

Now here we have a -3sin(X) function:

The formula, as u would imagine, is Y=sin(X) and Y=-3sin(X)

And last but not least is the Y=sin(2X) function:

The formula for this is Y= sin(X) and Y=sin(2X).

ENJOY and love me for this cause i'm TIRED have a good night ya'll much luv!!!!!!

(>O_o)> .: Periodic Functions:. <(o_O<)

2006-05-16T18:26:00.000-05:00

The first class of math Mr. K gave us this questions to do.

Convert to Radicals: A) 105 B) 11 C) 450
Solutions:

A)

B)

C)

Convert to Degrees: A) (7*3.14)/6 B) 3.52 C) -2
Solutions:

A)

B)

C)

after that Mr.K gave us a chart ( I can't remember what we are ask to do for this one, but I think we are ask to graph this chart).

Instructions on how to graph.

1) press the "STAT" Key, in the L1 column put the numbers 1-12( 1-12 represents the months) and in L2 column put the hours of Sunlight.
2) Press the "STAT" Key again and then go to the "CALC" menu by pressing the right arrow key. Once in the "CAlC" menu press the up arrow key once and you'll see the "SinReg" Function, then press enter (Now in your main screen you should see a SinReg thing).
3)Now hit "2nd" ( second function) key and press "1" this will put your L1 column, then hit the "," then "2nd" "2" this will put your L2 column, add a "," again, then hit the "VARS" key and go to the Y-VARS menu by pressing the right arrow key once, then press the number 1 or pick the first one on the list. After that pick Y1 .( In your Main Screen you should have this:
SinReg L1,L2,Y1 )
4)Once you press enter, the calculator will do all the calculations for us and it will put it in the "Y=" menu.
5) turn on the plot 1 ( To turn on the plot one menu hit the "2nd" "Y=" then press enter twice.),Once the plot1 is on go to your "Zoom" menu then pick "ZoomStat" or press the number 9.
6) hit the "GRAPH" hey and the calculator will show you a picture.

If the picture didn't show up then you should go to the "MODE" menu and put it on RADIAN.

We learned a little about Sin function, a Sin graph looks like this.
The equation of this line is......I'm not sure if it's y= Sin (X) or y=A SinB(x-c)+D.
tomorrow our teacher will teach us more about this Sin thing.

The next scribe will be KHAN.

Scribe ; Periodic Functions

2006-05-15T19:27:00.000-05:00

Hello everyone =] So today we only had one class but we also started our next unit: Periodic Functions (circular functions). Mr. K started off the class by asking; Why are there 360° in a circle? After much discussion, we answered (Nick in particular) that it was because it can be divided evenly by many numbers:
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360.

But Mr. K also showed that the initially, the military put 400 gradiens into a circle. Most likely, they wanted 400 gradiens because 100° could be set per quarter. Although 400 can be divided evenly as well:
1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
..360 can be divided by many more numbers.

But another question was presented: Is there a natural way of measuring angles in a circle? And the answer being Radians. Mr. K showed on the board that the number of times that the radius will fit in a half circle is exactly π. And if you go around the whole circle, the radius will fit into it 2 π times. Radians have no unit, there's no particular 'measurement'. Here's a picture of what a circle would look like divided into radians.

As shown above, we can convert degrees into radians. Thus, radians is the natural way of measuring a circle. After we learned this, we tried a few simple problems that just dealt with converting degrees into radians: (making sure to show every step possible..)

40°/180° = θ/π
θ180/180 = 40π/180
θ = 2π/9

And then we started talking about how you can solve triangles from within the unit circle by using the pythagoreom theorem.

Also, when using the unit circle, the radius will always be 1, always. By the way; Pythagorous was incredibly ugly and thought that beans had souls..very interesting. haha. Anyway, back to math. You can actually convert that to a sinusoidal graph:

Also called a sine wave. Any graph that repeats = periodic. Which is exactly what this wave is (2π is the period). The period is described as the number of times it takes to repeat. This consists of a minimum, maximum and average. Also, it never goes past the max and under the min.

And thaaaat boys and girls was today's class ;) Oh and, tonight's homework is on page 216, number 1 to 7.

The scribe for tomorrow is R-E-I-G-N *have fuuuun!*

Scribe (Ivy-5/12/06)

2006-05-12T22:06:00.000-05:00

Today we have 2 classes.....

First class we finish everything that it needs to be done , and I guess most of us... didn't finish everything....hehe...

Second class.....we did this Personal Financial Assessment..it was kind of a test... if someone miss the 2nd class they better take the assessment..eyy..I guess i'm going to edit this later... need to go to work.. well I'mworking midnigts....

and next scribe will be STEPH.

Scribe

2006-05-11T19:45:00.000-05:00

First off I'd like to thank Dom for making me scribe and interrupting my evening by making me do this

Here we go, we had a group question again today, thats all.

Twins Are Not Always Alike

Amber and Angela, twin sisters, make the following investments for retirement. In both cases the financial institution pays 8.25% per annum compounded monthly.
Amber deposits $100 per month from her 20th birthday until her 30th birthday (121 payments).
After her last deposit, she leaves her money with the financial institution until her 50th birthday.
Angela deposits $100 per month from her 30th birthday until her 55th birthday (301 payments). (Remember, the payments are calculated for the end of the month)

(a) Calculate the value of each investment.
(b) What percent of the final value did each sister pay into the investment?

A)
Amber
TVMSOLVER
N = 121
I% = 8.25
PV = 0
Pmt = 100
FV = [Solve] = 18779.52
P/Y = 12
C/Y = 12

Then she lets it sit till shes 55

TVMSOLVER
N = 300
I% = 8.25
PV = 18779.52
Pmt = 0
FV = 146637.48
P/Y = 12
C/Y = 12

So she has $146637.48 when she turns 55 years old

Angela
TVMSOLVER
N = 301
I% = 8.25
PV = 0
Pmt = 100
FV = [Solve] = 99839.84
P/Y = 12
C/Y = 12

Angela has $99839.84 when she turns 55 years old

B)
Amber
(Payments X Number of payments)/Future Value = Percent of Total that was payed
(100 X 121)/146637.48 = 8.25%
Amber pays 8.25% of the final value

Angela
(100 X 301)/99839.84 = 30.15%
Angela payes 30.15% of the final value

Scribe

2006-05-10T22:27:00.000-05:00

Hi guys im your scribe today :P

Well today in the first class we did a group assignment on mortgages

Ex. Mrs. Jones, Mrs. Jones

Mrs. Jones has decided to buy a home. She requires a $65,000 mortgage. The mortgage interest rate is 7.75%, and she will repay the mortgage with monthly payments. She needs to decide whether she will select a 20- or 15-year amortization term. How much do her monthly payments increase, and how much money will she save if she chooses a 15-year term instead of a 20-year term? Would you advise Mrs. Jones to get a 15- or 20- year mortgage? Why?

Using the Tvm Solver we figure out both the 20year term and the 15year.

The 20 year mortgage

N = 240 (12*20)
I% = 7.75
PV= -65000
PMT = (Alpha Solve) = 528.7248824
FV = 0

P/Y = 12
C/Y = 2

The 15 year mortgage

N = 180 (12*15)
I% = 7.75
PV = -65000
PMT = (Alpha Solve) = 607.2865553
FV = 0
P/Y = 12
C/Y = 2

So you take the monthly payments we just solved and multiply it by the number of months in a year and then multiply it by the number of years.

(528.73*12*20) = $126895.20
(607.29*12*15) = $109312.20

So now we can figure how much interest the mortgages for the 20 and 15 year are by subtracting $65000 from each of the numbers we got.

So For the 20 year mortgage (126,895.20-65,000)= $61,895.20
And For the 15 year mortgage (109,312.20-65,000)= $44,312.20

So I would advise Mrs. Jones to take the 15 year mortgage payment plan if she can afford to pay the monthly payments. Because If she takes the 15 year mortgage plan she will end up paying $17,583.00 less in interest. (61895.20-44312.20) = 17583.00

In the second class we just did the work we were given earlier.

And some student named Pat made a discovery about our textbooks. Canadian mortgages by law can only be compounded semi-anually. So on your TVM solver C/P always = 2 when dealing with canadian mortgages.

Well thats everything we did.

Tommorows scribe will be Shane (haha)

Scribe

2006-05-10T00:03:00.000-05:00

Ahh, sorry guys, I didn't get home until a few minutes ago and realized I still had this to do. Damn you Muuxi, damn you :P (Kidding, kidding ;) )!!

We actually didn't do much today in class, just worked some more in our text book. At this point we should be well in to Page 178-179 (1-7) ... Unfortunately I've fallen behind a little. I hope you guys are up to par! There was also that investigation on page 184 I believe.

Mr. K talked about how he's paying weekly on his house, because it shaves off years of payment and thousands of dollars are saved. Remember, when making payments, you want accelerated weekly, but then every 3 months there's an extra payment (52 weeks in a year, not 48).

We have one more class tomorrow to work on all of our stuff from this unit.

I'm pretty sure that's it, and again, I am so sorry that this is late.

Dom is tomorrow's scribe.

Scribe

2006-05-09T07:48:00.000-05:00

Hello everyone..
Sorry guys i was working til 4:00am.
today we have two classes.
First period Mr. K talked to about Buy Or Rent a house? The answer is easy Buy if you can afford, Mr. K also explained the benefit of buying a house. If we assume that Mr. Ks house bought $100,000 but Mr. K didn’t had that much cash in his pocket, but he loaned from the bank so after 7 years his house has value of $200,000 at the same Mr. K was making his monthly payment, so let’s assume that he paid 50,000, and now he wants to sell his house the price of $200,000. First ,he has to pay 50,000 to his bank then he’ll get the rest of the money.
Let us say that you live my house because you rented so every payment that you make I’m paying my mortgage, so it’s better to buy your own house if can afford.
The other thing that we talked to about in class today was when you are a new house buyer you have one chance because normally when you are buying a house you have to have 25% of the value of the house but if you are a new or this your first house you only have to make 5% of down payment, and this deal you’ll never get again.
The second class Mr. K gave us chance to work our assignment.
Here is our home work for today.
Page 184 section 4.5 make sure you start with investigation then examples and last exercise 1-7 and also section 4.6 investigation and exercise 1,2 and 3. So homework start page 184-194 good luck
Sorry again about being late.

Kakuro Sunday

2006-05-07T11:07:00.000-05:00

'A Kakuro consists of a playing area of filled and empty cells similar to a crossword puzzle. Some black cells contain a diagonal slash from top left to bottom right with numbers in them, called “the clues”. A number in the top right corner relates to an “across” clue and one in the bottom left a “down” clue.

The object of a Kakuro is to insert digits from 1-9 into the white cells to total the clue associated with it. However no digit can be duplicated in an entry. For example the total 6 you could have 1 & 5, 2 & 4 but not 3 & 3. Sound simple? Be warned it gets hard and is as addictive as Sudoku.'

Click here for more Kakuros.

(Thanks again to Think Again!)

The Crazy Inflatable Flailing-Arm Man's Scribe

2006-05-06T14:19:00.000-05:00

Hey kids,

Thursday. We didn't do a whole lot, we finished P. 170-171 , as everyone was WAY behind (that took up 1.5 classes), and afterwards my K. taught us about Credit card debts. Did you know credit cards compound Interest 365 times a year? Mr. K. Said it was better to get a credit card with a slightly lower interest rate, than to get one with X-amount of months of no interest, and a slightly higher interest rate, as in the long run, you'll wind up saving money. He also said we should upload all of our files to our thinkfree.com or Irows.com web-based word processors, as if we need to, we can reach them from home. He also reiterated that companies that charge interest are more willing to give you a far better interest rate if you negotiate between them and other companies.

It was mostly a work-based class, and so we really didnt do a whole lot in terms of learning new information.

Mondays scribe will be: Muuxi

And remember:

WE'RE NUMBER HALF!
WE'RE NUMBER HALF

2006-05-03T16:53:00.000-05:00

GNIGOLB NO GNIGOLB

This Vector section is kind of easy. Just remember if your are given TAIL to TAIL its always the paralellogram and if you are given TIP to TAIL its the triangle. Just study the terms and the formulas and you'll do just fine. Notin much to say...

scribe

2006-05-03T13:08:00.000-05:00

Today Mr. K talked to us about some things.

You can have a Decreasing Investment or an Increasing Investment.
Decreasing is something like a car where you're paying.
Increasing is something like an RRSP, where you're getting money.

Three types of Financial________ (i forgot what they're called, so if someone remembers please let me know and ill edit this)
-RESP - Registered Education Savings Plan
-TBill - Treasury Bill
-GIC - Guarantee Investment Certificate

Three types of Risk Investments:
High- Where you invest a lot of money, but there's a chance that you can loose it all. Ex. Investing on someone who is doing an oil dig.
Medium- Ex. Investing on something from Apple.
Low- Investing a low amount of money. You may not get much back from interest but you're guaranteed to get your money back.

Investment Portfolio
Where you invest over several banks in all three types (RESP, TBill, GIC), and in all three risks (High, Medium, Low).

Effective Interest Rate
The Interest Rate that you would need to get the same amount of money (future value) if you only compounded once.

Example:
A bill for a credit card indicates an Annual Interest Rate of 18.5% and a Daily Interest Rate of 0.05054%. What is the effective rate?

We'll use $100 for a principal value as an example.

So on your TVM Solver:
N = 1
I% = 18.5
PV = -100
PMT = 0
FV = (Alpha Solve) = 120.3161266
P/Y = 1
C/Y = 360
PMT: Begin

Now that we have the Future Value or the money we'll get, we can get the Effective Interest Rate by changing C/Y to 1, and Alpha Solve on I% :

N = 1
I% = (Alpha Solve) = 20.31612664
PV = -100
PMT = 0
FV = 120.3161266
P/Y = 1
C/Y = 1
PMT: Begin

So the Effective Rate would be 20.316%.

Homework: Page 171 #1-7

Next scribe: Nik # 1/2

HEy MR.K

2006-05-03T00:48:00.000-05:00

Hello yeah i prolly wont be in school until next week due to a death in the family. I am sorry to inform u so late but its the best i can do and i will talk to u more about it wen i get bak.
NIKKI

Scribe for May 2/06

2006-05-02T17:56:00.000-05:00

So today we had a two math periods. The first period we went to the computer lab. The second period we were in the class room and took notes on vectors.

First thing we did was take a look at the graph on p.174 in our text books. This table has to do with residual values for cars. The table is pretty straight foreward. The percents are the percent of the origional price of the car.

After that we were given the accual values for the correct anwser for question #1 on p. 178. The anwser in the back of the book is wrong.
These are values you plug into your caluclator.

N: 36 ( the months leased)
I%: ? ( what were trying to find out)
PV: 24500 (the purchase price of the car)
PMT: -345 (monthly payments)
FV: -14500 ( purchase option)
P/Y: 12 (monthly payments per month)
C/Y: 12 (compounding periods per month)
PMT: end BEGIN

When anwsering a question like this on a test or exam you are supposed to copy the screen of your calculator like I did above.

And with all this in the calculator the interest should come to 4.1% ( I'm not sure about this anwser because I don't have my calculator) To find this out you highlight the I% coloum and then press Alapha Solve.

Mr. K also talked about why the Present Value and the Future Value have different signs. (-,+)
When dealing with a delcining investment the PV and FV have different signs. While increasing investments have the same signs for PV and FV. A example of a increasing investment would be like a RRSP. The only reason I can explain why this is is beacuse if you think about with a decreasing investment (eg. leasing or buying a car) you are giving away/losing your money. You don't really get it back. You never get it back in the form of money. Increasing investments are different. If you put money in a RRSP you get the money back sort of.

Well that was the first period of math. The second class we got our vector notes for our dictionary: ( sorry there are no pictures)

Vectors:

All About Angles:

(vertically) opposite angles: when 2 lines intersect the opposite angles are congurent.

Pararellel Lines and Congruent Angles:

Transversal: A line that intersects two or more parallel lines.

Interior Consecutive Angles:

The interior consecutive angles bound by a transversal and two parallel lines are supplementary ( sum to 180)

Alternative Angles:

The angle on alternate sides of a transversal are congruent.

Corresponding Angles:

Angles on corresponding sides of a transversal are congruent

A Quick Trigonometry Refresher

"SOH CAH TOA" used in right triangles

SOH: sin: opposite/adjecent

CAH: cos: adjecent/hypothenuse

TOA: tan:opposite/adjecent

Any other triangle can be solved using the SINE or COSINE LAWS.

The Sine Law

Can be used when at least one angle and opposite side pair is known as well as either one other side or angle.

SIN A/a = SIN B/ b = SIN C / c

or

a/SIN A = b/SIN B= c/SIN C

The Cosine Law

Used only under one of these two conditions:
i) SSS (3 given sides)
ii) SAS ( 2 sides and a Angle)

a^2= b^2 + c^2 - 2bc CosA
or
b^2= a^2 + c^2 - 2ac CosB
or
c^2= a^2 + b^2 - 2ab CosC

Vector

A quantity that has both a magnitude (size) and a direction. It can be represented by an arrow. The arrow indicates direction and it's length indictates magnitude.

The 5 (3?) Ways to Indicate a Vector's Direction

1) bearing:
-0 degrees due north
-angles measured clockwise from 0
-Always written as a 3 digit number. include a leading zero if necessary
-may or may not be written in square brackets

2) using degrees and compass directions ( the next to things will make little sence. If you don't understand just look at someones dictionary that was there in class)

EX:
60 degrees North of East is indentical to 30 degrees East of North

20 degrees South of West is indentical to 70 degrees West of south

3) using compass dirrections and degree

EX

N 50 degrees W is indentical to W 40 degrees N

E 15 degrees S is identical to S 75 degrees E

Well thats all the notes we got. ( sorry about the whole no pics thing) The test for vectors will be on friday I belive. You should double check that because I'm not to sure. There are review questions on p. 341 question 1-9. Don't forget to do your blogging on blogging.

And the Scribe for tommoro is NIK

Scribe for May 1/06

2006-05-02T16:02:00.000-05:00

Sorry everyone that this scribe post is a day late. I was unaware of that I was the scribe. I don't remember exactly what happened, but I'll try to talk about everything new we learned and then do the scribe post for today.

Well Mondays class was in the Mac Lab. First thing we did was get the "Buying or Leasing template". To find it you have to click on Go on the top menu, then click on connect to network I belive. Then you type SMB://DMC018/2STUDENT$ into the adress bar. ( I can't remember if its case sensative) After that you find and click on Mr. K's folder and open the Buying or Leasing template. Then your supposted to copy it into your folder.

Then we where taught how to do the same thing the the spread sheet does but on our TI-83 Calculator using the TVM Solver. If you have a TI-83 + you just access it by pressing apps then its the first option Finance. If you only have the TI-83 I think there is its own button for Finance. This is what the screen looks like:

N: number ( how long you plan to lease it)
I%: the interest rate
PV: the present value ( which when comes to leasing it is the purchase price)
PMT: payment ( the payments made. Usually negative)
FV: Future Value ( usually the purchase option price. Also negative )
P/Y: Payments per year
C/Y: Componding periods per year

All you do is plug the information you have onto the screen. It also works the same way with investments. If there is one thing that you do not have a value for you simply highlight it then press alpha slove and you will be given the value.

Well thats all I can recall from yesterdays class.
The scribe post for today will be up later tonight.

Vectors Review Links

2006-05-02T00:26:00.000-05:00

It's a little late but here are the links I promised you ...

An interactive illustration of Parallel Lines and Pairs of Angles. (You can find more info and a quiz here.)

Learn about the Sine Law.

Learn about the Cosine Law.

Oscar Had A Heap Of Apples. (huh? ... go ahead, click that link ... you know you want to.)

A Java Applet for Adding and Subtracting Vectors

Watch this video of a vectors application. (More info and animations here.)

We'll put some notes on this in your math dictionaries tomorrow in class. ;-)

Vectors (B O B)

2006-05-01T23:25:00.000-05:00

This unit was the most easiest unit so far in this course.Specially using Pythagorean Theorem was the most easiest one. Other formulas like sin and cosin law were also ok.But finding the angles were the only thing i found a bit harder. i Hope we do get some notes on finding these angles before the test. Thas all!

vectors - b.o.b

2006-04-30T21:57:00.000-05:00

i thought this unit went by pretty fast. yes i did. soooo....i thought this unit was tough. its so confusing like im not quite sure how to figure out triangles when theres lotsa triangles in the problem that you have to solve for...it gets really crowded and confusing. so thats what i have been trying to really focus and study on mostly.

scribe

2006-04-30T21:16:00.000-05:00

So on friday we only had one class and it was shortened because we had an assembly. Mr K was explaining to us how we could become millionaires if we saved a certain amount of money from our paycheques every pay day. He showed us with the TVM Solver on our calculators. On the TI-83's we press the Apps button, choose the finance menu and then choose the TVM Solver.

this is what you should get on your screen.

N = number of deposits [month]
I% = annual interest rate as a percent
PV = principal or starting value [opening balance]
PMT = payment [negative value for investments]
FV = future value
P/Y = number of payments per year
C/Y = number of compounding periods per year

after you enter in all the known values you have, highlight the value you want to find then press Alpha solve.

unfortunately i dont have my calculator with me so i cant show you guys step by step what we did to make us millionaires, but i will definately post it up as soon as i get it back.

tomorrows scribe will be jason.

(>O_o)> .:Blogging on blogging:. <(o_O<)

2006-04-30T12:47:00.000-05:00

I found that this unit is in the middle of easy and hard. The easy part of this unit is when your drawing a diagram and solving the triangle using our calculator, and the difficult part of this unit is when your putting angels. We have to be careful on were we put it because on this unit it is very easy make mistakes, for example, you didn't put the right angle were it should go, then your answer would be wrong because of that mistake. I think that a little notes about the angle thing would help us a lot, Well for me that would help because I think that I might forget it.

BOB "VECTORS"

2006-04-30T12:16:00.000-05:00

This unit is kinda hard because in order to to solve some triangles problems we need to have a basic skills on trigonometri which maybe some of us have forgot those stuff,, because we learned it when we were grade 10 or grade 11, but anyway it's a good thing to remember again those things. I never thought those triangle problems and solutions can be applied to a more realistic types of problems like the problems that we did in this unit. The only things that maybe I need to work on is figuring out the right diagram for the word problems and proper labeling of side lenghts and angles, in that way it would be much easier to solve the question that asking......

Blogging on Blogging (Vectors - Ivy)

2006-04-29T20:46:00.000-05:00

all right..... what do i know about vectors...well....you know about the angels, it makes me confuse.... but i figure it out someway. well hopefully...i don't know if im going to do good in this unit..but i need.to do good..or else i'm not going to get my credit.... i know i did bad in probability and statistics...i didn't really go look on my note or review so it's my fault...and i am working fulltime in the evening.. but anyways.. well.. problem is in this case..... in grade 10 i didn't understand trigonometry the sohcahtoa thing or the cosinlaw i don't even know how the heck i passed that course..but anyways....i've been looking through my notes and i was trying to understand it...and i actually did get it..i just need to take more time to look on my notes.. and hopefully i'll pass.

BOB Post

2006-04-28T17:40:00.000-05:00

Hey kids,

I enjoyed the vectors unit. The only thing i was confused about was the laws of complimentary angles, etc. I couldn't remember this from last year so i had some trouble with that. other than that, the biggest problem was making sure i got the angles right, and the length of the lines. other than that, i had fun with the vectors unit. I liked it mostly because I had just finished that unit in my physics class.

thanks,

Nik # 1/2

... WE'RE NUMBER HALF!
WE'RE NUMBER HALF!!!

BOB on Vectors

2006-04-27T22:17:00.000-05:00

To me this chapter seemed little short. so far we had no notes on this chapter, and i gues we are not going to have one, as we began a new chapter "Personal finance". i had some difficulties on Vectors chapter. the hard part was getting the rigth shape i.e. the drawing of the triangle. if you lose control of this step, then your whole work is completely nothing. so i got to do practice on getting the right stuff. then i gues the math part will be lot easier. hopefully things will go as predictated. thats all folks.

Blogging on Blogging

2006-04-27T07:56:00.000-05:00

i found this unit pretty easy, but i had a problem with how to figure out the angles and if you don't know how to figure out the angles you are in trouble. But Dom show me easy way to do it thanks man. Most of the classes i was a way even Mr. K told me that he's little bit worrying about me if i understand the material, but i guess i'm doing fine so far.
good luck everyone.

BOB - Vectors

2006-04-26T23:37:00.000-05:00

I just want to say that this unit was somewhat hard and somewhat easy. Everything that we did so far seemed quite easy. Especially if you took Physics. By far, the biggest problem I had was figuring out the angles. Plus, I find that it's very easy to make mistakes when doing the problem solving. Either because you're not reading the problem carefully or you somehow get the directions mixed up. Hopefully I won't make those mistakes during the test. Well, that's all I have to say . . . later.

The Crazy-Inflatable arm-flailing tube-man's Scribe

2006-04-26T22:32:00.000-05:00

Hey Kids,

Sorry the scribe is a little late. But here was the Day:

We've Started a new unit: Personal Finance. For this unit, you will need both a Thinkfree.com account, and an Irows.com account. today, we worked on page 154 in our texts. the unit thus far is a reiteration of what we did in grade 11 personal finance, however we will be doing everything over the internet, using spreadsheets. I suggest you review how to use Excel spreadsheets, using page 154 for tomorrows class. This unit will be done mostly with Spreadsheets, so you will need to have an inane understanding of precisely how to use a spreadsheet. We had some trouble saving our stuff to thinkfree office, so it is highly recommended you register to Irows.com tonight, as you will be unable to do this through the school computers. your thinkfree account should also be up and running. KNOW YOUR PASSWORDS. This is critical. Many people forgot their passwords and got nothing done. If you'd like to get anything done tomorrow, it comes highly recommended by doctors and pharmacists that you do this.

We WILL be in the Computer lab every day this week and next. Hope you know how to use an Imac!!!

P.S. Tomorrows scribe will be..... RUBIE!

Blogging on Blogging

2006-04-26T21:10:00.000-05:00

This unit went very fast...

I think I have an all right understanding of this unit (I've been mistaken in the past!), though I must say, I'm really glad it's over. I'm not too fond of vectors at all. :P There are a few things I might struggle with tomorrow, but with some study hopefully I'll nip that in the butt. I am fairly comfortable with the drawings, I just have to remember to factor certain things in to what I'm drawing.

Good luck everyone, I hope you guys do well. :)

Vectors

2006-04-26T16:10:00.000-05:00

Well here's my little blog on this unit for vectors. Althought Mr. K said that everything kind of goes downhhill after statistics, I was kind of surprised at how much I actually struggled with this unit. I don't know what it was about the unit. At first I had problems drawing the diagrams asked. But after I overcame that, I started having trouble with the entire problem. Like I mean, for some reason, I just couldn't interpret what I was being asked. But as we did more and more problems, it became better. Here are the key things that I needed to remember. When drawing the diagrams, make sure you draw them big, because it can become quite confusing, and not to mention messy and this is what can cause you to get the incorrect answer. Another thing about drawing the diagrams is to know exactly in what direction it's going. What I mean, is that you should know and familiarize yourself with the 5 ways that you can write directions.

For example:
N40° E is 40 degrees to the right of the North.
65° S of W = 65 degrees going downward from West.

So I guess I just wasn't used to the directions and such. Another useful thing you should do is labelling all the angles in the diagram even if you don't use it. It's just a good habit of doing that so that you don't miss any important information you might need. Other than that, everything else was pretty straight forward. Luckily, I managed to become somewhat comfortable with doing these problems before the pre-test. Hopefully I can keep it up for the test :P

pre-test day!!!

2006-04-25T23:34:00.000-05:00

well, nothing really happened today, just had our pre-test. which i found, pretty tough and confusing for me. so i cant really explain any of the questions here..because i dont get them myself. sorry!! soo all i can say is just review all our past homework and remember all those formulas and stuffs....and im sure, the test will be a piece of cake...oh i wish!! wish i had something else to write about, what a waste of a scribepost. ahhh. kay well, good luck everyone on studin' and on the test! k, later!!

-corrie

* oh, and tomorrow's scribe will be Nik # 1/2

HEY EVERYONE!

2006-04-25T08:24:00.000-05:00

just wanted to let you guys know ahead of time that todays scribepost won't be up anytime soon...but it will be up, just late. sorry guys, all because of work! k, later!

- corrie

Scribe

2006-04-24T20:28:00.000-05:00

Just so you know, I was caught by surprise and didn't know that I was suppose to be the scribe for today since I didn't read the last scribe post. Luckily not much happened today so I'll give a brief description of what happened in class.

In the morning, Mr. K talked about a new site for us to use. The URL is am40s.pbwiki.com. Next he put us into groups to work on a problem with multiple vectors. We just use the COSINE LAW or the SOLVETRI program on our calculators to solve the problem. Some had trouble with the problem and Mr. K decided not to take in the group assignment so we all worked on the problem together.

In the afternoon, we continued to finish solving the problem since we ran out of time in the morning and then we had a homework test. Then he assigned us some questions to do in the textbook for homework.

HOMEWORK: p. 341, #1-9 (I don't think we have to do #1 since it seems more like an experiment.)

NEXT SCRIBE: Corrie

The DaVinci Code Quest Sunday

2006-04-23T15:40:00.000-05:00

It started last week. Google releases one puzzle each day for 24 days until the movie "The Da Vinci Code" is released in May. So far 7 puzzles have been released. You have to solve the puzzle to reveal a clue. Then you have to answer the clue question(s) to advance to the next puzzle. You can win a prize for solving all 24 puzzles. Now I realize this is all about marketing and they're really just trying to get as many of us as possible to go see the movie but the puzzles are really cool! Google searching often helps to find the answers. One of the puzzle questions can be answered using The Fundamental Principle of Counting and the very first (sudoku-like) puzzle uses a couple of mathematical symbols.

Challenge 1: What is the question that can be solved using The Fundamental Principle of Counting and how do you use the counting principle to find the answer?

Challenge 2: What mathematical symbol is used in the very first puzzle and what number does it represent? (Not the "delta," in a later puzzle it has a different meaning.)

You have to sign up for a Google Homepage in order to play, but that's a free and very useful service. After that you can begin the game. Click on the US button to start 24 days of fun! (Actually, 17 because you could work through the first eight today.) Don't forget to also find the answers to the Challenge Questions above!. ;-)

Solving Vector with given 3 magnitudes.

2006-04-22T07:44:00.000-05:00

Hi guys sorry for the delay,,, Mr. Kuropatwa introduced a new type of problem in vector which is kind of harder than the other problems.. But still we can use the parallelogram method. So this is the example of that kind of problem.

3 forces of 30N, 45N, and 50N act on a body. The first is in the direction 50* west of north, the second is in the direction of EAST 30* NORTH and the third is on the bearing 135*. Find the resultan force...
Here is the solution:

There is another method we can use to solve this type of problem ..... the triangle method, it is somewhat similar to paralellogram method because they using the same angles to solve a problem,,, their only difference is that triangle method is using a tringle.....

for the next scribe its Andrew

Vectors

2006-04-21T01:42:00.000-05:00

2006-04-20T23:34:00.000-05:00

Today we had two periods. Mr.K was not present for today, but there was a sub Ms. Adam. she let us do our previous vectors homeworks and the assighments she handed out the previous day. then she assigned us group work. After that she gave us new assignment "Vector Problems set 3". Ask Mr.K on friday if you don't have one. Ms. Adam did on the board questions #4 and #8.
page 328.

#4. A small aircraft on a heading of [225] is cruising at 150km/h. it encounters a wind that blows toward [345] at 35km/h. find the aircraft's resultant velocity.

#8. A kayak is paddled at 8Km/h towards [330] while an ocean current carries the kayak at 3.2km/h towards [170], what is the resultant velocity of the kayak?

* i will post the graphical image of #4 later, but i couldn't upload the graphic image of #8.

* I think it would be nice if Mr.K showed us how to use the SIN Law, and when to use it, as it is sometimes a long method.

that's all folks.

tomorrow scribe is PATRICK. i was filling in for Patrick tonight, i.e. i fill in Patrick tonight, he would do the following night. Anywho bye byeeeeeeeeeeeeeeeeeeeeeeeeee.

Magnitude and Direction

2006-04-20T19:22:00.000-05:00

Scribe!!!

Here is my scribe now. Sorry for the delay. This was the work sheet we worked on Wednesday.
And since Mr. K wasn't in class to give us the answer here is what i got.

Measure vector V shown Below using ruler and protractor.

1. What is the magnitude of the vector represented by the arrow? Show how you arrive at your answer. Be sure to include units with your answer.

Ans. Since we used this scale , 1 cm = 2.5 km/h, we have to multiply 2.5 to 10 cm (lenght of the arrow mesured with a ruler in cm).

lenght(cm) x Actual magnitude = Reality magnitude
10 x 2.5 = 25
reality magnitude = 25 km/h

2. What is the direction of the vector? Write the answer in five different ways.

Ans.
Bearing of 250 Degrees
70 degree south of west
west 70 degree south
30 degree west of south
south 30 degree west

That all folks. If my last answer is wrong please dont hesitate to post the right one.

TO MR. K

2006-04-20T00:12:00.000-05:00

Hey mr.k,
sorry fo the late post but i must let u kno that i will not be attending Thursday's, or tomorrows class cause i will b at sissler high school attending the workshop for my law class and yeah i will get wat i missed from the scribe that day k good nite buh bye

Magnitude and Direction

2006-04-19T18:34:00.000-05:00

Scribe
April 19 2006

Hey you guys. My scribe will not be up today. IT will be up Tommorow as soon as I get the Right answer for the questions. Anyways Pa3k is the next scribe

(>O_o)> .:Vectors:. <(o_O<)

2006-04-18T18:55:00.000-05:00

Hi everyone, today we did a lot of stuff in our class because we had two periods of math today, so let's get it started. At the beginning of the first period class, Mr. K gave us some problems to solve and he also reminded us about SOHCAHTOA. SOHCAHTOA means Sin= O/H, Cos= A/H, Tan= O/A. O means the opposite, A is the Adjacent ( Next to; neighboring) and H for Hypotenuse (Note: The hypotenuse is the longest side of a right triangle).
*Sin^-1, Cos^-1, and Tan^-1 are called
Arc Sin, Arc Cos, and Arc tan......This functions means the same thing.*

Here are the problems that Mr. K gave us:
1) Find: tan A, angle A, Length of AC

A) Tan A= O/A
Tan A = 5/12
Tan A = .4166

B) Angle A = arc tan (.4166)
Angle A = 22.61 degree

C) Length of AC
C^2= 25^2 + 5^2
C^2= 169 (Take the square root of C^2 and 169)
C = 13

2) Find: Sin R, Angle R, Length of QR

A) Sin R = O/H
Sin R = 11/25
Sin R = .44

B) Angle R= arc sin (.44)
Angle R= 26.10 degree

C) Length of QR
25^2= 11^2 + a^2
(25^2)-(11^2)= a^2
504 = a^2 ( Find the square root of 504 and a^2)
22.44 = a

3) Find : Length of XZ and length of XY

A) length of XZ
Cos 37= 32/H
H= 32 / Cos (37)
H= 40

B) length of XY
z^2 = x^2 + Y^2 - 2xyCos Z
z^2= (32^2 + 40^2) - (2*32*40*Cos (37))
z^2= 579.49 (square root both sides)
z= 24.1

4) Find: length of AC, Angle A

A) length of AC
b^2= a^2 + c^2 - 2*a*c*Cos B
b^2= (5.7^2 + 4.5^2) - (2*5.7*4.5*Cos (78))
b^2= 42.07 (square root both sides)
b= 6.49

B) Angle A
a/Sin A = b/SinB
5.7/Sin A = 6.49/Sin (78)
Sin A = (5.7*Sin (78))/6.49
Sin A = .8591
Arc sin (.8591)= 59.21 degree

5) Find: Angle C, b

A) Angle C
a / Sin A = c / Sin C
5.1 / Sin (28) = 3.8 / Sin C
Sin C = (3.8*Sin (28)) / 5.1
Sin C = .3498
arc Sin (.3498) = 20.47 degree

B) length of b
Step 1: Find Angle B so that we can use the sin law or the cos law.
Angle B = 180-28-20.47 = 131.53 degree
Step 2: Use sin law ( it's easier to work with :P)
a / Sin A = b / Sin B
5.1 / Sin (28) = b / Sin (131.53)
b= (5.1* Sin(131.53) / Sin (28)
b= 8.13

Mr. K also gave us two kinds of programs for our calculater. The programs is used to solve triangles, If you missed the class today be sure to ask someone to give you the program.
To access this programs:

1) Press the [PRGM] Key and then press [1]. The calculator will use the sin law and the cos law.
2) Press [PRGM] key and then press [2]. This will identify all the missing angles and sides.

For the second period of math, Mr. K gave us more problems to work on:

1) Hezy and Partick paddle their canoe 5.5 km west and then 4 km south. How far are they from their starting Point? What direction must they paddle to return to the starting point by the shortest route?

Therefore they are 6.8 km away from the starting point and must paddle north east to return to the starting point.

2) Forces of 210 N and 85 N act at an angle of 78 degree to each other. Find the resultant force and the angle it makes with the smaller force.
The resultant force is 242.38N, at 57.94 degree to 85N force. (sorry that I can't show you guys the solution but I'll have the solution by tomorrow).

Well today has been a crazy day and our homework is on page 322, numbers 1-4 and the next scribe will be (>O_o)> .: HEZY :. <(o_O<) .

SCRIBE

2006-04-18T00:54:00.000-05:00

Hi Im your scribe for today. Well Im sorry I couldnt put the post up earlier. I was put on the spot by somebody so go easy on me lol.

Today in class we did a review on vectors.

Vector: a diagram which shows both direction (North,East,South,West) and magintude. Ex. of magnitude (force,weight, distance,etc.)

We learned about the 5 different directions.

Ex.

They are as follows:

Bearing of 045°
North 45° West
East 45° North
45° North of East
45° East of North

Notice that they are all different but mean the same thing. Same direction

*Note right angles are equal to 90°. (45+45=90)
Same as if the angle was 60°. (60+30=90)

We learned how to add vectors to find the resultant. Ex. Tug-o-war A force of 50N pulling east and a force of 60N pulling West.

Resultant is 10N west

Another Example:
Pulling a tree stump out of the ground. A force of 50N pulling West and a force of 50N pulling at a bearing of 40°.

We can make a copy of the vector and add it to the original one. Because it has the same direction and magnitude we can do the following to help find the resultant.

Example 2:
Given the same exact diagram but different situation. A golfer hits a ball 50ft west and 60ft with a bearing of 050°
The following example is a triangle. You can now use the Cosine law to figure out the resultant vector. c2=a2+b2-2abcosC

*Note the Cosine Law only needs to be used once and should only be used if met under one of these circumstances:

You are given side, side, side
or side, angle, side (which was given in this example).

Well this is what we did in class. Hopefully you can understand it.

*Homework was what we were given before pg 307 #'s 1-8
and the new stuff is on pg 318 #'s 1-9*

Next Scribe is the only person left which is Reign. Then it starts all over again.
Cya

Blogging on blogging

2006-04-15T11:46:00.000-05:00

What can I say about statistics.. I think firs time I had hard time understanding, but right now I’m doing well. And also I believe the only way to understand this unit is to do more work. I guess the sheets that Mr. K gave us were very helpful. Good luck guys

Blogging On Blogging

2006-04-12T21:39:00.000-05:00

I guess I'll start this post off by saying what everyone's been saying which is, the statistics unit was very hard. And apparently I haven't been doing well. The toughest part of the whole unit, in my opinion, was the confidence interval. I'm actually okay when it comes to doing the calculations. My only problem is understanding what the numbers mean and what's actually going on in a certain problem. And because I don't know what's going on in a problem, I tend to do the wrong things and make mistakes trying to figure out what the answer might be to that problem. IF I'm LUCKY, I might actually pass the test. At least I know that I'm going to get ONE mark for having this blogging on blogging post done. }:-(

*REMEMBER SISYPHUS!* {;-)

Blogging on blogging

2006-04-12T16:21:00.000-05:00

I had a really hard time understanding this section (stastics) but now i kinda get it. I think the only key to pass this section is try and try examples and thats what i did. It really helps to stick to someone that knows this stuff. Patrick and Reign helps me to understand and me as well corrects them ,a little bit, if i knew i was right. The last 2 sheets that Mr. K gave us, really helped me. Thats all I can say. Good luck to you guys and take a good look at the calculator commands, Math vocabulary and i was hoping that Mr. K will post some practice quiz today.

blogging on blogging

2006-04-12T07:59:00.000-05:00

the first few classes of this unit I thought was really easy but as we got more into depth with the unit I started to have trouble with it. my only trouble with the unit is the calculator functions, I keep getting mixed up with what functions go with what questions. butwhen we did the pretest I did ok and I wasnt having much trouble. now I just have to practice understanding what the questions are asking for. to do that I just need to practice doing more problems. hopefully I do ok on the test tomorrow. goooood luck everyone!

blogging on blogging

2006-04-11T22:42:00.000-05:00

well this unit sure was difficult. the first few classes weren't that bad. learning to calculate mean and standard deviation was a piece of cake. but as classes went on, i'd have to say that the stuff that i kinda got but kinda got confused was the binomial ones. like today the sub handed out worksheets and there were questions like question 6 on the first worksheet that was handed out. but with a little team work, i was able to get it and understand how it was done. so a little more practice with that should be good. yeah. kay, gnite, bye!

Blogging On Blogging

2006-04-11T21:38:00.000-05:00

I agree with my other classmates that statistics is hard, because i otfen find myself having trouble with some of the questions from the probability unit.....Our 3rd unit on statistics is somewhat confusing as well, because of those many calculator comands that need to be remembered. There is more than one way to solve a problem using the calculator, that's what made me confused in the begining, but my own way to compensate to that problem is to remember only one calculator command that can gave the same answer, like for example getting the area of the normal curve graph can be get by fidding z-scores then use shadenorm to show the graph, and the other way is solve it directly without showing the graph, so from those 2 steps i just oftenly use one of those and stick on it because it gave the same answer anyway, in that way I never be confused what calculator command to be use....This unit, in my opinion is really helpful because the data, the problems,the solutions, etc, can really applied in everyday life.

Blogging on Blogging

2006-04-10T18:46:00.000-05:00

Well Statistics is easily the hardest chapter that we have covered. Its really really calculator orientated. I think thats what sets it apart from most units. I pretty much understand most of the unit. It's kinda weird but i understand most of the later stuff we did in the unit. I'm really gonna have to review the early stuff we did in the unit. The Statistics test is gonna be a test I'm gonna have to study for. I'm just gonna review my dictionary or read the blog and do some review questions. If I do all this I think I should be fine. I did better on the pre-test than I expected. But thats not saying much cause I didnt have the highest expectations for it. I fluked out few anwsers which was kinda suprising.

Well thats about it.
Cya.

SCRIBE

2006-04-10T16:57:00.000-05:00

Hey whats up everyone. Im the scribe for today so I'll go over what happend in class today.

First thing at the begining of class Mr. K handed back a bunch of old work for past units. All I can say from looking at my marks then is I miss the marks i got in the Marticies unit. Anyways I think after that Mr. K anwsered some questions people had on blogging on blogging. I'm not sure what the origional question was but it involved finding the area of part of a curve multiple ways.

The first example he gave was find area of everything under the Z score of -2. One way to do it is: by using shadnorm function of your calculator. With using shadenorm with Z scores the first digit you plug into your calculator is the low value, which in this case is -5. ( this is because, I'm not quite sure of this number but 99.99% of data is between 5 standard deviations, so using -5 is more than enough to get everything on the low end) Then you hit , then plug in the high value, in this case it would be -2. This is what You should get. (note: shadenorm draws a graph)

shadenorn( -5,-2)= o.o25

Another way to do the same question is by using the normalcdf function of ur calculator. The only difference between shadenorm and normalcdf is shadenorm draws a grapgh.

Normalcdf(-5,-2)=0.025

Another way to do the same type of question is with using the real/normal values not the Z-scores. Basically the only difference between this and the question above is when using the normal values you need to plug the mean and standard dev. into your calculator along with the low and high values. The Mean for the example was 62 and the standar dev. was 6. We were supsota find the % of data up to the Z score of -2. Well one way of finding what the normal value of a Z-score of -2 is with the mean of 62 would be to plug it into that formula:
z=x-x(mean)/standard dev. But and easier way to do it would be to just to subtract the amount of Z scores you want to find from the mean. Kinda hard to explain. The low value we want to find sould be equal to -5 Z-scores like in the first example. And one Standard dev. = 1 Z-Score would to find -5 Z-score would would take the mean and subtract it from 5 standard dev.

62-(5 x 6) = 32 < this is our low value

So to find the high score you basically do the same thing but you only subtract 2 Z-scores for the mean

62-(2 x 6)= 50
Then all you have to do is plug the information you have into your calculator. You can either use shadenorm or normalcdf. Either way you should get the same thing

shadenorm(32,50,62,6)= .025
normalcdf (32,50,62,6)= .025
(remember you have to plug in the mean and standard dev. to let the calculator now that your not using Z-scores)

And then after this we were given our statistics pre-test. After that we got into groups to discuss our anwsers and then like usual only one person had to hand one paper with the group members names on it. Well thats about it for what we did in class today. The last thing I got to say is remember to do your blogging on blogging before your test. I'm gonna do mine now while I'm logged into blogger.

Cya

Blogging on Blogging

2006-04-10T03:19:00.000-05:00

statistics was the hardest chapter of all. i think. doing more problems helped us alot. if we would have done the pre-test on friday. i think the result would have been bad. what scares me on this chapter is when the question doesn't mention what type of distribution to use. it lets you figure out what type of distribution to use. Doing this part is the hardest of all to me. i have couple of problems. that i would love to see answered in class, after the pre-test, before the real test. the question are as follows:

1) The weight of babies born at HSC averages 8 lbs, 10z (there are 16.0z in 1 lbs).

a) Find the percentage of babies with a birth weight between 7 lbs and 9 lbs.

b) Find the weight , w, such that the percentage of babies with a birth weight greater than w is 60%.

c) Find the weight w, such the percentage of babies with a birth weight less than w is 25%.

2) A college aplitude is scales 5000 that its scored approxiate a normal distribution with a mean of 500 and a standard deviation of 100.

a) find the probability that a student selected random will score 800 or more points.

b) find the score x, such that 76%, of the student have a score.

i) less tahn x
ii) more than x

*that! thats all folks.

Blogging on Blogging (Statistics)

2006-04-09T22:59:00.000-05:00

I found statistics the most hardest chapter so far in this course. But as we do more problems in class it gets more easier to understand these type of problems. But still i have some problem in understanding the (binomial,pdf and cdf) and (invnorm) commands in calculator. I can't figure out when to use these commands. But if we do a few more problems in class based on these commands then i think i will be ready for the test.

Blogging on blogging

2006-04-09T18:11:00.000-05:00

Statistics is the second hardest lesson that we have done because there are a lot of things to remember specially on the calculator part. I always have to read my dictionary and do my homework so that I can remember all the stuff that we have learned during that day because if haven't read my notes or do my homework I would probably be lost right now. Finding the mean, z-score and the unknown values was the easiest part of the lesson, but IM having a little problem on using invnrom because I don't know when to use it. The binomial distribution, normal approximation and confidence intervals are the hardest questions to do. I think that if we spent a little more time on doing exercises with this type of questions will help me understand them better and hopefully be ready on our test this Thursday.

Scribe for The Day Before yesterday!!!!!!!!!!!!!

2006-04-09T14:49:00.000-05:00

Hey folks, sorry i'm a bit late on posting my Scribe post, Computer problems, you see.

Anyways, on friday, we did mostly problems, in preparation for our Pre-Test on Monday. This was helpful, as i now understand what we were doing in this unit.

Here are the Questions:

Let Them Grow!

The Following Data represents the ages of trees drawn as a random sample of trees in a park in manitoba. The DAta were collected by park officials, and the numbers represent the number of rings in the trunk of the tree. Each ring represents one year of growth for a tree.

26 30 48 22 47 42 25 25 29 5 18
4 23 16 36 26 36 35 36 2 39 15
37 29 37 16 15 48 9 12 41 41 32
26 14 5 6 46 21 15 1 26 43 27

(a) Use your calculator to determine the mean, median, range, and standard deviation for the Data.

(b) Use the results of #1 to determine if the sample is normally distributed. Explain your reasoning.

(c) What would the Z-score of a tree with 33 rings be? Explain how you arrived at your answer.

(d) If you assume that the data aer normally distributed, what percentage of trees would have from 17-38 inclusive rings? Explain how you arrived at your answer.

ANSWERS:

(a) 1 var stats (L4)
_
X=27.72
σ=13.4323
Median: 26
Range: 1σ= 12.295-39.18

(b)16/44=64%
(all within 1 σ)
_
(c)Z=(X-X)/σ
=.39308 σ is 33 rings

(d) NormalCdf (17,38,27.72,13.4323)
=56.16%

(e)_ _
(X-1.96σ, X+1.96σ)
-0.6,52.05

%margin of error: (1.96σ)/n=.598
=59.8% margin of error.

At Aborder Crossing in Canada, customs agents decide which vehicles they will search for undeclared goods as the vehicles enter Canada. Records show that on average 28 percent of the vehicles searched contained undeclared goods.
A New Customs Employee, agent sparks, searched 392 vehicles and found undeclared goods in fewer than one hundred vehicles. The officer in charge, officer Pound, did not do so well in his high school math, but he does know that 28 percent of 392 is about 110 vehicles and so he gave agent sparks a reprimand and a pay cut.

In your opinion, did officer pound do the right thing in giving sparks a pay cut? Carefully explain your reasoning. Support your answer with appropriate statistical information.

ANSWERS:

P=.28
q=1-P
1-.28=.72
q=.72
_
X=np=109.76
σ= (npq)=8.8897

100/392=.25510
invNorm(.25510)
=-.6585

Sum of Prob:
P(<100>
=12.36%

The New Zeppos Are in!

Car Dealer Dan is selling a new car that has just arrived in Manitoba - A Zeppo. He tested 40 cars for gas consumption. and the number of miles per gallon for each car is shown in the table. Assume that the distribution is approximately normal.

30 34 31 33 32 29 31 24 25 33
34 3030 34 29 35 35 33 31 33
36 34 31 32 28 40 29 35 32 33
31 34 29 29 31 39 35 29 32 25

Questions:

(a)Find Mean And Standard Deviation for the Data. Round your answers to one decimal place.

(b)Find the probability that any car selected will have a fuel economy of 35 miles per Gallon (MPG) or better. Round your answer to on decimal Place.

(c) What percent of cars will drive from 27-37 Miles per gallon? He needs this information for his advertising campaign. Round your answer to three decimal places.

(d) Dan anticipates selling 400 zeppos in one year, and wants to offer up a free barbecue to any new car owner whose car does not measure up to a certain level of fuel efficiency. after one year of operation. he does not want to give away more that 20 barbecues. What level of fuel efficiency (in MPG should he guarantee? Round your answer to the nearest whole #.

ANSWERS:

(a)
_
X=32
σ3.46
_
(b) X-X/σ= Z
(35-32)/3.46
=.867005
NormalCdf(.867005,5)
=.19296, or 19.3%

(c) 27-32/3.46=-1.445
37-32/3.46=1.445
normalCdf(-1.445,1.445)
=.85154, or 85.2%

(d) 20/400
=.05, 0r 5%

invNorm(.05)
=-1.6448536

(1.6448536)(3.46)+32=
26.3088, or 26 MPG he should guarantee if he only gives away 20 barbecues.

Good luck with the Math pre-test on monday morning!

Four Colour Sunday!

2006-04-09T14:06:00.000-05:00

You may have heard that any map can be coloured with four colours in such a way that neighbouring countries receive different colours. That it can be always done is one thing. How to do it is another. Are you ready to start colouring?

(Thanks again to Think Again!)

SCRIBE FOR TODAY!!!!

2006-04-06T21:00:00.000-05:00

Chello, Chello, Chello
Yes i am today's scribe and ummm i'm not sure how to put pictures on this thingy cause i'm not a big computer freak well i mean i just dont like drawing and i just dont kno how lol:) SRY
So when i put "DIAGRAM" threres prolly a diagram of a 95% confidence interval ok kool, here we go.

Today we started off with some morning announcements and then Mr.K told some jokes, one was really good that i thought was true and then the others were all right and yeah thats wat we did to start off our day :) Oh today was a single class day!

We also did some dictionary notes and here they are:

Constructing Confidence Intervals

Step 1: Decide on the desired degree of confidence
Example: 95%

Step 2: Determine, with the aid of a diagram, the area in the trials of the normal curve.
Example: A Diagram of a 95% Confidence Interval Goes here Sorry:)

Step 3: Using tables or InvNorm(area) on your calculator find the values of Z-score low and Z-score high.
Example: InvNorm(0.025) = -1.96
Z-score low=-1.96 Z-score high=1.96

Step 4: Use the values Z-score low and Z-score high to construct your confidence interval as follows: (Meu-Z score X standard deviation, Meu+Z score X standard deviation)
Example: The 95% confidence interval for a normal distribution with M=63 and Standard Deviation=8 is: (63-(1.96)(8),63+(1.96)(8)) OR (47.32,78.68)

Percent Margin of Error

For the normal approximation of any binomial distribution we find the percent margin of error as follows: % margin of error= Z score(Standard deviation)/ n X 100

Z score is the appropriate Z score to generate a given confidence interval.
Standard Deviation symbol is the standard deviation symbol
n is the total number of trials in a given binomial experiment
Example: Given the bove data taken from a binomial experiment that was done 50 times(n=50)
% margin of error= (1.96)(8) / 50 X 100% = 31.36%

Theres your dictionary notes for the day and sorry for my illeteracy for symbols and suff lol please forgive:)

Now today we looked at a table of Z scores in our book on page 355, that table we must know how to use because it will be given to us on our exam at the end of the year during the time when we cannot use our calculators.

Today we also did a little question on the board that involved constructing a 95% confidence interval and finding the % margin of error for the amount of people wearing jeans in a mall out of 340 people so here it is:

n=340 p=238/340 = .70
q=.30
M=np=238 (M-1.96(8.45),M+1.96(8.45))
nq=102 (238-1.96(8.45),238+1.96(8.45))
(221,255)

Standard deviation=the square root of npq
=square root of 340(.70)(.30)
= 8.45

% margin of error= (1.96)(8.45) / 340 X 100 = 4.87%

All of this means that if you repeat this experiment we are 95% confident that19 times out of 20 the data will fall between 221 and 255, so we will get an answer that is = to 238+/- 4.87%

We also have homework on PAGE 145 # 1-3, and we have a pre-test tomorrow so be sure to STUDY and dont forget k :)

Well that rap's it up for my scribe hope u can understand it lol but yeah have a good day and stuff BUH BYE THANK U

p.s tomorrows scribe will be NIK #1/2 :)

Blogging on blogging

2006-04-06T00:30:00.000-05:00

Well, it's that time again. Blogging in hope of finding answers before the test. So it's official, statistics is by far the hardest unit we've done. Well, that's what I think :P There are so many functions that you need to know on your calculator. I've found that if I haven't reviewed my notes for one night, it's hard to remember what did what, nevermind everything else you need to know. Finding z-scores and unknown values are easy. One thing I'm a bit 'iffy' on, is when you're given the percentage of the area under the normal curve and you need to use invNorm to find the value/z-score. But more importantly the most difficult problems are the binomial distribution, normal approximation and confidence intervals questions. It does take a lot of work to do the questions, but I think familiarizing ourselves more with the calculator is what's needed. Hopefully, with the help of a lot more practice, I can get everything figured out..

SCRIBE

2006-04-04T19:36:00.000-05:00

How you guys doing?

It’s just another bad day for me, and I’ll tell you why.
First, we had only one class today and Mr. K gave us a quiz but I thought it was just a group work, and I did very bad this quiz. It was 10\10. Guess how much I got. I did very badly that is not means I got 1\10 but if you think that, then you are too close. I got 3\10 but don’t think I’m stupid, because I did very badly, at the same time I’m still telling you that I did bad, but here is what I want to say, that was my mistake. I knew the material but I just misunderstood but you know it was a experience for me because I’ll never do it again at the same mistake.
Mr. K said anybody who got less than 8\10, you are in trouble, then what you think about me, I’m in a big trouble, but remember not only me I know somebody else also in a trouble.
So why can’t we come up with something different.
I get one suggestion and let us hear from you or give us your view.
Here is what I would like to suggest, first, if you understood the material and you know you doing fine, ask your friend or other classmates if they have a trouble or if they don’t understand what is going on, because you can help them, and also I believe they feel comfortable with you. If you don’t understand the material or you think that you need little help ask your friends say I need help and that is not shame that is how you learn.

Those who have time the days that we only have one class, let us come together and do something constructive i.e.(Homework).
If we come together, I’m telling you we can do a lot and I have experience for that, because before the spring break I had trouble with probability but in spring break we were meeting every two days once me , Caitlin and Mohamed. We couldn’t believe it how much we can do it. And that was helpful. Thanks Caitlin and Mohamed.

The rest of the period it was just writing notes in our dictionary.
Here you go

MORE CALCULATOR FUNCTION YOU SHOULD KNOW

TO FIND THE AREA UNDER THE NORMAL CURVE BETWEEN 2 KNOWN Z-SCORES

METHOD ONE

Calculates the area and draw the graph.
ShadeNorm(low value, high value, mean,STD.Dev.)STD.Dev Means standard deviation.
If you do not enter values for mean and STD.Dev. the calculator uses the standard normal curve; i.e. Mean=0 STD.Dev=1
Access: 2nd [Vars] [>][1]

For the standard normal curve we uses these { window} settings

Xmin=-5 Xmax=5 Xsc1=1
Ymin=-.2 ymax=.6 Ysc1=.1
Adjust the window setting if you use the values of Mean and STd.Dev that are different from the Mean=0 and STD.Dev=1.

Method two

Calculate the area; does not draw a graph.
Normalcdf(law value, high value, Mean, STD Dev.)
Access; 2nd [vars][2]

If you want to find the Z-Scores from which you know the area under the curve and below that Z-Score:

InvNorm[area}
Access: 2nd [Vars][3]

If you want to know the probability that a particular value will occur in a normal distribution.

Normlpdf {Value, Mean,STD.Dev}
Access: [2nd ][Vars][1]

The above command is similar to the one below in a binomial distribution, to calculate the probability that a particular number of “successes” will occur we use:

Binompdf(# trial, probability, of success, # success)

If you want to list (and perhaps store) the probabilities for all possible (# of “successes”, for zero to the max omit. The last parameter

Binompdf(trials, probability of “success”

Access[2nd ][Vars][0]

To find the sum of the probabilities in a binomial distribution between two given “number of successes”
(this similarto using ShadNorm, or Normalcdf for normal distribution )

We use: binomcdf(# trials, probabilities of success, low # successes, high # successes)
Access: [2nd ][Vars][A]

I think that is all for today.
Make sure that you did your homework page 130 #1-8.
And also think about your blogging on blogging.

I want to see changes done by this Thursday, because we only have one class.

There is two things can happen, whether you help for someone, or you get help.

NEXT SCRIBE IS RUBIE

Why Should I Learn Math?

2006-04-04T14:50:00.000-05:00

This is taken from an article (Math Will Rock Your World) from Business Week. A few snippets:

Y'wanna get a really interesting job working with people on lots of interesting things?

But just look at where the mathematicians are now. They're helping to map out advertising campaigns, they're changing the nature of research in newsrooms and in biology labs, and they're enabling marketers to forge new one-on-one relationships with customers. As this occurs, more of the economy falls into the realm of numbers. Says James R. Schatz, chief of the mathematics research group at the National Security Agency: "There has never been a better time to be a mathematician."

Learn math!

How'd ya like a six figure salary?

...new math grads land with six-figure salaries and rich stock deals. Tom Leighton, an entrepreneur and applied math professor at Massachusetts Institute of Technology, says: "All of my students have standing offers at Yahoo! (YHOO) and Google (GOOG)."

Learn math.

D'ya wanna to work on the biggest most cutting edge issues of our day?

This mathematical modeling of humanity promises to be one of the great undertakings of the 21st century. It will grow in scope to include much of the physical world as mathematicians get their hands on new flows of data .... "We turn the world of content into math, and we turn you into math," says Howard Kaushansky, CEO of Boulder (Colo.)-based Umbria Inc., a company that uses math to analyze marketing trends online.

Learn math.

Y'wanna make one of the most significant contributions to the betterment of humanity?

"The next Jonas Salk will be a mathematician, not a doctor."

Learn math.

What are the implications for k-12 education?

Outfitting students with the right quantitative skills is a crucial test facing school boards and education ministries worldwide. This is especially true in America. The U.S. has long leaned on foreigners to provide math talent in universities and corporate research labs. Even in the post-September 11 world, where it is harder for foreigners to get student visas, an estimated half of the 20,000 math grad students now in the U.S. are foreign-born. A similar pattern holds for many other math-based professions, from computer science to engineering.

The challenge facing the U.S. now is twofold. On one hand, the country must breed more top-notch mathematicians at home, especially as foreigners find greater opportunities abroad. This will require revamping education, engaging more girls and ethnic minorities in math, and boosting the number of students who make it through calculus, the gateway for math-based disciplines. "It's critical to the future of our technological society," says Michael Sipser, head of the mathematics department at Massachusetts Institute of Technology. At the same time, school districts must cultivate greater math savvy among the broader population to prepare it for a business world in which numbers will pop up continuously. This may well involve extending the math curriculum to include more applied subjects such as statistics.

Learn more math!

"But I don't like math. Besides, I don't need it. I'm going into the humanities or business!"

As mathematicians expand their domain into the humanities, they're working with new data, much of it untested. "It's very possible for people to misplace faith in numbers," says Craig Silverstein, director of technology at Google. The antidote at Google and elsewhere is to put mathematicians on teams with specialists from other disciplines, including the social sciences.

Just as mathematicians need to grapple with human quirks and mysteries, managers and entrepreneurs must bone up on mathematics. Midcareer managers can delegate much of this work to their staffers. But they still must understand enough about math to question the assumptions behind the numbers. "Now it's easier for people to bamboozle someone by having analysis based on lots of data and graphs," says Paul C. Pfleiderer, a finance professor at the Stanford Graduate School of Business. "We have to train people in business to spot a bogus argument."

Ya gotta learn more math!

Yes, it's a magnificent time to know math.

'Nuff said.

Statistics (Blogging on Blogging)

2006-04-04T01:24:00.000-05:00

I'm really struggling with tonight's homework (page 130). It' s strange, because I thought I understood it in class, but now it looks like a bunch of gibberish to me. I have an okay grasp on the stuff we did before this. I hope you guys understand this better than I do. :-/

Scribe

2006-04-03T18:29:00.000-05:00

Andrew here, and today we had two classes.

In the morning Mr. K reminded those who haven't tagged three sites must do so and there will also be a test next week. There were two problems we had to do and it took the whole class time to do those questions, mainly the second one.

1. 1200 light bulbs were tested for the number of hours of life. The mean life was 640 hours with a standard deviation of 50 hours. Assume the life in hours of light bulbs is normally distributed.

a) What percent of light bulbs lasted between 600 and 700 hours?

Z = (600 - M)/S = -0.8

Z = (700 - M)/S = 1.2

ShadeNorm(-0.8 , 1.2) = 0.673075

b) How many light bulbs could be expected to last between 600 and 700 hours?

0.673075 * 1200 = 807.69

Now the second question (which uses binomial distribution) took the morning class and the second class to answer, PLUS we had to do another question (which uses binomial distribution and normal approximation).

2. A shipment of 200 tires is known to include 40 defective tires. 5 tires are selected at random and each tire is replaced before the next one is selected.
What is the probability of getting:

a) at most 2 defective tires

First find the probability of getting a defective tire.

40 / 200 = 0.20

Also, make a list in L1. Your list should look like this:

Go to the home screen and press 2nd function VARS to go to the distribution menu and select the binompdf ( .

binompdf(# of trials (n) , probability of success (p))

binompdf( 5 , 0.20) -store-> L2

L2 should look like this:

To find the answer to a) you must go to the home screen and press 2nd function STAT and then go to the MATH menu and choose sum ( . SUM will add all the probabilities from the lowest value to the highest.

sum( List , low value , high value )

sum(L2 , 1 (refer to the 1st image; you are actually choosing ZERO on the L1) , 3 (you are choosing TWO because at most you have 2 defective tires.)) This syntax should look like this:

sum( L2 , 1 , 3 ) = 0.94208

b) What is the probability of getting at least 1 defective tire?

sum( L2 , 1 , 1 ) = 0.32768

1 - Ans = 0.67232 , 0r , sum( L2 , 2 , 6)

The sum( L2 , 2 , 6 ) answer seems easier to explain, so the defective tire can either be the 1st, 2nd, 3rd, 4th, or 5th tire which is why the lowest value is 2 and the highest value is 6.

c) What is the probability of getting 2 or 3 defective tires?

sum( L2 , 3 , 4 ) = 0.256

And finally, on to question 3.

3. Customs officers estimate that 10% of vehicles crossing the Canada-US border carry undeclared goods. One day they randomly searched 350 vehicles. What is the probability that 40 or more vehicles carried undeclared goods?

n = 350

p = 0.10

q = 0.90

Now there are 2 methods to solving this problem. ONE being the binomial distribution method, the other being the normal approximation method. There are also 2 methods within the normal approximation method. You can either use Z-scores or RAW data.

Binomial Distribution: Uses n and p.

binompdf( 350 , 0.10 ) -store-> L1

sum( L1 , 41 , 351 ) = 0.2088192368

Normal Approximation: Uses n, p, and q.

Method 1: Z-scores
(Note: I'm still unsure of what to actually do since I sort of forgot how to do this)

M = n*p = 35

S = square root (n*p*q) = 5.61248608

Z = (40 - M) / S = 0.8908708064

Z = (350 - M) / S = 56.1248608

normalcdf( low value , high value )

normalcdf( low Z , high Z ) = 0.1864992046

Method 2: Raw Data

normalcdf( 40 , 350 , M , S) = 0.1864992046

(Note: for some reason using binomial distribution and normal approximation gives different answers but are also really close, and I have no idea why)

WELL, that's about all we did in both classes. Anyone who reads this should make COMMENTS in case I've made mistakes.

HOMEWORK: page 130, questions 1-8

NEXT SCRIBE: Muuxi