Tuesday Dec 20

Today in math Mr. Max showed us " The one sided piece of paper" He made a 3d type object. He then had Schure colour the one side of the paper with a green marker and that proved his theory of the one sided piece of paper.

Next Mr Max showed us the Klein Bottle. I thought it was really neat, there is no inside and no outside.

Then Mr Max gave us a puzzling problem. That made us really think why the rectangle was bigger than the other the diffrence was only 1, and still no one could figure it out. He gave us hints to. He said we could think about it over the break and try and figure it out.
















<--Klein Bottle


http://www.dm.unipi.it/~frigerio/files/klein_bottle.jpg


Have a great christmas break everyone!!

90th Post!!!!!

Mr. Max is at home sick today... :(

We are to be workin' on either:
1. Tessellation Assignment
2. Circle Questions (opitional, #1 - 39, random test sometime this week)
3. AM catchup

=================================================

December 20th
Ok I'm board and it's my last geo. class before Christmas break. I find some of the circle questions a tad difficult (fun though, I admit). I also realized that none of the circle "laws" are on the blog!!! I'll do that.


Cirlce Geometry

1. If a central angle and an inscribed angle in the same circle both intercept the same arc, then the central angle has a measure of twice the inscribed angle.


2. If a diameter or radious happens to intercept a chord at a perpendicular, then that chord is bisected at the intersection point. ***Converse is also true.

3. If a circle contains an inscribed angle such that the angle intercepts a semicurclaular arc, than the inscribed angle has a measure of 90 degrees. ***Cinverse is also true.


4. If two angles are inscribed in the same cricle and they both intersept the same arc then they are congruent.


5. If there exista a line tangent to a circle then the tangent line is perpenduclar to the radius/diameter at the point of tangency.


6. If a point exists in the exterior of a circle and two unique lines tangent to that circle exists through that point then the segments created fromthe points of tangency to the exterior point must be congruent.


7. "The sum of the measures of the interior Angles of a Polygon."


============================================

The notes on circles we did in class.
The pictures (accept weapons of math destruction) were created my myself using various programs. More are coming soon, just didn't have enough time before the holidays to create them all.

December 17

Today we started with Mental Math. It was probably the most toughest one i did! If you did good on it well congrats to you!
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
We haven't yet set a date for when the tessalations (number 9) is due yet but sometime this week....... So get busy and get it done!
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Mr. Macs is checking everyone's budget assignment if you did not finish yet.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Today Mr. Macs is teaching us about "Simple/Compound Interest"

Simple*
->Interest is calculated EXACTLY once

Compound*
->Interest is calculated continually, at the end of every compounding period

Interest: (Think two perspectives)
An amount of money generated through the use of 3 variables.
>Principal Amount (P) $
>Interest Rate (r) %
>Time (t) years

Simple:
I=P.r.t (Interest (by it self))

Compound:
A=P(1+r/n)^n.t (Amount (Principal plus interest))

P= Principal ($)
r= Rate (%)
t= Time (years)
n= number of compoundings per year

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Everybody should have wrote the example down that he gave us so i am not going to type it all out but this is it summed up:

In the 5th year Bob's total value of his investment is $1276.29
This is called the compounded amount(Interest was added (compounded) to thw principal each time).

This way was using the simple way and finding out his earnings for each year than adding them on to the next.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

An easier way to get the same number would be: (compound way)

A=P(1+r/n)^n.t
=1000(1+0.05/1)^1.5
=1000(1.05)^5
=1276.29

HOLY!!! Did you notice that this =1000(1.05)^5 looks like the equation y=a.b^x!!
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Another way you can find this answer is also using excel!! (you can use excel for so many things!)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Well that's what we did today!! I hope everyone had a great weekend and only 5 more days of school left!!!!! YEAH!!

For tomorrows blog Semba you are the blogger!! Have fun!

December 14/07

Today Mr.Max's was away so Mr.Buckner was our sub.

Our assignment is to work on Exercise 2 (in the circle booklet) all 36 questions. Next week we will be quized individually on a randomly picked questions out of the exercise. Also we are to work on the tessalation project which is Exercise 3 question 9. and if your done all that you can work on accelerated math.

Have a good weekend everyone. Hope you have all your christmas shopping done

Thursday, December 13th

Today in class we had a work period to work on our budgeting assignment using our spreadsheets.

Tomorrow Mr Max is away so we will have a sub in. This mean Mr Max will not be here to check out budgets, so the last day for budget checking will be on monday.

Today we recieved the booklets on circles. The deal with these booklets is that we don't have to do all the questions in Exercise 2, but we have to KNOW HOW to do all the questions. Mr Max said he would be checking by getting us to come up and do random questions from the booklet for him.
The only question from Exercise 3 that is assigned is question #9.

Mr Max also said that he will be assigning accelerated math soon**

December 12

Today was a work period to work on our budgeting booklet Mr. Maks has assigned for us. Today he taught us how to calculate annual property tax and annual home insurance is order to answer some of the questions.

Here is how to calculate property tax along with an example:

You multiply the value by how many mills then divide that by 1000.

eg: The home is assessed for property tax purposes at $30,000, the mill rate is 61 mills.
$30,000 x 61/1000= $1830

Here is annual home insurance along with an example:

You divide the value by 100 then multiply that by the cost per $100.

eg: Home insurance based on a home value of $50,000 at a cost of $0.62 per $100.
$50,000/100 x 0.62= $310

As a class, we also discussed the fact that facebook has been blocked in our school and how upset people are. Many classmates had person opinions about this subject and many were upset.Many caim that it is a important communication device that is a very important and useful tool in their everyday life. There is some talk that the facebook homepage will be unblocked and as of now, everyone is hopeful.

Tomorrow the scriber is "Patzer."

Today is Day 1, which means long blocks. We started off by doing mental math. Mr.Max made a clear note that he dislikes facebook...but yet has an account. I dont get it it? Haha! We then made spreadsheets for budgeting.
Today we learned how to turn on all formulas on a spread sheet and this is how:
All you need to do is press the control key and the tilde symbol(the key right beside the number one). Your spreadsheet will now show you all of the forumlas you have entered into it.
We all have our spreadsheets figured out and are now working on 4 other budgeting problems. We dont have a certain due day yet but we will shortly.
I'd like to give a happy reminder to everyone that there is only 14 days till christmas...YAY!
The scribe for tomarrow is Minish. Have a Great Day everyone!

Monday, December 10, 2007

First of all, today was Day 2, short blocks. We started off with mental math.
~Just something to do-- look up "Fisonacci" on wikipedia and search the patterns he created.

We started a new unit today- Monthly Budgeting. We started to create a spreadsheet to help with the problems in the package that Mr. Max gave us on Thursday. We didn't get very far in this unit today because class was almost over. So Mr. Max said we will continue from where we left off tomorrow.

If my scribe was "cheap".. it is only because I didn't have much to work with. Sorry if it didn't help with much homework.

Friday, December 7th, 2007

Todays Class was an interesting class. First, it was Day One which means that it is long blocks. We came into class and Mr. Max said that we weren't going to have a mental math, instead we had to take wooden blocks and we played the "Tower Game". The tower game is a game where there are three rows and you have to move the tower of wooded blocks to make the same tower in another place. But you can't have a bigger block on top of a smaller block. For example:
1 block = 1 move
2 blocks = 3 moves
3 blocks = 7 moves
4 blocks = 15 moves
5 blocks = 31 moves

We tried to figure out how many moves there would be for the amount of blocks we had, for the majority of the class. Then we got on a topic of billionaires. We had a discussion about are veiws of billionaires and if they are selfish or not. Then for the remainding of the class we had to research "The Bill And Melinda Gates Foundation". There was no homewrok assignment.

December 4, 2007

Since yesterday was a snowday, Mr.Max gave us an extension on accelerated math. The 43 objectives are now due at 5pm today.
Today in class we had a work period.

Tomorrow Mr.Max will be teaching us about finances. So he said it would be good if we figured out how many weeks are in a year and other stuff like that.

There is also tutoring after school with Mr.Max on Wednesdays till 5pm.

Hope everyone had a good snow day yesterday.

*****The scribe for tomorrow is Chev*****

Monday, Dec 3, 07

Good morning everyone!


In today's class Mr.Max talked to us about circles again. He explained about which shape we would get if we "cut" a cone using a "razor blade". The following page Mr.Max made during class should explain what I mean to say better.


If a straight horozontal cut is made the shape made should be a circle.


If a diagonal cut is made, the shape should be an elipes (oval).


If a vertical cut is made with a slight slant, the shape should be a prabola.


If a straight vertical cut is made, the shape should be a hyperbola.




The equation used to create an image of a circle or an elips is
(x)^2+(y)^2=(r)^2
The center of the circle will always be at the origin (0,0), unless you move the center point. You do this by using (h,k) ((h,k) is the center of the circle).
The equation you would use will than be (x-h)^2+(y-k)^2=(r)^2

November 30th

Hey today as all know Mr.Max was away, so Mrs.Turton was our sub for the class.

Today are assignment was to work on Accelerated Math. This is due to the fact that there are 43 objectives due on Tuesday December 4th. Hope everyone is somewhere near there.

Well since its a work period, I'll briefly discuss what the presentation this morning was about.

The presentation was on addictions. There were 3 guys who came to talk to us, Trevor, Steven, and Rollin.

They each shared some of their struggles with their addictions to alcohol and drugs. All had said that they remember sitting through these presentations when they were in high school and saying that they would never smoke or do that stuff. They also wished they had talked to their parents, school counsellors and teachers. They are here to help not to hinder.

They also said that is was like an illness of the mind that you bring on yourself. They all recall thinking that they weren't good enough, or they were like chameleons that would just blend in with which ever crowd of friends they were hanging with.

Rollin went through the loss of his wife and son, although now him and his son have a great relationship. Rollin can relate to what his son is going through in school and they have agreed to be best friends through all high school and talk about everything. Also while he was in his addictions stage he was involved in a biker gang. he was also attacked during his addictions due to gang membership. He was stabbed tried to commit suicide twice and lost everything, his house, car, everything, and yet he is still here to share his story. He is helping to make a difference in Winnipeg by coaching boxing, he recently opened up a center that anyone can go to. Tune into APTN on December 26 to see one of his moving boxing shows in which he helps street kids. Rollin has been sober and drug free for 5 years now.

Trevor was introduced to drugs when he was in grade 7 or 8 and as he recalls he was high when he attended a presentation like this in high school. He dealt drugs on and off. He hates rehab centers. He went through many in just a year. He is glad that he changed his way from alcohol and drugs. He has been sober for a year and a half now.

And last but not forgotten is Steven. He has always felt different. One day his mom pointed out a man at a 7-11 that looked feminine and said that he was "gay". Steven simply asks what does gay mean? His mom is like a guy who is attracted to men. Now Steven had always had trouble when it came to commitment with his numerous girlfriends he just couldn't commit. He would always be like "I'll try harder with the next one". He would quite often drench his pain and his sense of not belonging by doing drugs and alcohol. He started to deal it too. His life is now great and he has realized that he is gay, but it doesn't matter to him. Steven has been sober and drug free for 2 years on December 13.

Even though they didn't know each other before the 12 step recovery program, they all had many things in common. All three of these men went through many hardships. They lost everything, they felt alone, lost, even rejected at times. They all feel in to the trap of drugs and alcohol addiction.

Now they are all happy to feel free for the first time in years. Even though they said they'd never get into any addictions it still happened. Peer pressure, is one of the main reasons people get into these situations. As they said its easy to say that you won't but harder to actually do.


Yeah i know its long and slightly repetitive but I found the presentation to be good and motivating.


**** REMEMBER: 43 objectives are due on Tuesday December 4th*******

Good luck and have a great weekend everyone.

P.S. I'm not sure who scribes on Monday

Hey class!

*We have a sub tomorrow so it will be a work period ..try to get lots done because 43 objectives are due on Tuesday at the end of the day*
*FYI a Free new version of graphmatica 2.0 can be downloaded, it shows intersects, tables etc.. *





Today: We worked on accelerated math and had a quick lesson on Circles..inscribed quadrilateral, incyclic quadrilateral


mL1+mL3=180 degrees


mL2+mL4=180 degrees

My Opinion on the wikipedia Banning
Wikipedia... is a truly convenient search engine not all the information is correct, and most people are aware of this. I think it's a good learning tool for those who can correct the errors on the site.


It shouldn't be banned from schools, but students and teachers should know that not all the information is correct and the site isn't totally reliable. Personally I think Wikipedia is such a popular site it sits on top with search engines like Google, Yahoo and Ask Jeeves. To find information quickly Wikipedia gives you specific, but not always accurate solution to your question. Its almost a bitter sweet situation.






(picture above)http://www.pixelache.ac/2005/files/_Wikipedia-logo_BWb.jpg

Wed. Nov. 28/2007

Today Mr. Max taught us about polygons. The first picture is of the diffrence between a concave and a convex polygon. The one with the "dinted in area" in red is concave.

This picture demonstrates the rule that there is always one less triangle that can be made then the number of sides, when the goal is the minimum number of triangles that can be fit in a regular polygon.

This picture shows us regular, equiangular, equilateral polygons.

These next two pictures demonstrate the formulas for finding the sum of the measures of the interior angles in a polygon.

n=number of sides

Mr. Max asked me to comment on wikipedia. From my experiance it is a good conveniant source of information.

Tuesday Nov.27

Hey everyone..
Today in math we continued working on circle geometry.

We started with circle number 3.
*If a circle contains an inscribed angle such that the angle intercepts a semicircular arc, THEN the inscribed angle has a measure of 90 degrees.
(Inscribed- when a line intercepts a semi-circle.)

Circle-4 If 2 angles are inscribed in the same circle and they both intercept the same arc THEN, they are congruent.
(Congruent- the same)

Circle 5- If there exists a line tangent to a circle THEN the tangent line is perpendicular to the radius/diameter at the point of tangency.
(Tangency- having contact at a single point or along a line without crossing.)

Circle 6- If a point in the exterior of a circle and 2 unique lines tangent to that circle exist through that point then the segments created from the points of tangency to the exterior point must be congruent.

That was the lesson for the day after that we continued working on accelerated math.
* The new deadline for accelerated math is next Tuesday!
Have a great week. The next scribe is Toderash

Tuesday Nov.27

Monday, Nov 26, 2007

Hey guys!

I know I'm kind of late for my posting but I still got it before next class.

Today, we didn't do mental math, it was a short block. Mr max had a lot to talk about.. I caught most of it anyways.

We learned about....... CIRCLES. =)!

It was a real hard time to keep up with him, but I hope all of you guys listened well!

To start it off .. everyone forget this 3d stuff .. well not forget, just for this unit thinger.

"Everything is happening in a flat surface, forget about anything behind it"

Before I let you look at the diagrams, you'll have to know some new or for some of you, old words.

Vocab!!

"Chord" - - a line segment joining two points on a curve

"Diameter" - - Any straight line segment that passes through the center of the circle and the endpoints are both on the circle

"Tangent" - - one point touching the circle, the line is on the outside of the circle

"Secant" - - a line that intersects two or more points on a curve

"Radii" - - Plural form of radius

"Central Angle" - - the vertex is always the center of the angle name.

"Inscribed Angle" - -vertex is touching the circle

"Arc" - A piece of circle
(major) ;;; associated with central angle >180)
(minor);;; associated with central angle <180)>

(semi-circle);;;associated with central angle = 180)

.. on to the diagrams that should help you with understanding!

I made these on EUKLID and paint =)!

AB is a chord,
so is KE.
KE is a diameter
and HI is a chord also.
CL is not a chord,
it's a radius.
Finally, DG is a tangent
and JF is a secant line.

Remind you of a poem? Haha.

is a central angle,
***notice that 3 letters name angles and
the vertex has to be the middle letter!!***
EIH is an inscribed angle.

Here is a representation of what the different kinds of lines there are.

• Segment, as you can see has no endpoints.
• Line has both endpoints, the circle.
• A ray has just one end point and it is one way.
  

I'm sorry since I didnt get a chance to put those Accelerated math problems on here!.. But, I just couldnt get the diagrams to look right. If this helps any, here are the statements that Mr Max wrote after demonstrating***

"If a central angle and an unscribed angle in the same
circle both intercept the same arc, then the central angle has a measurement of 2wice the unscribed angle."

And!!

"If a diameter of a radius happens to intersect a chord at a perpendicular, then that chord is bisected at the intersector point."
**** the converse is true also..... meaning that "if a chord is bisected by a radius or a diameter then the angle of intersection is perpendicular."

*******29 days till cmass!!!!!!!!!!!!!!!!!!!!!!

Remember: Circles

-- MM# 24 --
-- There was no lesson today --
-- Informational folders (that may help you with AM) found at J:\Coursework\Math\Applied Math 30SA-1 --
-- It's recommended that we 'refresh' our vocabulary for our new circles unit (can be found in 'that' folder under geometry) --
______________________________

November 21

Hey!!!

So I know everyone is trying so hard to catch up on thier excelerated Math!!! So keep going today is a work period to get some excersises done!!! Good luck on getting everything done on time!!

http://img371.imageshack.us/img371/3194/thumbsupag3.jpg
And tomorrow Semba you are the blogger tomorrow! And there are 43 objectives due at the end of the month!

Scribe for Tuesday Nov. 20

OK I have taken the duty of scribing today!


So frist we did mental math and had a disscussion on a "saying" that was said in class when we had to find the product of the word fish. And we also got distracted on the topic of what salmon and tuna look like in live fish and sushi form.


Then we did:


Linear Equalities:


(graphing rules with logic testing)





Consider this:





-8x+4y-3>=0





The question is:





What do I do with this if I have no Graphmatica?!?


First you have to put it in a form your calculator will accept


4y>=8x+3





devide the equation by four to get





y>=2x+3/4 *( NOTE: it is two x because 4 goes into the 8 twice)*





NOTE: What i know!!!

• i know that the corresponding linear equation goes through(0,3\4)



• there is a line slope of 2

Here it is graphed:

(and yes i am using Graphmatica but that is because i am doing this at home and do not have the original screen shots)

Now which way do i shade it?Because in your graphing calculator you choose which way it unlike Graphmatica doesn't do it for you.






Do you shade blue or green???(so chosen for the colours because of the gray cup finalists)
now you choose a spot to see this is best if you choose 0.
yiou look at the eqation:
(you enter 0 as both the x and y values)
0>=2(0)3\4
0>=3\4
(the two is gone because 2 multiplied by 0 is 0)

you know that this equation doesn't woprk because 3\4 is not less then or equal to 0. so you know that you have to shade what is less then 0.
So you shade blue!!!!

I think that was about it.
We then finished the class with working on our Accelerated math.

• we have 40 objectivbes due by the end of the month
• there are TADD povillions tommorropw in 4 and 5 block
• and i am not sure who scribes tommorrow (SORRY)

Monday, November 19

Ok, so today was short blocks so we didn't really get to terribly much accomplished. The class was basically a work period used for accelerated math and corrections of our questions that were homework last week. That doesn't really give me much to scribe about so I thought I would post some links that might be of use to someone.

Linear Programming:
http://mathcentral.uregina.ca/beyond/articles/LinearProgramming/linearprogram.html

"Friday's Fantastic Voyage in Room 204"- November 16th Scribe

We started off the day by doing our 22nd Mental Math Quiz.

We next individually went up and had a homework check on our questions that were due today on "Solving Linear Programming Problems."(One we picked ourself and one chossen by Mr. Maks)

These questions were similar to a previous unit we did on "Linear Equations." So i think that most of out class caught on fast, even though you used a slightly different technique to solve the questions.(Using the Zone of Feasibility) For this reason, it seems like we are all doing quite well and understanding the questions assigned.
While we were waiting to have our homewrok checked, we worked on Accelerated Math. In fact, we pretty much had the whole class to work on Accelerated Math to finish our forty some objectives that need to be completed for the end of the month. The scriber for Monday's class is "Patzer."

So today is Day 2 and that means short blocks. We started off the class with Mr.Max talking a bit. He explained he was very proud that we learned the linear programming material so quickly, and repeated the questions we have due for tomorrow! Today is a work period.

Mr.Max explained to me that since it was a work period I had to be creative. I believe this has to do with math and is sort of fun haha. Enjoy...

"Remember all those rationals and irrationals, the ones we got confused?
I still get them wrong and I am not very amused.

Digits and decimals, too many D's
But wait until we start on those x,y, and z's.

Powers of 10 are expressed by exponents in many ways,
But, remember, there is only one and that is to have them raised.

Counting all those zeros makes me very crazy,
So use that scientific notation and don't be so lazy.

Collections of elements in sets are a breeze.
Elements follow a pattern just like 1,2, and 3's.

A variable is a symbol like x which has 1 value, not 2.
If you put the right variable in an open sentence, the statement will be true.

Factoring numbers can be such a bore!
But, prime numbers are the best since the factors are only 1 and itself, and nothing more.

Basic axioms of algebra leave you in awe,
But not to understand them is one major flaw.

The most important axiom is the distributive one.
It's the one we used the most, but it wasn't that fun.

Reciprocals are the numbers that always do a flip upside down.
Inverses are very different and in their own special way turn around.

Numbers are variables are jumbled disorderly,
Are called equations and are only solved algebraically

Solving inequalities can make you want to die,
But, there are only 3 choices: greater than, less than, or equal to, so there is no need to cry.

Polynomials can leave you in such a disarray,
But, just remember there are coefficients and constant terms and then you will be straightened out today.

Products of binomials can take you so long to do a few.
But, just skip the steps and use FOIL without a big to do.

Figuring out ordered pairs can leave you in such a mess.
But, if you remember the x-axis, y-axis, and origin, you'll do them with success.

Systems of linear equations can be solved in 4 different ways.
Substitution, addition method, determinants, and graphing with different rays.

The slope always equals rise over run.
If you remember this you'll always get those problems done.

Quotients of 2 polynomials are called Rational Algebraic Expression.
If you don't reduce them fully they will leave you in a great big depression.

Square roots and cubic roots leave me very puzzled,
But the index and radicand leave me troubled.

Square-free integers can't be broken down anymore.
They are like 2,3, and 5, but never integers like 16 or 4.

Reference: http://www.missioncollege.org/depts/math/ly/kim.htm

Well thats about all for now! Remember everyone we have 2 questions due tomarow off of Exercise 5!

Have a Great Day :D

Wednesday, October 14th.

The first thing that we did today was that Mr. Max told us our assignment that will be due on Friday. The assignment is to do two of the eight problems on page D-10. One of the questions that we are required to do is our choice. The other question that we are required to do is Mr. Max's randomly choice of pick. For the rest of the class we worked on this assignment that was just assigned. This assignment is due Friday, November 16th.

Note: Approximatly 42 objectives on Accelerated Math will be due on November 30th.

Good luck Senior Varsity Volleyball teams! SINK THE SHIP!

Tuesday, November 13th

At the beginning of class, we had a rather large discussion about Accelerated Math, which took too much time that we couldn't do mental math. We came to the conclusion that we need to complete until the end of the next two units that we will be doing which is Circular Geometry and Linear Programming. It will be approximately 42 objectives by NOVEMBER 30th

- We than gathered in our groups we were put into on Monday, and completed our question that was assigned to us.

Good Luck to volleyball girls + boys! SINK THE SHIP

Solving Linear Programming Problems

Answers for: Exercise 5, Page D-9, Question 3

Let x = long sleeved shirts
Let y = short sleeved shirts
a) 4x + 3y <= 120
b) 3x + 1y <= 60
d) (0, 40) (20,0), but answers can vary
e) The best solution on the graph is where the two inequalities intersect, making it a critical point which is (12, 24).
Profit made:
12 long sleeved shirts = $13.20
24 short sleeved shirts = $14.40

click on to enlarge

Math Question Exerscise 5 question 4

Standard computer-1.5hours electronic manufacturing and 1 hour of assemble time
Deluxe Computer-.5 hour of electronic manufacturing and 2 hours of assembly time

Letx= standard
Lety=Deluxe

a)the in equality for the electronic manufacturing time :
5x+.5y<30>b)1x+2<70

c)took let statements and put them in graphmatica

d)the two possible solutions are: (10,30)and(15,10)

e)the location of the best solution is the intersections of the lines
Critical points
(0,35)=6300
(10,30)=7900
(30,0)=2500

Solving Linear Programming Problems: Question 2

A rectangle to be constructed has a length less than twice its width, its perimeter is at most 48 units, and its area is at least 32 square units.

L=length(x)

W=width(y)
a)Inequality that represents the relationship between the length and width.

~ l<2w

b)Inequality that represents the perimeter.

~2(l+w)<=48

c)Inequality that represents the area.

~ l*w>=32

d)Graph these inqualities

e)Give two possible solutions for the dimensions of the rectangle.
-(10,10)
-(5,15)
-(18,8)

People who did this wonderful question!!!
-Ashley
-Alexis
-Alissa
-Haley
-Kat-lynn

Unit 2 Summary- Non-linear equations

Here is just a brief outline of this unit.

x- linear
x^2- quadratic(one curve)
x^3- cubic(two curves)
x^4- quartic(three curves)
x^5- quintic(four curves)

Standard form
y=ax^2+bx+c

Vertex opening form
y-k=a(x-h)^2
Where (h,k) are the vertex coordinates.

In this equation, the value of "a" tells us the opening.
If a>0, parabola opens up
a<0, opens down
a=1, standard
a>1, narrow
a<1, wide

Parabola with a minimum value is "cup" shaped.
Parabola with a maximum value is "cap" shaped.

Domain= all values of x
Range= all values of y

Axis of symmetry- # of x-axis that passes exactly through to vertex

Cubic function- has no absolute min or max value, only has relative values.

Zeros- were lines passes through x-axis

My Apologies!!

Hey guys, i'm pretty sure tomorrow is my day to scribe for the blog, but i've been away in Flin Flon all weekend and we were supposed to leave today but its been snowing really bad and the roads arent in the greatest conditions, so we're staying an extra night. if it'd be alright that whoever that is scheduled to scribe on tuesday would switch me that'd be great!

thanks

Non linear Functions Test Review

In this unit we learned alot of new material some hard some easy. Like how to find the vertex of a parabola. First you graph the parabola on your calculator, then press 2nd trace, stroll down and selcect either minimum or maximum, now press enter and you should see it on your screen. ( Maximum=cap shaped, Minimum=Cup Shaped). We also learned types of functions.
x^1= Linear no curves, x^2= Quadractic 1 curve, x^3=Cubic 2 curves, x^4 =Quadratic 3 curves, and x^5 Quintic= 4 curves. We learned about Cubic functions, all cubic functions are in this form y=ax^3+bx^2+cx. Then we learned about domain and range I struggled with this part, Domain= X values and Range =y values. Type of vertex openings. a>0-opens upward,
a<0-opens>1-narrow parabola. Overall this unit was harder than the first unit for me.

Unit Two Test Review

Our Unit that we just finished studying is called "Non-linear functions".

We learned about:

*Linear Functions
- x^1 - is a straight line.
* Quadratic Functions
- The form is: y-k=a(x-h)^2.
- x^2 - has one curve.
* Cubic Functions
- The form is: y=ax^3+bx^2+cx.
- x^3 - has two curves.
* Quadratic Functions
- x^4 - has three curves.
*Quintic Function
- x^5 - has four curves.
* Exponential Functions
- The form is: y=a*b^x.

We also learned about:

* Domain
- The domain is all the x values.
* Range
- The range is all the y values.
* Function
- When the function passes the vertical line test. Which means it can only have one point vertically.
* Relation
- Every straight line is a relation.
* Maximum Value
- The maximum value is the highest point on a parabola. When there is a maximum value this means that the parabloa opens downwards.
* Minimum Value
- The minimum value is the lowest point on a parabola. When there is a minimum value this means that the parabola opens upwards.
* Axis of symetry
- The axis of symetry is the middle verticle line on a parabola. ( x=h )
* Vertex
- The vertex is the highest or lowest point on the parabola.
- a>0 - opens up.
- a<0>1 - narrow parabola.
- a<1 - wide parabola.

New Commenting Post! haha

HEY GIRLS! LETS COMMENT ON THIS POST NOW!
yayyy.
let's help eachother with our math.

November 8

For today's block, we were assigned different options to spend our time on...

1. Work on the take home assignment - Non Linear Functions
2. Complete a unit summary on the blog in order to recieve extra marks on the test
3. Continue working on accelerated math objectives.
4. Begin to learn Linear Programming using http://webct.merlin.mb.ca/webct/entryPageIns.dowebct
For user name and password, enter "demo".

For extra help on our self test, we have set up a "blog chat" by commenting on "The Take Home Assignment" post. Remember not to plagiaris or you will get nothing but a 0 and a possible failed math credit! Good luck chuck!

Unit Review Study

The Mechanics behind what we've learned so far:

Functions-passes the vertical line test and creates a set of even numbers
Relations-every line is a relation
Domain -represents all the x values
Range-represents all the y values

Functions-
x^1-linear-straight line
x^2-quadratic-one curve
x^3-cubic-two curves
x^4-quadratic-three curves
x^5-quintic-four curves

The Virtex openings-
a>0-opens up
a<0-opens down
a<1-wide porabola
a>1-narrow porabola

note*
maximum=cup shaped
minimum=cap shaped

`~`*Good Luck!!*`~`

Thursday, Nov 8, 07

Sorry that I didn't post anything yesterday, but I was having computer troubles. Any way, like chocolatelover18 said, we got to work on the test yesterday, but we couldn't talk to each other about the test, out loud, and we don't have to hand the test in physically. We can do it anyway we want, as long as it is appropriate.
Today we did mental math 19, than Mr.max gave us some options to work on, in no prior order to do them in.
1. Finish take home assignment (test)
2. Do a unit summury for marks
3.Work on Accelerated Math
And 4. By linking from our blog, and using "demo"/"demo" as user name and passward. Start learning the next unit (on purpose).

The Take Home Assignment

Instructions:

Hand it (whatever it becomes) by Friday @ 11:20 a.m.

The idea here is to prove to me that you've learned some things in this section of the course. Use any/all resources available to you (including Graphmatica, Excel, your calculators, etc.), but CONCENTRATE on the QUALITY, APPEARANCE, and GENERAL MATHEMATICAL WORTHINESS OF YOUR RESPONSES. The format of your responses is up to you, but consider that perfection is the goal. Creativity should be considered when you are CREATING your responses. Plagiarism of any kind will be rewarded with a zero grade on the assignment, in addition to my disdain for your lack of personal integrity.

Impress me. Challenge yourself.

RM

Nov 6
Today’s plan in math
- Test Review
- Practice Test Questions

First we started the class of with Mr.Max handing out the review questions for the test. Then Mr.Max started putting up the review for the test. The unit we are reviewing for is Non Linear Functions.
Test Review – Non Linear Functions
1. Mechanics- For this section we should know the following things.
- Functions/relations
- Domain/range
- Calculator Stuff (Tracing, calculating, windows, zooms, tables, graphs, intersections, etc.
Graphmatica Printing
-First you open up graphmatica.
-Put in your equation, press enter.
-Then at the top left hand corner of the screen you should see a button called “copy graphs”.
- Click on it, and now you have copied your graph.
-Now open up word.
-Right click and select paste.
- Now you can print!
(**DO NOT HIT PRINT SCREEN ON GRAPHMATICA always print off word, if you do print off graphmatic I suggest hiding from Mr.Max.)
2. Quadratics “Actual important stuff in the course”
Y-k=a(x-h) ^2 vertex opening form
y=ax^2+bx+c=standard form
(H, K) = the vertex of a parabola

How to find the vertex of a parabola.
1. Graph the parabola on your calculator.
2. Press 2nd trace
3. Next select minimum or maximum, and press enter.
X=linear (no Curve)
X^2= Quadratic ( 1 Curve)
X^3=Cubic(2 Curves)
X^4=Quartic(3 Curves)
X^5 Quintic (4 Curves)
Cubics
· Box volume or relative min/max problems.
· Cubic Functions are all in this form y=ax^3+bx^2+cx
Exponentials
· No “e” questions
· You will have to use exp reg to create y =a.b^x
*Before Mr.Max had to leave he had a “crazy idea”, this crazy Idea was instead of us having our test tomorrow in class, and we would take home our tests and hand them in on Friday! The next scribe is Bass.

Non Linear Functions Unit Summary

In this unit summary, we learned about Non Linear Functions.

Quadratic functions can be seen in two different forms...
standard form: y=ax^2 + bx +c
vertex opening form: y - k = a (x - h)^2

In vertex opening form, the a value tells us opening.
If a>0, parabola opens up.
If a<0,>1, parabola is narrow.
If a= <1,>

Ex) y - k = a (x - h)^2
y - 1 = 2 (x + 2)^2
y - 1 = 2 (x - (-2)) ^2
Answer: (h, k) = (-2, 1)

Cubic functions can also be seen in two different forms...
standard form: ax^3 + bx^2 + cx + d = 0
function form: f(x) = ax^3 + bx^2 + cx +d

A cubic equation can have no exponent larger than 3.

Exponential functions are all in the form y = ab^x. Generally, we see exponential graphs look like this...

To solve a basic exponential problem we have to create lists on our calculator and use ExpReg to sove the equation.

Non-Linear Function Unit Summary

I learned what domain (x values) and range (y values) are.
Ex: (3,2), (8,9), (12,-8)
Domain : 3, 8,12
Range: 2, 9, -8

How to use Graphmatica and my calculator to find the domain, range and other questions answers. I also learned how to do questions with “e” in them like the amusement park questions, and how to print from Graphmatica.

Printing from Graphmatica:
Enter the equation, change the window setting if needed to properly see the graph, use copy graphs (it is the fifth button from the left), go to word, right click, paste, and re size and add titles and so on if wanted.

We also learned of equation forms:
y-k=a(x-h)^2
y=ax^2+bx+c (standard form)

These are for quadratics.
We also learned how the exponents show how many “bumps” are in a function.
Linear:zero
Quadratic: one
Cubic:two
Etc…
And by using excel how to find the volume of a box.

I found learning Domain and Rage difficult since I had no idea what I was doing. I found the Amusement park questions very easy from the beginning and was able to do well on those. I still find creating stat plots difficult but am getting a lot better at it!
I found this unit to be fun and a little challenging but over all there was a lot to learn.

Hey everyone, its a new week after parent teacher interviews .

I hope everything went well for every one.

Note* there is a math test on Wednesday on "Non-Linear Functions" apparently objectives 1-17

we didnt do mental math today because it was short blocks and we need to correct questions

we corrected the questions pg. A-7 10,11,12,13

Questions

10. for question 10 we used graphmatica typing in y=147x16x^2 and pressing enter we zoom in to see that 337.6 is the maximum hight,

then to trace the one second point you press point evaluate (on the menu at the top of the scaeen)

11. a)using graphmatica one again we type in y=4x/3-x^2/90 and enter

the maximum hight of the football is 40 feet

b)120ft

c)35yrds=(35x3)=105ft ...yes

d)35yrds(2.5feet)

*Trick* y=ten (it shows football and crossbar)

12. using excel spreadsheets we worked it out

total revenue ($)=(#of fares)($cost per ride)

letx=#of $1fare increases

lety=total revenue in $

y=(300-15x)(10+x)

after we figured eveerything out we put ot on a spread sheet

*You can also do this question the precalc way" by doing the let statements and doing the elimination method

13. Question 13 is quite similar to 12 you use the same methods

y=(4000-60x)(0.50+0.01x)

lety=$revenue total

x=no. of increases

We corrected excersise 2, #2(we used excell)

Other than the Harry Potter out burst haha, we also have a Practice test tomorrow just to review and go over a few things , ask questions and correct more questions

TEST DATE MOVED TO WED.

*~*make formula sheets and study study study Good Luck Class!!*~*

November 1 blog scribe

• Hey Everyone I am subbing for the scribe today!!!!
• Toderdash is scribing on Monday
• There is no school tomorrow
• Test Tuesday
• 25 objectives due by 3:40 today
  
  Today we did mental math! some very lovely questions about 35 kids coming to the door and each getting 6 candies how many did I give away and how 10 candies are $.25 each how much did it cost to buy the Candy? This took up a good 10-15 minutes of class.
  
  We then saw a picture of of Mr Max family
  And noted the pumpkin to the right of the picture it was throwing up!!
  
  
  

Then we worked on Accelerated Math.
Alot of people were having problems with the amusment park questions so this is how to do it:




The amusement park
1991-190000 this is four years (important to remember)
1995-469000
These are the answeres given:
A) f(t)=190000e^(0.216t)
B) f(t)=190000e^(0.226t)
C) f(t)=279000e^(0.226t)
D) f(t)=279000e^(0.216t)

This is an exponential situation
There has been an exponential growth.
These are your window settings.
X min -2
X max 6
Y min -100000
Y max 500000

You cannot be C or D because it is not the original number of people so that brings down to a fifty-fifty chance, the only difference is the exponents you have to try both of them in your calculator, and the answers are very close together.
You have to trace at 4 years because the polls are four years apart.
One of the numbers should be closer to the amount of people attending the amusement park in 1995 than the other so it is the answer.

Wednesday, Oct 31, 2007

Hey! Today, we didnt do Mental Math. Kind of dissapointed, its always so fun. He let us do some mental math, and while we do that, he is supposed to catch up on his marking. A couple people have troubles with some questions that came up on their Accelerated math. Simple as that, we get lead into a discussion..

e = 2.71828 2nd + LN - those are the buttons you need to press to get to e.

• 
  Here is an example that Mr max introduced:

During 1991,
140000 people visiting the Amusement Park
1995,
373 000 people visiting the Amusment Park

a) F(t)* t is x * = 14 0000 e 0.245t
b) F(t) = 140000 e 0.255t
c) F(t) = 233000 e 0.245t
d) F(t) = 233000 e 0.255t

That A-value is the y-intercept, so we know we have to get rid of C and D.

If you put in 140000 times E to the power of .245x, into the y= ..
Nothing will happen till you do something smart with your window settings.

________________________________________________

There was a type of questions that Chev brought up, here is what I caught from the discussion we had.

Endangered Species type of Question:

There is a list of information on numbers you will get with the question.. with that info, you do the following:
Remember:

Press :Stat + Enter, then you see the Lists. Put the info in!.
You load, the year into L1, population into L2, and Log P into L3.

There will be two parts of it that it'll tell you to do, a) and b).

a) Find the linear equation of the year&LogP
If you press, Stat + Calc + LinReg (ax+b) *number 4* + 2nd + L1*number 1* + comma + L3 .... enter.
b) Exponential equation of year&LogP
If you press, Stat + Calc + ExpReg* number 0* + 2nd + L1 + comma + L3... enter.
a.. LinReg L1,L3 (just to help you).
b.. ExpReg L1,L2

__________________________________________________

Just a couple reminders:

• 25 Accelerated Math Objectives due tomorrow!
• Math test on Tuesday
• Moga Madness today!
• Happy Halloween!

Lesson: Exponential Functions (non-linear functions)

"Hole puncher, where are you!? It usually comes to me when I call it."
- Mr. Max :)

We started with Mental Math. #17

Things from mental math:

x - linear (no curve)

x^2 - quadratic (one curve)

x^3 - cubic (two curves)

x^4 - quartic (three curves)

x^5 - quintic (four curves)

Pascals Triangle

- All Hallow's Day/All Saints Day (Nov 1) is after All Hallow's Eve (Oct 31)

- 7 months have 31 days

Homework Check for pg A-7 to A-9

25 objectives due thursday at 3:40

Exponential Functions

This slide is the summary notes for the lesson (exponential functions will always be in the form y=ab^x), and how exponential functions should generally look (rabbits multiply quickly over a certain period of time).

This slide is of your first example (hope you can read the example). We did two examples today. This one is about the intensity of light at a certain distance below the surface of a pond.

"You are a little frog sitting on a lily pad basking in the August sun. Something happens that the lily pad is pulled out of underneath you, and you find yourself a meter under the surface of the water."

The point of that was to 'illustrate' how the intensity of the light is less as you go deeper into the pond. If you were pulled a meter under the water you still see a lot of light around you because only 3% of the light was lost. We caught on quickly to the obvious - the intensity of light at the surface of the water is at 100%.

With this information we came up with our equation based on the question (get my drift?). We came up with I(d) = 100(0.97)^d. We chose this equation (out of the possible two/four) because it is a.
Where the 0.97 is the percentage of sunlight you see one meter below the surface of the water.
With that equation we entered it into our calculator/graphed it (substituting I(d) for y and d for x), and got something very similar to what Max has on the slide. We determined that a was the correct answer after observing the graph (at 0 meters below the surface we received 100% of the sunlight, at one meter 97% of the sunlight was showing through, at two meters we were able to see 94.09% of sun rays).

This slide is the second example. I'll 'retype' the question since you can hardly see it in the picture.
"Early in the 1900s, an airplane manufacturer was able to increase the time its airplane could stay aloft by constantly refining its techniques. Using a graphing calculator, determine which exponential equation best models the data."
With this question we are given a table with 'years after 1900' and 'time aloft'.
With the green on the slide Max isolated exponential equation and wrote "do regression!", so that's what we are going to do (with our calculators... in point form because this post is beginning to grow like the bunnies).

- Determine which piece of information/variable is dependent (y) and independent (x). In this case 'time aloft' would be dependent so it will be labeled L2. (likewise the independent variable would be L1).
- On you calculator enter your information in the stat plot (If you don't know how/forgot go to 'the old math blog' or :chevy:'s post... apparently. This is also the top left clip on the slide). You might want to turn on that stat plot also.
- After you have your plot you could use zoom 9 or the window settings that are on another clip on the slide above. There you have the plot (right above the window settings).
- To draw the exponential regression (trying hard not to call it linear regression), go to STAT, CALC, 0:ExpReg.
- You end up back at your home screen. Press L1, 'comma', L2, 'comma'. To get the Y1 (as illustrated on the slide) go to VARS, Y-VARS, 1: Function, 1: Y1, Enter.
- ENTER, and you have your a and b variables which should tell you your answer.
- To see the regression simply go back to your graph and 'see' it.

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

All info. came from inside the classroom and out of my keyboard (accept for pascals triangle which is a link in itself).
A point of interest... you can never have zero light. There will never be perfect and complete darkness.
People seemed to think my cartoon on my last post was pretty good, I'll give yea another one (which will likely end up as my signature with a smiley face just below it).

Which variable is dependent and which is independent? Where is the title for that matter?

:)

Reminder: Word Problem Stratigies (mixtures/investments)

Ok, I can see loads of people are having trouble with some of the word problems. I was having problems with the fertilizer questions until I went back in my notes and realized the antifreeze example/question we went through in class is exactly the same. Then I experimented with the other questions in the same fashion and It wasn't too hard. I'll go through the antifreeze question (that we all should have in your notes).

Ex) Antifreeze A is 18% alcohol. Antifreeze B is 10% alcohol. How many liters of each should be mixed to get 20L of a mixture of 15% alcohol?

Step 1: Create Let Statements (be specific!)
Let a = the number of liters required of the 18% solution
Let b = the number of liters required of the 10% solution

Ask yourself... "what am I solving for?"

Step 2: Create two equations with two variables in each
L1: a + b = 20
L2: 0.18a + 0.10b = 0.15(20)

The second statement is basically (based on the let statements):
type of the first solution times liters of that solution + type of the second solution times liters of that solution = type of mixture you want times liters of the solution you want.

Maybe thinking of it like that will help y'all (I'm sure that's how Mr. Max has been saying it), instead of... point eighteen times 'a' plus point ten times 'b' equals point fifteen times twenty.

Step 3: Solve
The easiest way would be to throw it in graphmatica, but I didn't have graphmatica handy so the next easiest way was within my calculator (let's just go down the line from easiest to hardest).

I'm going to isolate b (the number of liters required of the 10% solution).
L1: b = 20 - a
L2: b = (3 - 0.18a)/0.10

I got L2 this way:
0.18a + 0.10b = 0.15(20)
0.18a + 0.10b = 3
0.18a + 0.10b - 0.18a = 3 - 0.18a
0.10b/0.10 = (3 - 0.18a)/0.10
b = (3 - 0.18a)/0.10

Remember ;)
2nd, CALC, 5: (intercept), ENTER * 3

Step 4: Create a statment to summarize your answer.
In order to create 20L of 15% alcohol antifreeze, mix 12.5L of 18% with 7.5L of 10% antifreeze.

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

All raw information came from our lesson in class and out of my keyboard


:)

Thursday, October 25th

So Mr.Max started off the class by telling us that, outside of math class and teaching, he has probably used applied math to solve problems a total of five times or less. And of those five times, he has used the stuff on maximum volume, so for all of you that were feeling depressed about our little chat last week on how we will probably never use anything we learn in math class outside of school, don't lose hope. :)


We started out by looking at the problem above ▲. Our "building material" was to be 22cm by 28cm, just like a piece of paper. So to make it into a box, we had to cut a square in each corner so the paper would fold nicely into a box. [origami anyone?] To make things easy we started with one cm off each side, but when we made this into a box our class found that the box was quite "shallow". So we thought, what would happen if we made the squares bigger?! While after trying this a couple times we found that the volume of the box seemed to be increasing. But then we kept going with this idea and figured out that, eventually, the volume stops increasing, starts decreasing, and the box begins to get very tall and skinny.



Then Mr.Max showed us that we can make an equation for maximum volume and put it into a spread sheet to generate answers or use our calculators. So to get the equation we started with the formula for volume:

V=(l)(w)(h)

Then we worked out that the formula so that we could plug it into our calculators:

y=(28-2x)(22-2x)(x)

So this basically means that x is equal to the height of the box, and the height of the box is the same as the amount we are taking off each side of the paper, or building material.

First of all Mr.Max showed us how to put it into our calculators. Start by going to Y= and type in the formula. Then hit graph and you should see a cubic function. (you will probably have to play with your window settings a bit) Now to get the maximum volume of this box, go to 2nd Trace, then hit 4. Now it asks for left bound, so move left of the vertex and hit enter. Now do the same for right bound, and then press enter again when it says "guess?".
****x will tell us what the height of the box should be, y will tell us the maximum volume****

If you did it right it will look something like that▼

Then we learned how to do it by spreadsheets. We put all the information into a spreadsheet by making a columns called length, width, height, and volume. So you start off by putting in the dimensions for the first couple boxes, then you can just drag the information down because Excel lets us do that. Then using your spread sheet skills work it out so that in the volume column Excel calculates "length x width x height". So now to find the dimensions of the box with the maximum volume, just scroll down until you come across the highest number in the volume column.

Both methods shown above will produce the same answers for calculating maximum volume. This is proven below:

Friday October 26th

Today Mr.Max was away, so we had Mr.Richer as a sub. Today we worked on accelerated math and on the assignment that is due on Monday.

HOMEWORK: Student Exercise Questions: Page A-8, Exercise 2, 1-3, AND Page A-9, Exercise 3, 1a-f. ALL DUE MONDAY.

How to get to the Word Problems folder:
1) go to my computer
2) then open Rsfiles
3) open the coursework folder
4) go to the math folder and open it as well
5) then go to our class which at the moment is the second folder (Applied Math 30SA-1)
6) then you should see a folder which is labelled "word problems". Open it.

How to find the Vertex of a Parabola:
1) graph the parabola on your calculator.
2) press 2nd, then Trace.
3) then choose either minimum(cup-shaped) or maximum(cap-shaped) and press enter.
4) your screen should now show you graph again. at the bottom it will be asking you to go to the left side of where you think the vertex is. Do so with your arrow keys and then slecting enter when you are on the left.
5) now it will ask you to go right of where you think the vertex is. Do this the same as step 4 except you go to the right.
6) after you've hit enter to finalize your point in step 5, you then move your cursor to where you think the vertex is and press enter.
7) the correct vertex should then appear at the bottom of the screen. It will also state whether you used maximum or minimum.

Hopefully this helps.

*Remember that you should have 25 mastered accelerated math objectives by Wednesday October 31.*

The scribe for Monday is Shure.