oh yea its Lauressa I forgot Mel!ssa is our next scribe

Hey guys ,

Well today in class we recieved our grades :( Some of us were suprised and for others well there's always room for improvement. Well when Mr.K handed out our tests from AGES AGO! we went over the questions we had problems with.

The units our tests were from were recently algebra, quadratic functions and trig.

There were just some of the questions that we went through together in class.

Quadratic Functions

Long answer :

A farmer with 750 feet of fencing wants to enclose a rectangular area and then divide it into 4 pens w/ 3 fences parallel to one side of the rectangle. What is the largest possible total area of the 4 pens?Step 1: Write an equation to match the question asked

2L + 5w = 750

Step 2: Get one of the variables by itself
2L = 750 -5w

Step 3: Solve for the variable
L =750/2 - 5w/2 ; L = 375 -5/ 2w

Aw = (375 - 5/2w)w Where one of the roots are at 0 (w=0)

1) 375 - 5w/2 =0

2)375 = 5w/2 Get w by itself, so in order to do that you multiply 2 by both sides, so it cancels out

3)750 = 5w > 750/5 = w w=150

750= 2L + 5w > 375 = 5w > w = 75


Im really sorry for the short blog today because we did so much in class but I couldn't get my computer working. Mr. K I need a one on one session on blogging, the programs on my computer weren't working some would't open. SOrry again to the class for that. NEXT time I promise it will be better. Sorry :(

REVIEW / THE ROAD TO A "NEW" DISTANCE FORMULA

Hey Guys!

Well on Friday's class we had Mr. Clark once again to fill in for Mr. K, and no time was wasted. To kick off the class, Exercise 20: Review 2 was assigned and is expected to be done.

As soon as that was established, our class as a whole had asked Mr. Clark to look over a few questions on Exericse 21: Circles on a Coordinate Plane (which was previously assigned) that we were having problems with.

4. Find the centre and radius, and sketch the graph for the following circles.
(c) x²+y2+6y-12=0
HINT: To solve, complete the square

and put into standard form of the equation of a circle
x²+y²+6y-12=0
x²-10x+25+y²-4y+4=25+4
(x²-5)2+(y-2)²=29
centre: (5,2) radius: √29

9. Sketch the graph of y=x²-2x+5. State the domain and the range.
HINT: The degree is 2, we have a parabola!
y=x²-2x+5
y=(x²-2x+1)+5-1
y=(x-1)²+4

HINT: Vertex is (1,4) and Y-Intercept is (0, 5)
Domain: (-, ∞) Range: [4, ∞)

10. Write a quadractic equation with roots 2±√3
HINT: Find Sum of Roots + Product of Roots
s.o.r. = 2+√3 + 2-√3
=4
p.o.r.= (2+√3)(2-√3)
=4-3
HINT: (√x)(√x)=x
=1
eq'n = x²-4x+1

11. Two sidewalks meet at right angles. At noon, Person A is 12 km north of the intersection, walking south at 2 km/h. Person B is 18 km east of the intersection, walking east at 4 km/h. At what time is the area of AOB a maximum?
HINT: Maximum.. think parabola.. think sign of a quadratic equation.. think vertex
Original Area = Base(Height)/2
= 18 km(12 km)/2
= 108 km²

After X hours A will be 12 km-2x
After X hours B will be 18+4x

New Area = (18+4x)(12-2x)/2
= (216-36x+48x-8x²)/2
= (-8x²+12x+216)/2
= -4x²+6x+108
HINT: lets complete the square to find the vertex
= -4x²+6x+108
= -4[x²-(3/2)x+(9/16)]+108+(9/4)
= -4[x-(3/4)]² + 441/4
Vertex (3/4, 441/4)

So that was all with Exercise 21: Circles on a Coordinate Plane.

Students then asked questions about our next assignment
Exercise 22:Distances between Points and Lines

We were all familar with the line distance formula
distance =√(x₂, x₁)²+(y₂-y₁)²

Mr. Clark then presented to us the "new" distance formula
Below is the points and lines distance formula
distance=ax₁+by₁+c/√a²+b²

i.e) Find the distance from Point (2, -5) and the line 3x+4y+9=0
distance=ax₁+by₁+c/√a²+b²
=3(-2)+4(-5)+9/√3²+4²
=35/5
=7

HINT: Keep the Pythagurian Triples in mind when solving these equations
a²+b²=c²
*3, 4, 5
*6, 8, 10
*5, 12, 13
*12, 16, 20
*8, 15, 17
7, 24, 25

So I guess homework for the weekend is all uncompleted exercises up until..
Exercise 22: Distances between Points and Lines

Have a good weekend and enjoy!

Scribe for Monday will be Lauressa
since you expressed your ready-ness to blog!

P.S. Images will be placed tomorrow if I find the energy, sorry.

FIRST SCRIBE FOR NOVEMBER

Today in class we got to look at mr.k's mac. He believes that Firefox is better than Explorer


Our homework is to make an account on del.icio.us and find 1 site for each unit we have studied so far using Firefox. del.icio.us allows you to save bookmarks which you are able to access from any computer no matter where you are.


This is how to do it:
- Open up firefox
- Type del.icio.us in the address box
- Click register
- Click install extension now
- Restart Firefox
- Go to help and click bookmarklet buttons for any browser
- Drag the post to del.icio.us button to where your tabs (beside latest headlines)
- Find 1 site for each unit that we have done so far
- To bookmark a site, click the tag button on your toolbar and save it
- Find a site for each unit we studied and bookmark it with pc30sf06 as one of the tags


Another thing to check out is http://k12onlineconference.org and go to Basic/Advanced Thinking scroll down to the second last post which is posted byAlan Levine. This shows you different education tools and how to use them.




We also started a new unit today called Analytic Geometry we started off with a diagram:

From this diagram you can pull out this information:
OP = r


You can change the distance formula which is (x-h)
² + (y-k)² = r into standard form.
Standard form for the equation of a cirlcle is (x-h)² +
(y-k)² = r²


If the coordinates for the center point of the circle was (2,color=blue>-1) the formula would be:
(x-2)² + (y-(-)1)
² = 9 and the radius would equal the square root of 9
which is 3

The graph for this formula would look like this:





So if you know (h,k) and the center point of a circle, you can write the equation of the circle.

Eg. If the coordinates of the center point is (-3,4) and the radius is 5 this is what you do:
substitute them in: (x+3)² + (y-4)² = 25 ** be careful with the signs
then you expand: x²-4x+4+y²+2y+1= 5
after that, simplify: x²+y²-4x+2y+1=0 which is the general
form
when you finish simplifying, complete the square: x²-4x+4+y²+2y+1=0+4+1
(x-2)²+(y+1)² = 5 and this becomes the original
equation


* you get +4 by taking half of -4 from "-4x" which is -2 and squaring it +1 by taking half of the 2 from "2y" and squaring it.


[ ! ] If you are ever given the diameter, remember that the radius is half of the diameter




Homework is not only creating an account for del.icio.us, Exercise 21 is also for homework OH.. AND THE SCRIBE FOR TOMORROW IS eeDce :)

hey guys I finally got the internet up and running so Im ready to start bloggnig

hey guys! well we had a test today so i'll just do my scribe tomorrow. sorry if this caused any inconvenience!

BOB V.3 ALGEBRAICALLY SPEAKING

Zeph hit some technical difficulties. I am posting his BOB for him.

Mr. Kuropatwa

---

let's see...i remember doing all this restriction with the variables stuff last year and i have no problems with that now. i understand more about why sum of the variables are called "extraneous" but i think that was the most confusing part in this topic. yeah...
i asked mr.k about the nature/characteristics of roots cuz that part was a drag to me but in the end, i understand now.
i'm ok with the solving for "x" thing in rational and radical and absolute equations. the only thing tricky for me is...it's just that there's so many steps that one false move means death.
the cool thing about this topic is that we saw a picture of a body on our calculator when we were doing one of the equations. i learned that interesting "pics" can be graphed on the calculator and they all don't have to be parabolas. i'm guessing that that's the hard part to this unit...understanding extraneous solutions and their graphs. thats about it for pre-cal algebra 30s...

have a HAPPY HALLOWEENIE!