BOB for Conics

hi everybody, one more unit is done and i was almost forget about the BOB for this unit. T_T .
Anyhow, i just do this BOB briefly.

I think this unit is not really, you just need to know the formula and understand the graph so you could know which formula is parabola, ellipse, or hyperbola.

About the formula, i think some of us already posted it, so i am not going to repeat it. :D

Anyway, Good luck all guys, test on Friday and don't forget your delicious link [which i also almost forgot :-"] ...

Hi everyone, it's Trinh for the scribe post for today.

First we found out why all of our satellites have the shape like it has nowadays. and the receiver is built at the focus of the parabola so wherever the radio rays, the GPS rays or any rays go, it will bounce in and intercept at the receiver which is the focus of the parabola.

Then we just quickly went over what we learned yesterday which are the formula of the vertical and horizontal parabolas. These formula is totally different but it actually the same with what we've learned before.
Just remember:
-When you see the x side square, it is the vertical parabola, if p is positive, then parabola opens up and if p is negative, the parabola opens down.
-When you see the y side square, it is the horizontal parabola, if p is positive, then the parabola opens to the right and if p is negative, the parabola opens to the left.


After that, we tried to solve the problem with this equation:


First thing we can easily see that there is a square in the y side so this i a horizontal parabola so we use this formula : (y-k)^2 = 4p(x-h)
and we can find the vertex with the coordinates (h,k) = (3,-1)
we also see that 4p = -8 so p must equals -2.
p is negative so the parabola opens to the left and the distance between the focus to the vertex and the vertex to the directrix is 2.
there is a question about how wide is the arms of the parabola?
we can see that the arms of the parabola intercept at the horizontal line which is x=0

we let x=0 and sub it into the equation. so i got
(y+1)^2 = -8(-3).
Then i expand the (y+1)^2, i got
y^2 + 2y + 1 = 24
subtract 24 from both side
y^2 + 2y - 23 = 0
then we factor it out and one solution is 3.8989... (approx 4) and one is -5.8989... (approx -6) so that is the wide of our parabola.

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We learned how to convert a standard form to the general form [ expand the equation ] and from the general form to the standard form [ complete the square ].

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We moved on with the circle.
we pick a point F to make the center of the circle, then draw a bunch of spots that have the same distances from the point F.

Use the distance formula, we found out the equation of the circle, just like what we did with the parabola.



And we solved the next problem about find the radius and the coordinate of the circle.



for this problem, we just complete the square to get the equation like the circle equation so we get the coordinate of the center. With the radius, remember to take the square root.

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Remember to do the homework, Generating ellipses.

Last thing is the next scribe is yíＮＡЙ

BOB for Combinatorics

Hi everyone, it's Trinh and the BOB for combinatorics unit.

At first in this unit, i got some troubles because i sometimes misunderstood the questions but now i think i am ok with it.

I think in this unit, we have to read the questions and think about it carefully, remember the pick and choose formula, remember the formula of how to arrange things on a circle and especially for the bracelets and necklaces.

Anyway, good luck on your test guys.
Don't forget your Delicious link..

BOB for Exponents and Logarithm

About this unit, i think there are some thing that we need to remember:

- A LOGARITHM IS AN EXPONENT. (Mr.K always says that we're going to forget that!!)

- The product law : log_bAB = log_bA + log_bB


- The quotient law : log_bA/B = log_bA - log_bB

- The power law : log_bC^k = k(log_bC)


- The change of base law:

- The exponential function : f(x) = e^x


- The natural logarithm : f(x) = ln(x)


About the formulas:

- A = P(1+r/n)^tn

- A = Pe<sup>rt

-</sup> A = A₀(m)<sup>t

-</sup> A = A₀(m)<sup>t/p

I wasn't in class for a last few days so i'm not sure if this is enough, but i think i kind of get it now even though i got some confused at first. Anyway, GOOD LUCK to every one. ^^</sup>

My Time line for the DEV :


- April 23 : make a sample problem for question #1 and find the answer on papers.

- April 25 : make a sample problem for question #2 and find the answer on papers.

- April 30 : do the final copy for question #1 and #2 on the computer.

- May 3 : make a sample problem for question #3 and find the answer on papers.

- May 8 : make a sample problem for question #4 and find the answer on papers.

- May 12 : do the final copy for question #3 and #4 on the computer.

- May 22 : combine all the 4 questions, fix them and prepare to publish online.

Due day : june 5.

BOB for identities..

One more unit is done... so i just go straight forward ...

In this unit, most we do are about sine and cosine.

Remember:



from that equation, we can easily get these implies by dividing both side by or

and we get :

or

then we studied about the sum and difference identities









since we got that, we'd know the expression for sin2x , cos2x, and tan2x


I don't think i got any problem with this unit and all thing below i think are the main idea of this unit.

Pre-test is tomorrow, Tue, April 7
Test is on Thu, April 9.

Good luck all ..

Scribe post for March 25..

Hi everyone,I'm Trinh and i'm the last one from the scribe list.
Anyway, I just go straight into what we've learned this morning because my network connection is not working really well. It could be disconnect anytime.

First, Mr.K put us into group and we started with some homework problems.
we apllied the sum and difference identity of so we can get the first line in the picture above. You could see that

and
Sub that number into the expression, we get the next line and we could find out the answer.


For the next question





We still using the sum and difference but this time is and , after you expressed, you'll see 2 opposite expressions, you could cancel it right away for short and there are left, that gives us .

The next question is more complicated than the first two,








then we started to prove how can we get the sum and the difference identities equation.




we've not finish this part yet and Mr.K said we're going to finish that tomorrow .

Another thing is about our mark, Mr.K will give a code for each of us so we can check out our mark online. He'll finish it on Friday or on the first day back to school after spring break. We have to go see him to get the code.

Tomorrow is PJ/Crazy Hair Day - The Chris Frolic Comedy Hypnosis Show ($2/ticket)
So make sure you have the ticket for the show tomorrow.

BOB..!?!?!

Hi everyone! I'm Trinh and this my first post so if i make any mistakes,which i would, free to comment and I'll fix it.


About this unit, first i got some troubles with the "+" and "-" sign in the sine and cosine functions but now I'm ok with that.

Two Functions : f(x) = AsinB(x-C)+D
g(x)= AcosB(x-C)+D

We could use these 2 functions to solve some problems and that's really "cool".
In those 2 functions, you must remember ( i saw everyone all noticed about this but i still repeat it) :
A : the amplitude: the distance of the max or min values from the Sinusoidal Axis.
B : determines the periods ( B is NOT the Period)
Period= or B=
C : determines the horizontal shifts
C > 0 : the graph shifted to the right
C <>
Warning: Watch the sign of C

D : determines the vertical shifts
D > 0 : the graph shifted up
D <>


And there are something about even and odd function

Remember that a function is even if its graph is symmetrical about the y-axis

f(-x) = f(x)

And a function is odd when its graph is symmetrical about the origin.
-f(x) = f(-x)

The reflection function of y = f(x) is y = f ^-1(x) (inverse function)

Warning: f ^-1(x)


I think it's enough for me. Just reminder again: pre-test tomorrow, friday 13 and test is on monday 16.


Good luck to you guys