Geometric Sequence

We learned about geometric sequences.
We have Recursively Defined vs. Explicity Defined
Recursively is you need the previous value in the sequence to get the next value.
*He wants us to think spreadsheet*
*Common ratio between terms in a geometric sequence therefore t3/t2=t2/t1=tn/tn-1=....etc.
* An expeirmental function with domain x€N
y=atimes b^x

Work Period

Last class was a work period. ANd he put in our accelorated math marks in edline. This was a very good thing because all the A.M I did made my mark go from a 55 to a 68!!! This brought me great joy. And I continued to work on my accelorated math all period.

More Probability

Big Idea: " the chronology of probability exprienment effects subsequent trials/experiments.
ex) flip a coin; roll a die ARE totally independent
no effect on each other at all each time the "reset" button is hit.

Replacement vs. No Replacement

Independent "reset"
ex) independent/dependent
Dependent-a)eat a sandwitch;long for a sandwitch later
independent-b)write a computer program to generate random #'s.

Ex) Box x/ 2 Red Marbles
Draw 2 marbles. 3 white marbles
P(Both marbles are white)

Probability

We first learned about sample spacing, which is like creating a picture about the situation your given. Using ordered pairs, or a chart.
*Next we learned about the two different event types, Simple and Compound.
A simple event- is when the sample space can not get any simpler then what it is.
A compound event- is two or more simple events are considered at once.

*Then there's the 2 laws of probablity, first being the addition law,"or". Basically if your trying to find the probability of A or B, you will have to add. The formula is on our formula sheet, it is a tad complicating.

*The second law is the multiplication law, "and". When your trying to find the probability of A and B, you will have to multiply.

Graphing Hyperbolas

*equation of a hyperbola. Either the x coordinate or y coordinate is negative. The coordinate that is positive is the way that the hyperbola opens.If you have +x and -y, the hyperbola is going to open left-right because x coordinate is positive. Your a value always goes with your positive value (x or y) But unlike circles your a value ( is NOT always bigger than your b value.

*sketching the hyperbola.
find the centre of the hyperbola. It's just the opposite sign of what's inside the brackets.
find the values for a and b. You have to square root the denominator to get your values. You can trace your transverse and conjugate axes. You can find your vertecies which are the endpoints for transverse axis. The vertecies are your starting points for your hyperbola.
*we now have to find the equation of the asymptotes to make our sketch complete and where to draw the hyperbola. Equation of a line: y=mx+b.So, you know your x and y values, they're the values of the centre (x=-2,y=1). You know the m which is the slope. After you find your b values, you can draw your asymptotes equations with dotted lines and then draw your hyperbola.

Conics- major / minor axis ( from formulas) - Transverse / conjugate axis

For ellipses, you have two axis, a major and a minor . the major axis is always the longer of the two.

For Hyperbolas, you also have two axis, a transverse axis and a conjugate axis

Transverse axis-connects verticies

*not always longer than conjugate axis

*length is alwas 2a units (a+a)

*there for length of conjugate is always 2b units (b+b)

More Conics

We learned thr conversion between general form conics and standrd conics.

Ax^2 + Bxy + Cx^2 + Dx + Ey + F = 0


complete the square:

you take: x^2 + 4x + 4

We can take a square and
(x+2)(x+2)
(x+2)^2

If we try to enter (X^2 + y^2 + 6x - 8y) = 11 into graphimatica, it will not map the equation because it cannot take the data. We use this form after we complete the square

(X^2 + y^2 + 6x - 8y) = 11
(x^2+6x+9)(y^2-8y+16) = 11 + 9 + 16
(x+3)^2 + (y - 4)^2 = 36

Using the general form:

(x-h)^2+(y-k)^2= r^2
(h,k) = center r = radius
enter (x+3)^2+(y-4)^2= 36