Scribe Post May 7

warm up:

1.
use applet to show:

a) <3,2> + <2,4>
b)<3,2> + <-5,1>

2.
Do p. 457/70

1.
We plugged in the two coordinates for each problem into the applet, and we added them together (found the sum). We observed the movements of the vectors and concluded that...

(vector between two terminal points of two vectors = Terminal - Initial)

A+(-B) = A-B
B-A=-(A-B)

v=i+2j = <1,0> + 2<1,0> = <1,2>
w=2i-j = <2,-1>

for the homework quiz on Monday we must remember:

we reviewed homework problems, and learned that when the magnitude of the vector sum must be 3. This is because the magnitude of cos60º and sin60º is 1. The coefficient of 3 then changes the magnitude's value to 3.

73:
<300,0>

" class="ee_img tr_noresize" eeimg="1" style="vertical-align: middle;">

" class="ee_img tr_noresize" eeimg="1" style="vertical-align: middle;">

to find the vector of A+B use...

because you have found the parallelogram created by the vectors of <300,0> and " class="ee_img tr_noresize" eeimg="1" style="vertical-align: middle;"> . knowing that one side of the parallelogram is 300 and the other is 125 use the given formula above to find the vector/resultant of "x".

Dot Product Notes:

if u= and v= then =u1(v1)+u2(v2)

ex/ u=<3,4> v=<-2,7>

=3(-2)+4.7

=-6+28
=22

p. 460/ 5 properties:

1. =
2.
3.
4.
5.

all variables above are vectors other than: all c's and last "o" in property 2
however, when you "dot" the vectors together your product is a scalar.

definition of "dotted products": take two components multiply them together and then add them

scalar is a real number = 17
vector is a directed line segment = ------>

1st Cool Result:



where theta is the angle between u and v



if = 1, vectors in same direction = parallel
if = -1, vectors in opposite direction = parallel
if = 0, vectors are perpendicular = orthogonal

orthogonal = perpendicular

2nd cool result:

the projection of u onto v (see u, in applet) is given by:

this 2nd cool result will be in class discussion on Tuesday

Today in class we did a lot of things. We started with a warm up that asked us to find the triangle with these given sides and angle:
A=26º
a=5
b=8
This gave us an ASS (angle, side, side) case, which we know presents an ambiguous case. An ambiguous case provides you with information that you could use to create two different triangles. During this warm up we were asked to solve each angle and side of this triangle along with its area. Students could have solved for two different triangles with these given sides and angle. After the warm up we explored and proved the ambiguous case by constructing a visual of these possible triangles on Geogebra.

As you can see in the visuals there are two different triangles with values:
A=26º
a=5
b=8
This proves the ambiguous case.
We calculated the other possible sides and angles using the theorem that:




By Monday we are to prove that (when given SSS or SAS):



(and also find the largest angle when given SSS)

And for Bonus points we have the option to prove Heron's Area Formula (when given SSS) of:
, where s is the half perimeter.

Scribe post 3/17

Today we got our tests back, reviewed question 9, and spent the rest of class doing supercorrections. Next class we will also have time to work on them, be ready to turn them in on Tuesday the 23rd. The homework is to work on supercorrections. Remember that our rough draft's of our quarter 1 projects are due on Tuesday the 23rd as well.

Tyler's Late Post

In class on Friday we took the first quiz on chapter 3 and then we went over our homework on pg. 253. The majority of the class time was consumed by the quiz. We did not go over any new materials, however we stressed a few laws of log to remember for the next quiz (which is tomorrow).

Notable Points:

1. The base property:


2. ln=e

I hope the class found everything else easy to follow with log. I apologize for the post being so late, most likely it wasn't any help to any of you. Homework for tomorrow is to study for the quiz. Review the HW from pg. 243, and 253 to study. There is also a HW assignment on pg. 253 due for tomorrow. Good luck to everybody on the test.

Here is a website that looks very useful for studying the rules of log: http://www.themathpage.com/aPreCalc/logarithms.htm

Friday September 11th's class

Some students were struggling using these calculators. They could not find the “abs” or figure out how to graph these equations. Seeing that the focus of todays class was using these graphing calculators, we need further instruction on how to use the different utilities on these calculators. Some forgot how to graph palaboras, solve quadratics, and use domain and range. Solving quadratics to find the domain of equations was another struggle we had. Few kids can remember the equations such as point slope, distance formula, midpoint formula, and others. When in front of us we can use them, however remembering why they work (as you explained in class) is different. We should go over the definitions of intervals (relative minimum/relative maximums) and odd/even functions. Other than those things the class did not have many questions. None of these stuck out as a great problem other than using the calculators.