Sunday, November 9, 2008

Circle Hyperbola

Hello ...
Sorry for the late post, but here's what we did on Friday.

First off, we went through the homework that were given on Thursday.

w + l + h = 80 cm
Length=10cm less than twice the sum
of width and height and twice the width exceeds the height by 6 cm. Find the width, length and height of the box.

~We didn't go over the procedure on how to solve this problem, but the answers were:
h = 18cm, w = 12 cm, l = 50 cm

Then there was the question from the book (Ex. 25 #1) Letter "c" was done by Ramina on the white board. For those who didn't get to copy the procedure, here it is...

1. a) 3x-4y+5z=2
4x+5y-3z=-5

5x-3y+2z=-11

(3) 3x-4y+5z=2 (3)
(5) 4x+5y-3z=-5 (5)

9x-12y-15z=6
+ 20x+25y-15z=-25
ˉˉˉˉˉˉˉˉˉˉˉˉˉˉˉˉˉˉˉˉ

29x+13y=-19


(2) 4x+5y-3z=-5 (2)
(3) 5x-3y+2z=-11 (3)

8x+10y-6z=-10
+ 15x-9y+6z=-33
ˉˉˉˉˉˉˉˉˉˉˉˉˉˉˉˉˉˉˉˉ

23x+y=-43


29x+13y=-19
(13) 23x+y=-43 (13)


29x+13y=-19
+ 229x+13y=-559
ˉˉˉˉˉˉˉˉˉˉˉˉˉˉˉˉˉˉˉˉ
-270x = 540

ˉˉˉˉˉˉ ˉˉˉˉˉ
-270 -270

x = -2


29x+13y=-19
29(-2)+13y=-19
-58+13y=-19

13y=58-19
13y=39
ˉˉˉ ˉˉˉ
13 13

y = 3


3x-4y+5z=2
(3)(-2)-4(3)+5z=2

-6-12+5z=2
-18+5z=2
5z=18+2
5z = 20
ˉˉˉ ˉˉˉ

5 5

z = 4


After this, we talked about a little something new called Circle Hyperbola.
It looks like this ...



A Circle Hyperbola can only have 0, 1, or 2 intercepts and no more than that. We can find the intercept by putting the equation on our calculator OR solve it algebraically. We did some examples as a practice on finding the intercepts of Circle Hyperbola.

► y=x-1
y=x²-6x+9

x-1=x²-6x+9
-10=x²-7x
x²-7x+10=0
(x-5) (x-2)
x=5 x=2
y=4 y=1

another example was...

►x²-y²=5
xy+6=0

y
²=x²-5 → y= √x²-5 (#1)

y=-6/x (#2)

-6/x=√x²-5
(-6/x)² = (√x²-5)²
36/x² = x²-5
x^4-5x²=36 (substitute x^4 to u=x²)
u²-5u-36=0
(u-9) (u=4)
u=9, -4
x²=9, -4
x=±3
x=3 , y=-2
x=-3 , y=2

After doing these examples, there were homework that were assigned for us to do. Exercise 26 (# 1-5) Also, don't forget to hand in your bonus mark homework sheets before Dr. Eviatar leaves!

-
-
-
Next Scribe ... Jamie

No comments: