This is a blog for my second semester pre-calculus 30s students. Have a blast!

Wednesday, April 05, 2006

Answer key for analytic geometry pre-test

Part I - MC:

1) a 2) c 3) d 4) d 5) c 6) b 7) c 8) a

PART II - SA:

1) using distance formula... r = 5.8

2) using substitution, elimination or graphing and finding the pt of intersection on your calculator
sol'n: (-4, -11)

3) 1 solution (as seen by graphing circle and straight line)

4) using distance (from pt to line) formula... d = 5 (root 13) / 13...(sorry about the lack of mathematical symbols, I never had a chance to download the software that produces them.

PART III - LA

1) Graph all lines on paper and find all 4 vertices (2 are y-intercepts, the other two are points
of intersection.
You must then find the equation of each diagonal line (using pt-slope formula from S2)...
The equations of the diagonals are: y = x - 2 and y = -(5/6)x + 4.
The point of intersection of these two diagonals is (3.3, 1.3).

2) You substitute all three points, (10, 1500), (20, 2000) and (30, 1500) into the equation and
you end up with the following 3 x 3 system:

1) 100a + 10b + c = 1500
2) 400a + 20b + c = 2000
3) 900a + 30b + c = 1500


2) - 1): 300a + 10b = 500 4)
2) - 3): -500a - 10b = 500 5)
4) + 5): -200a = 1000


...therefore a = -5

....after more substitution... b = 200, c = 0

...therefore sol'n = (-5, 200, 0)

.... h(t) = -5t^2 +200t

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