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Friday, March 10, 2006

Scribe # 21

Sorry for the late scribe, I had work until 10. Okay well in class today we did another pre-test for the test tomorrow. It took the whole class, so that's all we did. The pre-test consisted of 5 questions.

The first two questions were multiple choice.

1) If f(x) = 2x2 - 3, where x is less then or equal to 0, then a function g that will have domain and range that are both different from those of f is:

a. g(x) = f(-x)
b. g(x) = -f(x)
c. g(x) = f-1(x)
d. g(x) = k f(x), k > 0

The answer for the first one was C. I'm not really sure why that's the answer, so if anyone can help me out on that one, it would be greatly appreciated.

2) The graph of a function f is a parabola opening upward, with it's vetex on the x-axis. The graph of a new function g, where g(x) = 2f(x), will have

a. the same domain and the same range as f
b. the same domain but a different range than f
c. a different domain but the same range as f
d. a different domain and a different range than f

Here's a diagram to help you understand this more:

So the answer for question 2 is A.

3) Given the graph f(x) below, sketch 1/f(x)

5)This water wheel rotates at a rate of 5 revolutions every 4 minutes. Its bottom edge touches the surface of the water.

a.The point A is on the wheel. Sketch a grpah ofthe height of the point A above the outflow water level as a function of time, starting at t = 0 seconds, with A as shown.

b) Write a sine and cosine equation for this function.

Sine Cosine
A= 5 A= -5
B=2pi/48 B= 2pi/ 48
C=12 C= 0
D=5 D= 5

h(t)= 5 sin [2pi/48 (t-12)] + 5
h(t)= -5cos [2pi/48 t ]+ 5

c) Find one time when the point A is 4 meters above the water.

4= -5cos [2pi/48 t ] + 5
-1= -5cos [2pi/48 t ]
1/5 = cos [2pi/48 t]
1.3694 = 2pi/48 t
10.4617 = t

d) For how long, during the revolution, is the point A within 4 meters of the water's surface?

By symmetry, A is within 4 meters of the water's surface for 2(10.4617) = 20.9235 seconds each revolution.

Well its almost 1 now, but I'm finally done. YAY! Sorry if everything seemed kind of rushed I'm just really tired now and I want to go to sleep. Oh yeah still waiting for help on question 1.

Anyways the next sribe is Emile.

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At 3/10/2006 2:45 AM, Blogger Regine said...

Maaan Jacky. Your scribes are always thorough. It helped me a bunch. Thankks. I told you you were smart...


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