Assignment 1

course MTH 164

There was about 4 problems I was lost on. In the answer part I wrote that I was unsure and lost on them. I need a little help to make sure I'm just not looking over it.

The problems you are asking about are in the Class Notes and/or the q_a_ for this assignment. You should complete the q_a_ and review any assigned Class Notes.

assignment #001001.

Your work has been received. Please scroll through the document to see any inserted notes (inserted at the appropriate place in the document, in boldface) and a note at the end. The note at the end of the file will confirm that the file has been reviewed; be sure to read that note. If there is no note at the end, notify the instructor through the Submit Work form, and include the date of the posting to your access page.

Precalculus II

06-10-2008

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18:26:44

query modeling exercise

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RESPONSE -->

confidence assessment:

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18:45:53

What is the distance between the peaks of the graph for which the angular velocity of the reference point is 3 rad / sec, and what are the maximum and minimum vertical coordinates if the circle is centered at vertical coordinate 12?

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To find the angular velocity of the reference point of 3 rad/sec you would take pi/3 rad. Then you use pi/3 * 180 degreees/pi. This would then give you 60 degrees. When the vertical coordinate is centered at 12 the maximum point would be 12 and the minimum point would be -12.

confidence assessment: 2

** At 3 rad/sec a complete trip around the reference circle takes 2 pi / 3 seconds, close to but not exactly 2 seconds. 2 pi / 3 seconds is the distance between the peaks on the graph of y vs. t.

If the circle has radius 5 the max and min will be 5 units above and below the center of the circle, at 12 - 5 = 7 and 12 + 5 = 17. **

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18:52:57

Given the values between which a cyclical quantity varies, how you determine where to position the circle that models the quantity, and how the determine the radius of the circle?

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To determine where to position the circle modles quantity you need to find the time required for a complete cycle around the circle is called the period of the cycle. The number of cycles perunit tie is usually called the frequency of the cycle. The anguar displacement per unit time is called the angular frequency of the cycle. The distance from the t axis to a point at maximum distance from the axis id called the amplitude. The amplitude concides with the radius of the circle.

confidence assessment: 2

Good. Compare with the following:

** The center of the circle will be halfway between the max and min values, which can be found by averaging the two values (i.e., add and divide by 2).

The diameter will be the difference between the max and min values and the radius will be half of the diameter. **

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19:03:19

What is the vertical coordinate of the center of the circle, and what is the angular velocity of the reference point, for the daylight model?

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I'm having a little trouble with this one in fiding the daylight model. I have went through the notes and the assignment and I'm not sure where it is. Could you please help me out so I can figure this out so I can understand it and study it.

confidence assessment:

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19:03:57

What is the vertical coordinate of the center of the circle, and what is the angular velocity of the reference point, for the temperature model?

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This is the same thing as before. I can't figure out where the temperature model is or how to go about answering this question.

confidence assessment:

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19:04:11

What is the vertical coordinate of the center of the circle, and what is the angular velocity of the reference point, for the tide model?

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Once again...I can't find the tide model. Not sure what too do.

confidence assessment:

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19:04:43

What is the vertical coordinate of the center of the circle, and what is the angular velocity of the reference point, for the ocean wave model?

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Same thing with the ocean wave model. I may be over looking these or missing them. I'm not too sure what is going on here.

confidence assessment:

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19:15:46

query ch. 5 # 78 15 in wheels at 3 rev/sec. Speed in in/s and mph: rpm?

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5rpm

confidence assessment: 2

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19:16:56

Explain your solution to this problem.

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I took took the radius of 15 inches and divided it by 3 revolutions/second. That is 15/3 to get 5 rpm.

confidence assessment: 2

Each revolution covers a distance equal to the circumference. You wouldn't divide by the number of revolutions per second.

** If 15 inches is the diameter of the wheel then the radius is 15 inches.

The angular velocity is 3 rev / sec * 2 pi rad / rev = 6 pi rad / sec.

905 pi rad / sec.

If you approximate this you get around 280 in/sec.

This is 280 in / sec * 1 ft / 12 in = 23 ft / sec approx.

A mile is 5280 ft and an hour is 3600 sec so this is

23 ft/sec * 1 mile / 5280 ft * 3600 sec / 1 hr. = 16 miles / hr approx.. **

Note that 3 revolutions / second is 180 revolutions / minute, since there are 60 seconds in a minute.

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19:17:23

Comm on any surprises or insights you experienced as a result of this assignment.

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I was unsure about a few problems and was a little lost. Need a little help on those.

confidence assessment: 2

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You've got most of the right ideas. See my notes, check out the assigned q_a_, and please let me know if you have additional questions.