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course mth 163
Mr. Smith, Sorry I am so far behind, but it took we a while to figure out how to do everything. I am trying to complete one assignment everyday for the next 8 days or so and I believe that will get me completely caught up. Sorry it has taken me so long to figure this out, but I've finally go the hang of it.
24-31-348
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You included your name here within your document. It was given in the place where the form requested it, and is the first thing I see when I look at the document, but it won't be posted. If you include it in the document and I don't notice it and deleted it, then it will be posted, which can compromise the privacy of your site.
You also put your access code into the text of your document. You should do so with emails, but with the form it's only necessary to give it in the space indicated on the form.
Assignment 2:QA
1. If you have not already done so, obtain your own set of flow depth vs. time data as instructed in the Flow Experiment (either perform the experiment, as recommended, or click on Randomized Problems and select Precalculus then Simulated Data for Flow Experiment , which can be accessed at http://164.106.222.236/interactivepro).
Complete the modeling process for your own flow depth vs. time data.
Use your model to predict depth when clock time is 46 seconds, and the clock time when the water depth first reaches 14 centimeters.
Answer:
14.92 cm
Answer:
47.78 sec
Comment on whether the model fits the data well or not.
Answer:
It does.
Even though you probably understand the process at this point, it can be challenging to get through these problems without making mistakes. An error on one step can throw the entire problem off, and result in a model that doesn't work at all.
There is a limit to how much time you should spend worrying about finding and correcting arithmetic mistakes. Of course it is important that you follow the solution procedures correctly, that you recognize when your model doesn't work, and that you do spend significant time trying to track down arithmetic errors. However if you believe you are doing the procedures correctly (other than a pesky arithmetic error or two), and have spent more than a couple of hours trying to track the error down, you should proceed to the Query and submit your responses through Exercise 1. Wait for your work to be posted before moving on to Exercise 2 below.
2. Follow the complete modeling procedure for the two data sets below, using a quadratic model for each. Note that your results might not be as good as with the flow model. It is even possible that at least one of these data sets cannot be fit by a quadratic model.
Data Set 1
In a study of precalculus students, average grades were compared with the percent of classes in which the students took and reviewed class notes. The results were as follows:
Percent of Assignments Reviewed
Grade Average
0
1
10
1.790569
20
2.118034
30
2.369306
40
2.581139
50
2.767767
60
2.936492
70
3.09165
80
3.236068
90
3.371708
100
3.5
MY MODEL= -1.317x^2+0.033x+1.475=y
It's best to obtain and use your own model. However if after reasonable effort (an hour or so) you fail to get a model that appears to make sense, you may use the model y = - 0.0003•x^2 + 0.041•x + 1.41 to answer the questions below. When you do the Query, you will be expected to show the work you have done up to this point. You should then indicate that your model doesn't seem to work, and state that you are using the y = - 0.0003•x^2 + 0.041•x + 1.41 model. This model isn't based on a very good selection of points, so it's possible to get a much better model, but this one will suffice to answer the questions.
Quadratic equations can't always be solved, so it is possible that some of the questions asked below will have no answer.
Determine from your model the percent of classes reviewed to achieve grades of 3.0 and 4.0.
Answer:
No real solution
Determine also the projected grade for someone who reviews notes for 80% of the classes.
Answer
: No real solution
Comment on how well the model fits the data. The model may fit or it may not.
Answer:
The model does not fit
Comment on whether or not the actual curve would look like the one you obtained, for a real class of real students.
No. I kept getting negative numbers at a decreasing rate. Therefore, it does not seem to fit a class of real students.
Data Set 2
The following data represent the illumination of a comet by the sun at various distances from the sun:
Distance from Sun (AU)
Illumination of Comet (W/m^2)
1
935.1395
2
264.4411
3
105.1209
4
61.01488
5
43.06238
6
25.91537
7
19.92772
8
16.27232
9
11.28082
10
9.484465
Obtain a model.
MY MODEL:24.034x^2-367.22x+1278.327=y
It's best to obtain and use your own model. However if after reasonable effort (an hour or so) you fail to get a model that appears to make sense, you may use the model 256•x^2 - 1439•x + 2118 to answer the questions below. When you do the Query, you will be expected to show the work you have done up to this point. You should then indicate that your model doesn't seem to work, and state that you are using the y = 256•x^2 - 1439•x + 2118 model. This model isn't based on a very good selection of points, so it's possible to get a much better model, but this one will suffice to answer the questions.
Quadratic equations can't always be solved, so it is possible that some of the questions asked below will have no answer.
Determine from your model what illumination would be expected at 1.6 Earth distances from the sun.
Answer:
y=752.30204
At what range of distances from the sun would the illumination be comfortable for reading, if reading comfort occurs in the range from 25 to 100 Watts per square meter?
Answer:
5.168
Analyze how well your model fits the data and give your conclusion. The model might fit, and it might not. You determine whether it does or doesn't.
Answer:
The model fits.
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You need to document how you solved these problems. I believe I've commented more extensively in the open query you submitted for this assignment.
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