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MTH 163
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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Practice Major Quiz Inquiry 1
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Problem Number 1
Problem: Obtain a quadratic depth vs. clock time model if depths of 46.35971 cm, 41.86877 cm and 39.52721 cm are observed clock times t = 6.429146, 12.85829 and 19.28744 seconds.
Problem: The quadratic depth vs. clock time model corresponding to depths of 46.35971 cm, 41.86877 cm and 39.52721 cm at clock times t = 6.429146, 12.85829 and 19.28744 seconds is depth(t) = .026 t2 + -1.2 t + 53. Use the model to determine the average rate which depth changes between clock times t = 17.7 and t = 17.701 seconds.
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What I understand:
I do understand that this would provide a model such to describe the descending water level (presumbly from a graduated cylinder)with a particular flow. To reinforce my understanding, I think this is showing at the first depth, this is the time taken(which I labeled t(sub)1. Second depth is t(sub)2, and so on.
What I do not understand:
How to first approach the question: what is the first step after recording all known data?
How to approach numerical data to x decimal points: Is it easier to round to three significant figures, or even to a whole number when graphing the model by hand?
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In the first box I've provided a copy of the question. In the second box I've provided what I do/do not understand. Any help you provide will be most appreciated.
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The quadratic model is
y = a t^2 + b t + c,
where y represents depth and t clock time. a, b and c are parameters to be determined.
You plug the coordinates of each point into the form, obtaining an equation for each point, in terms of the parameters a, b and c.
You then solve the three simultaneous equations for a, b and c.
Those values are plugged back into the original form to get your quadratic model.
This is all done within the first few assignments, which you should also review.
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You're welcome to send my your work, and/or additional questions, related to this problem.
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#$&*
MTH 163
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Question Form_labelMessages **
Practice Major Quiz (cont.)
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I graphed then modeled (to the best personal estimation) for reference, then I substituted the depth 17.7 and 17.701 into the equation .026t^2 - 1.2t + 53 and obtained the times 39.90554 and 39.90526043, respectively. I added the two together and divided by 2, the number of items, to average. I arrived at the average of the two numbers being 39.90540022.
Am I on the right track?
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I can no longer see the preceding document so I'm not sure what question you're answering here.
However I don't believe that 17.7 and 17.701 are depths. I believe they are clock times.
When 17.7 is substituted for t you get depth 39.90554, not clock time 39.90554.
If you add two depths together you get the average of the two depths. This is simply an average of two quantities, which in this case is not the average rate of change of anything.
To get the average rate of change of depth with respect to clock time, you need to apply the definition of average rate to the question. This definition will tell you what needs to be divided by what, and how to find the two quantities to be divided.
Start with the definition and see if you can reason this out.
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