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18:10:11 `q001. You should copy and paste these instructions to a word processor for reference. However you can always view them, as well as everything else that has appeared in this box, by clicking the 'Display Everything' button.
1. For the next question or answer, you click on 'Next Question / Answer' button above the box at top left until a question has been posed. Once a question has been posed you are to answer before you click again on this button. 2. Before clicking for an answer, type your best answer to the current question into the box to the right, then clip on the 'Enter Answer' button. 3. After entering your answer you will click on 'Next Question / Answer' to view the answer to the question. Do not tamper with the information displayed in the left-hand box. 4. If your answer was incorrect, incomplete or would otherwise require revision, you will enter a self-critique. If you learned something from the answer, you need to restate it in your own words in order to reinforce your learning. If there is something you feel you should note for future reference, you should make a note in your own words. Go to the response box (the right-hand box) and type in a self-critique and/or notes, as appropriate. Do not copy and paste anything from the left-hand box, since that information will be saved in any case. 5. If you wish to save your response to your Notes file you may choose to click on the 'Save As Notes' button rather than the 'Enter Answer' button. Doing so will save your work for your future reference. Your work will be saved in a Notes file in the c:\vhmthphy folder. The title of the Notes file will also include the name you gave when you started the program. 6. After clicking either the 'Enter Response' or the 'Save as Notes' button, click on 'Next Question / Answer' and proceed in a similar manner. In the right-hand box briefly describe your understanding of these instructions, then click 'Enter Answer'.......!!!!!!!!...................................
RESPONSE --> I am to use the Next Question / Answer button to move on to the next step or question in the program after I use this box to either enter a self-critique or any other comments explaining what I learned from the explanation of the question.
If I want to save my response to the Notes file, I use the "Save as Notes" button which stores them in a file in the c:\vhmthphy folder for access. I assume that if I save the notes, I still need to enter them as a response but I'm not sure..................................................
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18:10:24 Your answer has been noted. Enter 'ok' in the Response Box and click on Enter Response, then click on Next Question/Answer for the first real question.
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RESPONSE --> ok
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18:17:34 `q002. Note that there are 10 questions in this assignment. The questions are of increasing difficulty--the first questions are fairly easy but later questions are very tricky. The main purposes of these exercises are to refine your thinking about rates, and to see how you process challenging information. Continue as far as you can until you are completely lost. Students who are prepared for the highest-level math courses might not ever get lost.
If you make $50 in 5 hr, then at what rate are you earning money?......!!!!!!!!...................................
RESPONSE --> $50 / 5 hr = $10 per hour is the rate at which I am earning money. I knew I was dividing the two because I was giving the overall amount and asked to find out how much money would I need to make $50 in 5 hours. (I'm not sure if I need to prove my visualization process with these easier problems.)
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18:18:25 The rate at which you are earning money is the number of dollars per hour you are earning. You are earning money at the rate of 50 dollars / (5 hours) = 10 dollars / hour. It is very likely that you immediately came up with the $10 / hour because almosteveryone is familiar with the concept of the pay rate, the number of dollars per hour. Note carefully that the pay rate is found by dividing the quantity earned by the time required to earn it. Time rates in general are found by dividing an accumulated quantity by the time required to accumulate it.
You need to make note of anything in the given solution that you didn't understand when you solved the problem. If new ideas have been introduced in the solution, you need to note them. If you notice an error in your own thinking then you need to note that. In your own words, explain anything you didn't already understand and save your response as Notes.......!!!!!!!!...................................
RESPONSE --> I understood everything in the answer.
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18:19:53 `q003.If you make $60,000 per year then how much do you make per month?
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RESPONSE --> $60,000 per year / 12 months = $5000 per month. Since this is another pay rate question, I know from the last explanation to use the total and divide it by the time.
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18:20:22 Most people will very quickly see that we need to divide $60,000 by 12 months, giving us 60,000 dollars / (12 months) = 5000 dollars / month. Note that again we have found a time rate, dividing the accumulated quantity by the time required to accumulate it.
You need to make note of anything in the given solution that you didn't understand when you solved the problem. If new ideas have been introduced in the solution, you need to note them. If you notice an error in your own thinking then you need to note that. In your own words, explain anything you didn't already understand and save your response as Notes.......!!!!!!!!...................................
RESPONSE --> ok.
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18:23:38 `q004. Suppose that the $60,000 is made in a year by a small business. Would be more appropriate to say that the business makes $5000 per month, or that the business makes an average of $5000 per month?
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RESPONSE --> I think it would make more sense to say that the business makes an average of $5000 per month. I think this because to make an even amount EVERY month with no fluctuation seems very unlikely to me. Saying that the business averages that much per month allows the business some room to make more money during a specific season as opposed to another depending on the economy and kind of business it is.
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18:26:10 Small businesses do not usually make the same amount of money every month. The amount made depends on the demand for the services or commodities provided by the business, and there are often seasonal fluctuations in addition to other market fluctuations. It is almost certain that a small business making $60,000 per year will make more than $5000 in some months and less than $5000 in others. Therefore it is much more appropriate to say that the business makes and average of $5000 per month.
You need to make note of anything in the given solution that you didn't understand when you solved the problem. If new ideas have been introduced in the solution, you need to note them. If you notice an error in your own thinking then you need to note that. In your own words, explain anything you didn't already understand and save your response as Notes.......!!!!!!!!...................................
RESPONSE --> I decided on my response not only by nearly everything the program stated as playing a factor, but also because an employee is more likely to earn almost the exact same every month if they're on salary and never get a raise and taxes/social security, etc. remain steady. I figured it'd be completely different for the small business and that confirmed my answer even more.
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18:28:16 `q005. If you travel 300 miles in 6 hours, at what average rate are you covering distance, and why do we say average rate instead of just plain rate?
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RESPONSE --> 300 miles / 6 hours = 50 miles per hour is the average rate I am traveling. We say average because I won't remain at 50mph exactly for 6 hours straight. At some point I'll have to stop, get stuck in traffic or buy outrageously expensive gas. Anything slowing me down will cause the 50mph to be an average and not exact.
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18:29:36 The average rate is 50 miles per hour, or 50 miles / hour. This is obtained by dividing the accumulated quantity, the 300 miles, by the time required to accumulate it, obtaining ave rate = 300 miles / ( 6 hours) = 50 miles / hour. Note that the rate at which distance is covered is called speed. The car has an average speed of 50 miles/hour. We say 'average rate' in this case because it is almost certain that slight changes in pressure on the accelerator, traffic conditions and other factors ensure that the speed will sometimes be greater than 50 miles/hour and sometimes less than 50 miles/hour; the 50 miles/hour we obtain from the given information is clearly and overall average of the velocities.
You need to make note of anything in the given solution that you didn't understand when you solved the problem. If new ideas have been introduced in the solution, you need to note them. If you notice an error in your own thinking then you need to note that. In your own words, explain anything you didn't already understand and save your response as Notes.......!!!!!!!!...................................
RESPONSE --> I didn't mention much about needing to go over 50mph in order to make 50 the average, but I still grasped the entire concept easily enough.
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18:33:15 `q006. If you use 60 gallons of gasoline on a 1200 mile trip, then at what average rate are you using gasoline, with respect to miles traveled?
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RESPONSE --> In order to get the average rate that I am using gas, I need to divide the distance by the total number of gallons used. So 1200 miles / 60 gal = 20miles per gallon is the average rate that I am using gasoline. Once again, this is an average because at different times I'd be using more gas to accelerate or my gas mileage would increase if I were on a highway as opposed to a city.
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18:38:41 08-25-2005 18:38:41 The rate of change of one quantity with respect to another is the change in the first quantity, divided by the change in the second. As in previous examples, we found the rate at which money was made with respect to time by dividing the amount of money made by the time required to make it.
By analogy, the rate at which we use fuel with respect to miles traveled is the change in the amount of fuel divided by the number of miles traveled. In this case we use 60 gallons of fuel in 1200 miles, so the average rate it 60 gal / (1200 miles) = .05 gallons / mile. Note that this question didn't ask for miles per gallon. Miles per gallon is an appropriate and common calculation, but it measures the rate at which miles are covered with respect to the amount of fuel used. Be sure you see the difference. Note that in this problem we again have here an example of a rate, but unlike previous instances this rate is not calculated with respect to time. This rate is calculated with respect to the amount of fuel used. We divide the accumulated quantity, in this case miles, by the amount of fuel required to cover those miles. Note that again we call the result of this problem an average rate because there are always at least subtle differences in driving conditions that require the use of more fuel on some miles than on others. It's very important to understand the phrase 'with respect to'. Whether the calculation makes sense or not, it is defined by the order of the terms. In this case gallons / mile tells you how many gallons you are burning, on the average, per mile. This concept is not as familiar as miles / gallon, but except for familiarity it's technically no more difficult. You need to make note of anything in the given solution that you didn't understand when you solved the problem. If new ideas have been introduced in the solution, you need to note them. If you notice an error in your own thinking then you need to note that. In your own words, explain anything you didn't already understand and save your response as Notes.......!!!!!!!!...................................
NOTES -------> Oops, I assumed the question was asking for miles per gallon. So the rate at which we use fuel means that they are looking for how much fuel per mile is used, not how many miles per gallon it takes.
PROGRAM NOTES/RESPONSE The rate of change of one quantity with respect to another is the change in the first quantity, divided by the change in the second. As in previous examples, we found the rate at which money was made with respect to time by dividing the amount of money made by the time required to make it. By analogy, the rate at which we use fuel with respect to miles traveled is the change in the amount of fuel divided by the number of miles traveled. In this case we use 60 gallons of fuel in 1200 miles, so the average rate it 60 gal / (1200 miles) = .05 gallons / mile. Note that this question didn't ask for miles per gallon. Miles per gallon is an appropriate and common calculation, but it measures the rate at which miles are covered with respect to the amount of fuel used. Be sure you see the difference. Note that in this problem we again have here an example of a rate, but unlike previous instances this rate is not calculated with respect to time. This rate is calculated with respect to the amount of fuel used. We divide the accumulated quantity, in this case miles, by the amount of fuel required to cover those miles. Note that again we call the result of this problem an average rate because there are always at least subtle differences in driving conditions that require the use of more fuel on some miles than on others. It's very important to understand the phrase 'with respect to'. Whether the calculation makes sense or not, it is defined by the order of the terms. In this case gallons / mile tells you how many gallons you are burning, on the average, per mile. This concept is not as familiar as miles / gallon, but except for familiarity it's technically no more difficult........................................................!!!!!!!!...................................
18:47:50 `q007. The word 'average' generally connotes something like adding two quantities and dividing by 2, or adding several quantities and dividing by the number of quantities we added. Why is it that we are calculating average rates but we aren't adding anything?
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RESPONSE --> We are calculating rates and aren't adding anything because the total amount (whether in miles or gallons or money) is already given to us. If one of the previous questions did not give the total of $60,000 per year but instead gave us 12 different monthly totals, we would need to add the monthly values and divide by 12 to get the average. These questions aren't laid out in that manner.
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18:52:36 08-25-2005 18:52:36 The word 'average' in the context of the dollars / month, miles / gallon types of questions we have been answering was used because we expect that in different months different amounts were earned, or that over different parts of the trip the gas mileage might have varied, but that if we knew all the individual quantities (e.g., the dollars earned each month, the number of gallons used with each mile) and averaged them in the usual manner, we would get the .05 gallons / mile, or the $5000 / month. In a sense we have already added up all the dollars earned in each month, or the miles traveled on each gallon, and we have obtained the total $60,000 or 1200 miles. Thus when we divide by the number of months or the number of gallons, we are in fact calculating an average rate.
You need to make note of anything in the given solution that you didn't understand when you solved the problem. If new ideas have been introduced in the solution, you need to note them. If you notice an error in your own thinking then you need to note that. In your own words, explain anything you didn't already understand and save your response as Notes.......!!!!!!!!...................................
NOTES -------> I think I just realized that I'm supposed to save all my responses as notes and not enter them like I have been doing. I thought I needed to enter them as notes only if I needed the explanation... If I need to redo any of this, let me know.
I feel I understood everything in the answer as to why we aren't adding any quantities but are still figuring out averages. I'm not sure my previous answer was as graceful or in depth though........................................................!!!!!!!!...................................
19:07:38 08-25-2005 19:07:38 `q008. In a study of how lifting strength is influenced by various ways of training, a study group was divided into 2 subgroups of equally matched individuals. The first group did 10 pushups per day for a year and the second group did 50 pushups per day for year. At the end of the year to lifting strength of the first group averaged 147 pounds, while that of the second group averaged 162 pounds. At what average rate did lifting strength increase per daily pushup?
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NOTES -------> Though I'm not sure how to figure this out, here's the process I came up with. Since we need the strength per daily pushup, I assume we need to figure out how many pushups were done by each group for the entire year. So for the first group, 365 * 10 = 3650 pushups for that year. For the second group, 365days * 50 pushups = 18,250 pushups for the entire year.
The only way I can figure out the answer is next to take the average amount each group lifted and divide it by the total number of pushups done for the entire year. So 147 lbs / 3650 pushups for the year = 0.0403 lbs per pushup gained. For the second group, 162 lbs / 18250 pushups = 0.0089 lbs per pushup gained. I'm not sure if my math is correct, but it kind of makes sense that since there was only a 15 pound difference between the final strength of the two groups, then group one will gain more strength per pushup since they did fewer ones. Since the second group did so many, each one gained less for the individual, but so many were done that it still totaled a 15 pound change in their strength at the end of the year. I have no idea if I'm write, but this is what I figured may work........................................................!!!!!!!!...................................
19:14:04 08-25-2005 19:14:04 The second group had 15 pounds more lifting strength as a result of doing 40 more daily pushups than the first. The desired rate is therefore 15 pounds / 40 pushups = .375 pounds / pushup.
You need to make note of anything in the given solution that you didn't understand when you solved the problem. If new ideas have been introduced in the solution, you need to note them. If you notice an error in your own thinking then you need to note that. In your own words, explain anything you didn't already understand and save your response as Notes.......!!!!!!!!...................................
NOTES -------> Hahaha ok I make things so much harder than they need to be. I think my process is, at the least, inventive but still horribly wrong.
I see how to get the answer. I was thinking more along the lines of comparing the two groups because in my mind, the weight per pushup would vary for the two groups since the second group did so many more than the first. But I see that I need to take the difference of the factors (both the weight and the number of pushups) and divide them to get the average, just as in the other problems........................................................!!!!!!!!...................................
19:17:45 `q009. In another part of the study, participants all did 30 pushups per day, but one group did pushups with a 10-pound weight on their shoulders while the other used a 30-pound weight. At the end of the study, the first group had an average lifting strength of 171 pounds, while the second had an average lifting strength of 188 pounds. At what average rate did lifting strength increase with respect to the added shoulder weight?
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RESPONSE --> There was a total difference of 17 pounds for the average lifting strength between the two groups. So, (hopefully like the last question) I would need to get the average rate of increase by dividing the differences of the weight used and the strength gained. So 17 lbs / 20 lbs = 0.85 lbs is the average weight that the lifting strength increased with respect to the average shoulder weight.
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19:19:37 08-25-2005 19:19:37 The difference in lifting strength was 17 pounds, as a result of a 20 pound difference in added weight. The average rate at which strength increases with respect added weight would therefore be 17 lifting pounds / (20 added pounds) = .85 lifting pounds / added pound. The strength advantage was .85 lifting pounds per pound of added weight, on the average.
You need to make note of anything in the given solution that you didn't understand when you solved the problem. If new ideas have been introduced in the solution, you need to note them. If you notice an error in your own thinking then you need to note that. In your own words, explain anything you didn't already understand and save your response as Notes.......!!!!!!!!...................................
NOTES -------> Yay I got it right, I just didn't explain that the .85 was the lifting pounds per pound of added weight as well as I should have. I'm not sure how correct my units were but I see how I need to state that the 20 lbs is referred to as added weight and not just lbs like the other factor.
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19:23:58 08-25-2005 19:23:58 `q010. During a race, a runner passes the 100-meter mark 12 seconds after the start and the 200-meter mark 22 seconds after the start. At what average rate was the runner covering distance between those two positions?
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NOTES -------> In order to get the average rate between those two distances, I think I need to figure out the differences between the distances ran and the time taken to run them. So 100m / 10 sec = 10m/sec is the average distance covered. I think since the problem said "covering distance b/n those two positions" implies that it is m/sec and not sec/m that need to be solved.
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19:24:21 08-25-2005 19:24:21 The runner traveled 100 meters between the two positions, and required 10 seconds to do so. The average rate at which the runner was covering distance was therefore 100 meters / (10 seconds) = 10 meters / second. Again this is an average rate; at different positions in his stride the runner would clearly be traveling at slightly different speeds.
You need to make note of anything in the given solution that you didn't understand when you solved the problem. If new ideas have been introduced in the solution, you need to note them. If you notice an error in your own thinking then you need to note that. In your own words, explain anything you didn't already understand and save your response as Notes.......!!!!!!!!...................................
NOTES -------> Ok good I interpretted the question correctly.
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19:31:23 08-25-2005 19:31:23 `q011. During a race, a runner passes the 100-meter mark moving at 10 meters / second, and the 200-meter mark moving at 9 meters / second. What is your best estimate of how long it takes the runner to cover the 100 meter distance?
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NOTES -------> I'm not sure if by "how long it takes the runner to cover the hundred meter distance" you mean the first 100m mark or the second 100m mark, or as before, the difference between the two. My first assumption was to divide 100m / 9m/sec = 11.11 seconds as the average it took to run the 100 meter distance, but I'm not quite sure.
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19:35:35 08-25-2005 19:35:35 At 10 meters/sec, the runner would require 10 seconds to travel 100 meters. However the runner seems to be slowing, and will therefore require more than 10 seconds to travel the 100 meters. We don't know what the runner's average speed is, we only know that it goes from 10 m/s to 9 m/s. The simplest estimate we could make would be that the average speed is the average of 10 m/s and 9 m/s, or (10 m/s + 9 m/s ) / 2 = 9.5 m/s. Taking this approximation as the average rate, the time required to travel 100 meters will be (100 meters) / (9.5 m/s) = 10.5 sec, approx.. Note that simply averaging the 10 m/s and the 9 m/s might not be the best way to approximate the average rate--for example we if we knew enough about the situation we might expect that this runner would maintain the 10 m/s for most of the remaining 100 meters, and simply tire during the last few seconds. However we were not given this information, and we don't add extraneous assumptions without good cause. So the approximation we used here is pretty close to the best we can do with the given information.
You need to make note of anything in the given solution that you didn't understand when you solved the problem. If new ideas have been introduced in the solution, you need to note them. If you notice an error in your own thinking then you need to note that. In your own words, explain anything you didn't already understand and save your response as Notes.......!!!!!!!!...................................
NOTES -------> Ok so the question was referring to both sections in the race. I was right with my idea to divide the 100m by the m/s, it just never occurred to me to average the 10m/s and 9m/s. I kept thinking along the lines of the previous problems where the difference between the two numbers were used and I knew that didn't apply here but I couldn't figure out what did. I also see how it would be easy for someone to simply average the 10m/s and 9m/s to get the average for the whole race but not just for a 100m distance.
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19:37:59 08-25-2005 19:37:59 `q012. We just averaged two quantities, adding them in dividing by 2, to find an average rate. We didn't do that before. Why we do it now?
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NOTES -------> We averaged the two quantities by adding them and dividing by two because we were given the separate factors needed for the final average, as opposed to being given the final average first. Like with the previous problems, we weren't given a list of the amount made per month for an entire year, we were given the entire salary earned. This problem did the opposite, hence the reason we needed to get the average by adding them and dividing them by 2.
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19:40:42 08-25-2005 19:40:42 In previous examples the quantities weren't rates. We were given the amount of change of some accumulating quantity, and the change in time or in some other quantity on which the first was dependent (e.g., dollars and months, miles and gallons). Here we are given 2 rates, 10 m/s and 9 m/s, in a situation where we need an average rate in order to answer a question. Within this context, averaging the 2 rates was an appropriate tactic.
You need to make note of anything in the given solution that you didn't understand when you solved the problem. If new ideas have been introduced in the solution, you need to note them. If you notice an error in your own thinking then you need to note that. In your own words, explain anything you didn't already understand and save your response as Notes.......!!!!!!!!...................................
NOTES -------> I didn't really consider the difference between some problems giving the amount of change as opposed to giving rates like the last problem. Hopefully I can spot this difference in the future and remember when it is I need to worry about the differences between the varying factors or average the rates given.
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