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course mth 173
Randomized Problems version 21#$&*
course mth 173
Solve the following by describing a picture, and by constructing a graph:1. If your total earnings up to week 7 are 98.73873 dollars, and your total earnings up to week 12 are 113.7387 dollars, then what are your average earnings per week? Why do we say average earnings per week rather than just earnings per week?
113.7387/12= $9.478/week.
We say average earnings per week b/c the earnings fluctuate. For example, the average up to week 7 was $14.1055 a week, but then went only went to $3 per week up to week 12. So therefore it is an average of $9.478 per week.
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You don't know how much money was made in a 12-week period.
You can't assume that the total made at week 0 was 0.
All you know is what happened between week 7 and week 12.
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####I understand what I did wrong on the problem below. The fact of where the trip started is unknown. However, I’m not clear on this problem. What do you mean we can’t assume the total made at week 0? No such thing as week 0. The first week of work would be week 1. It said the total earnings (amount made from work) through week 7 was $98.73873. It’s clear we don’t know what was earned each week, but why isn’t possible to get an average earned through the first seven weeks? What am I not seeing?
@& You don't know when the earnings started either.
A week doesn't accrue until the end of the week. SInce the numbering of weeks begins at the beginning of the first week, the clock time in weeks at the begining is 0. The clock time doesn't reach 1 week until the end of the first week.
In any case we don't know what the earnings were at any time other than 'up to week 7' (which technically might in fact be week 6, where week 7 would be 'up through' week 7).. We can start counting weeks at any point; there's no reason to suppose that earnings are zero at whatever point we choose, for whatever reason, to begin counting.
So our information doesn't tell us how much was earned during the first seven weeks. All we figure out is how much was earned during the 5-week period in question.
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2. If you are earning money at an average rate of 9 dollars per week, and if at the end of week 8 your total earnings are 70.43631 dollars, then what will be your total earnings that the end of week 14?
14- 8= 6weeks
6*9=54
70.43631 + 54 = $124.436
3. If your total earnings up to week 7 are 48.54274 dollars, and if you earn money at a constant rate of 7 dollars per week, then at what week will your total earnings be 55.54274 dollars?
55.54274 - 48.54274 = 7
Week 8
4. If an automobile is at milepost 580.3036 after having traveled for 8 hours and at milepost 653.3036 after having traveled for 17 hours, then what is its average speed? Why do we say average speed rather than just speed?
During the first eight hours the average speed was 72.538 mph, and only 6.64 mph to milepost 653.3036, therefore the average speed overall 653.3036/17 = 38.4296 mph. It is called average speed rather than speed because the speed fluctuates because of traffic or weather, so it becomes an average of speed during the entire length of travel.
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Very few trips along roads with mileposts (e.g., interstates) start at milepost 0.
Ao there is no reason at all to suppose that the trip started at milepost 0. We don't know where the trip started.
All we know is where the car was after 8 hours, and where it was after 17 hours.
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5. If an automobile is traveling at the rate of 37 mph, and is at milepost 323.3186 after having traveled for 9 hours, then what milepost would be after having traveled for 15 hours?
15*37=555
323.3186+555= milepost 910.319
6. If an automobile is traveling at the rate of 69 mph, and is at milepost 537.8707 after having traveled for 8 hours, then after how many hours of travel will it have reached milepost 17?
537.8707 - 17=520.871
520.871/69= 7.55 hrs.
7. If the water in a uniform cylinder has depth 129.9148 cm at clock time 6 seconds and depth 153.9148 cm at clock time 16 seconds, then at what average rate is the depth changing? What we say average rate rather than just rate?
153.9148 - 129.9148 = 24
16-6
24/10=2.4cm/sec. It is called average rate because the depth isn’t changing at a constant rate, therefore it is an average rate.
8. If the depth of water in a uniform cylinder is changing at an average rate of 16 cm/second between clock times 7 s and 15 s, and if its depth at clock time 7 seconds is 108.3893 cm, then what is its depth at clock time 15 seconds?
108.3893cm + (16cm/s * 8)= 236.389cm
9. If the depth of water in a uniform cylinder is changing at an average rate of 33 cm/second as it depth changes from 306.043 cm at clock time 10 seconds to 339.043 cm at an unknown clock time, then what is the unknown clock time?
339.043- 306.043 = 33cm
11sec.
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Overall good, but you made extraneous assumptions on two of the problems.
So be sure to check my notes and let me know if you don't understand what you should have done.
If you aren't sure, you're welcome to resubmit by inserting your revisions, questions, etc., into a copy of this document.
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Check my note and let me know if the earnings question still doesn't make sense, or if you have questions related to my latest note.
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