course Mth 173 Ān_~dgStudent Name:
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21:48:21 `q001. Solve the following problem by describing a picture, and by constructing a graph. Describe your picture and your graph in detail. Do the same on subsequent problems: 1. If your total earnings up to week 6 are 56.2 dollars, and your total earnings up to week 11 are 66.2 dollars, then what are your average earnings per week? Why do we say average earnings per week rather than just earnings per week?
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RESPONSE --> 56.2 / 6 = 9.37 66.2 / 11 = 6.02 (9.37 + 6.02) / 2 = 7.69 average earnings per week We say average per week instead of just per week because we don't always earn exactly the same each week.
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21:49:50 The most common errors on this problem involve things like dividing 56.2 dollars by 6 weeks and/or dividing 66.2 dollars by 11 weeks. Having made these errors there are various ways is to put the results together to get an incorrect answer. The reason such calculations are meaningless is that you have no information about the total earnings at week 0. Total earnings might be measured from some time other than week 0 (e.g., fiscal years and calendar years don't usually coincide). So you don't know that it took 6 weeks to earn the 56.2 dollars, or 11 weeks to earn the 66.2 dollars. What you do know is that between week 6 and week 11 earnings increased from 56.2 dollars to 66.2 dollars, which means that you earned 10 dollars in the 5 intervening weeks. That's the only information given; any other assumption is extraneous and could well be wrong. So the conclusion is that 10 dollars were make in 5 weeks, so the average rate is 2 dollars per week.
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RESPONSE --> I thought about doing that, but I wasn't quite sure. I guess it is true what they say about assuming... :)
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21:52:56 `q002. Solve the following by describing a picture, and by constructing a graph: If an automobile is at milepost 421 after having traveled for 8 hours and at milepost 475 after having traveled for 15 hours, then what is its average speed? Why do we say average speed rather than just speed?
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RESPONSE --> 475 - 421 = 54 miles 15 - 8 = 7 hours 54 miles / 7 hours = 7.71 miles per hour on average We again say average speed because we don't know how fast it took the automobile to go the first 421 miles. We only know how far the automobile went after 7 hours.
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21:53:19 The common error here is to divide 421 miles by 8 hours, or 475 miles by 15 hours. Both calculations would make the clearly questionable assumption that whoever is traveling started from milepost 0. Most people who drive up and down an Interstate highway don't drive to the beginning before they start. What is known is that someone traveled 54 miles in 7 hours. That makes the average rate 54 miles / (7 hrs) = 7.7 miles / hr, approximately. Bad for a car; impressive if the traveler is on foot.
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RESPONSE --> OK
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21:55:22 `q003. If the water in a uniform cylinder has depth 199 cm at clock time 7 seconds and depth 228 cm at clock time 16 seconds, then at what average rate is the depth changing? Why do we we say average rate rather than just rate?
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RESPONSE --> 228 - 199 = 29 cm 16 - 7 = 9 sec 29 cm / 9 sec = 3.22 cm per sec We say average because we don't know where the water depth started and at what ecaxt time. So on average, the water is changing at a rate of 3.22 cm / sec.
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21:56:10 A graph of depth vs. clock time will have the points (7, 199) and (16, 228). The rise of this graph is from 199 cm to 228 cm, a rise of 29 cm. The run of this graph is from 7 sec to 16 sec, a run of 9 sec. The slope, which is rise / run, is thus 29 cm / (9 sec) = 3.22 cm / sec. The rise represents the change in depth, the run represents change in clock time. So the slope represents change in depth / change in clock time, or the rate at which depth changes.
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RESPONSE --> This answer is not what the question asked. I would have answered the right question if I had known it.
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22:00:07 `q004. If you are earning money at an average rate of 15 dollars per week, and if at the end of week 9 your total earnings are 133.16 dollars, then what will be your total earnings that the end of week 17?
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RESPONSE --> You are earning an average of $15 per week. There are 17 - 9 = 8 weeks between week 9 and week 17. So $15 x 8 weeks = $120. To get the total, $120 + $133.16 = $253.16.
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22:00:15 Between week 9 and week 17 there are 17 - 9 = 8 weeks. At 15 dollars per week the earnings would be 15 dollars / week * 8 weeks = 120 dollars. Adding this to the initial 133.16 dollars you end up with total earnings of 253.6 dollars.
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RESPONSE -->
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22:01:49 `q005. If an automobile is traveling at the rate of 48 mph, and is at milepost 285 after having traveled for 6 hours, then at what milepost would it be after having traveled for 11 hours?
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RESPONSE --> 11 hours - 6 hours = 5 hours 5 hours x 48 mph = 240 miles milepost 285 + 240 miles = milepost 525
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22:01:58 Between hour 6 and hour 11 is 5 hours. The distance traveled during that time will be 48 miles / hr * 5 hr = 240 miles. This will put the car at 285 miles + 240 miles = 525 miles.
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RESPONSE -->
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22:08:43 `q006. If the depth of water in a uniform cylinder is changing at an average rate of 21 cm/second between clock times 9 s and 19 s, and if its depth at clock time 9 seconds is 178 cm, then what is its depth at clock time 19 seconds?
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RESPONSE --> 19 sec - 9 sec = 10 sec 21 cm per sec x 10 sec = 210 cm 178 cm - 210 cm = -32 cm at 19 sec Is this possible?
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22:09:20 A graph of depth vs. clock time would contain the point (9, 178), representing the 178 cm depth at clock time 9 sec, and would have slope 21, representing the rate at which depth changes with respect to clock time. The graph point correspoinding to clock time 19 seconds will lie 10 units to the right of the first point. The run between the points will therefore be 10, representing 10 seconds. If the run is 10 and the slope is 21, then since rise / run = slope we have rise / 10 = 21, so the rise is 210, representing the change in the depth. Thus the depth changes by 210 cm.
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RESPONSE --> This again is not the answer to the question that I had.
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22:12:19 `q007. If your total earnings up to week 4 are 20.91 dollars, and if you earn money at a constant rate of 6 dollars per week, then at what week will your total earnings be 36.91 dollars?
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RESPONSE --> $36.91 - $20.91 - $16 $16 / $6 per week = 2.67 weeks to earn $16 4 weeks + 2.67 weeks = 6.67 weeks to earn $36.91.
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22:12:29 Earnings change by 16 dollars, changing at a rate of 6 dollars per week. It therefore takes 16 dollars / (6 dollars / week) = 2.67 weeks for earnings to change from 20.91 dollars to 36.91 dollars.
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RESPONSE --> OK
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22:14:47 8. If an automobile is traveling at the rate of 51 mph, and is at milepost 202 after having traveled for 4 hours, then after how many hours of travel will it have reached milepost 15?
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RESPONSE --> milepost 202 - milepost 15 = 187 miles 187 miles / 51 miles per hour = 3.67 hours to go 187 miles 4 hours + 3.67 hours = 7.67 hours to reach milepost 15
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22:14:55 From milepost 202 to milepost 15 is 187 miles. At 51 mph it will take(187 miles / (51 mph) = 3.7 hours to travel this distance.
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RESPONSE --> OK
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22:16:54 9. If the depth of water in a uniform cylinder is changing at an average rate of 12 cm/second as it depth changes from 61.7 cm at clock time 6 seconds to 93.7 cm at an unknown clock time, then what is the unknown clock time?
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RESPONSE --> 93.7 cm - 61.7 cm = 32 cm 32 cm / 12 cm per sec = 2.67 sec 6 sec + 2.67 sec = 8.67 sec
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22:17:11 A graph of depth vs. clock time will include the point (6, 61.7), representing the depth of 61.7 cm at clock time 6 sec, and will have a slope of 12, representing the 12 cm/s rate at which depth is changing. The point at which depth is 93.7 cm will lie 32 units above the first point, representing the 32 cm depth change. Since slope = rise / run we have 12 = 32 / run so run = 32 / 12 = 2.75. Since run is change in clock time, this run represents the 2.75 second required for the depth change.
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RESPONSE --> OK
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