course Mth 272
I asked you a question before about submission technique for this assignment, being that it was not a SEND file, and so I am assuming by me doing it through the questions form it is still appropriate. I feel confident about the first part of Assignment 0, but the second part was very confusing simply because I had an impossible time figuring out how I could describe a picture, graph, etc. for each problem. I tried to solve them as best as I could, but I have no graphs for you. I mentioned that in a different question form, and your response about how to make a graph for one of the problems still did not quite make sense to me. If I am to get little credit for the assignment because I am not describing graphs I don't know how to make from the answers that I got, then please let me have some kind of another chance after you hopefully offer me a solid explanation. Thanks.
Assignment 0 for 272Daniel Sapp (dps212@email.vccs.edu)
-Calculus I Introductory Problems First Set, Version 1
Questions 1-9
1. If you earn 154.9823 dollars in 11 hours, at what average rate are you earning money, in dollars per hour?
154.9823/11 = $14.0893 per hour
2. If you travel 116.9053 miles in 9 hours, at what average rate are you traveling, in miles per hour?
116.9053/9= 12.98948
You are traveling at an average rate of 12.98948 miles per hour.
3. If a ball rolling down a grooved track travels 48.73081 centimeters in 9 seconds, at what average rate is the ball moving, in centimeters per second?
48.73081/9= 5.414534 cm/s
4. If you are earning money at the average rate of 66 dollars per hour, how much do you earn in 8 hours?
66*8= $528 in 8 hours
5. If you are traveling at an average rate of 75 miles per hour, how far do you travel in 6 hours?
75*6= 450 miles
6. If a ball travels at an average rate of 42 centimeters per second, how far does it travel in 10 seconds?
42*10= 420 cm in 10 seconds
7. How long does it take to earn 183.9925 dollars at an average rate of 21 dollars per hour?
183.9925/21= 8.761547 hours
8. How long does it take to travel 98.46438 miles at an average rate of 15 miles per hour?
98.46438/15= 6.56492 hours
9. How long does it take a rolling ball to travel 26.29359 centimeters at an average rate of 7 centimeters per second?
26.29359/7= 3.756227 seconds
Assignment 0, part 2, for 272
Daniel Sapp (dps212@email.vccs.edu)
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?
First you find the average per week earnings for the first 7 weeks. 98.73873/7= $14.10553 per week for the first 7 weeks.
Then I subtract the first 7 earnings from total 12 weeks, which leaves the dollars earned in the last 5. 113.7387-98.73873=$15.05997 total for the remaining 5 weeks. I then divide that number by 5 to come up with the weekly earnings for that period. 15.05997/5= $3.01199 per week. To get the average per week for the entire 12-week period, I have to add the two period’s weekly earnings together and then divide by 2.
(3.01199+14.10553)/2= average of $8.56 earnings per week. We say average because it is not an exact representation of the earnings each week, but rather an estimate, assuming fluctuation, for the whole period.
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?
(X+70.4361)/14=9
9*14=126-70.4361=55.5639 in last 6 weeks, total earnings of $126
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, which is just one more week of pay at a flat rate of $7 per week, so just tack on one week to the previous earnings, which totals 8 weeks.
Week 8 earnings $55.54
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?
580.3036/8= 72.538 8/17= 0.4706 72.538*0.47= 34.09 avg mph for first leg of trip
653.3036-580.3036= 73 miles for remaining leg 73/9= 8.1 9/17= 0.53 proportion of trip left
8.1*.53= 4.29 average
4.29+34.09=38.38 average mph for entire trip
CHECK WORK- 38.38mph*17hr=653 miles total
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?
323.3186/37= 8.7 hours mph (rounded to 9mph in the problem I am guessing?)
.X= new milepost
X/37=15
15*37= X= milepost 555
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?
**Professor Smith, I am assuming that the car is starting at mile 537 and going down, not starting at zero. If the question is trying to ask how long will it take to go 17 miles, then let me know and I can rework it.**
537.8707-17= 520.8707 miles
520.8707/69= 7.55 hours (or 0.25 hours if only going 17 miles)
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?
129.9148/6= 21.6525 cm/sec for the first depth
153.9148/16=9.6197 cm/sec for second depth
Average= (21.6525+9.6197)/2= 15.6361 cm/sec average
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?
15-7= 8 seconds
16 cm/s*8s= 128cm
108.3893+128= 236.3893 cm depth at clock time 15s
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?
339.043cm-306.043cm= 33 cm difference in depth
If rate is 33 cm/seconds, and the depth has changed 33 com in the unknown amount of time, then only one second has passed, so total time= 11 seconds.
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