Log in
HomeStudy Guides420,000US230,000

MAT 127 Final: S06final

27 views13 pages
turquoisegnu128
31 Jan 2019
School
University of Maine
Department
Mathematics and Statistics
Course
MAT 127
Professor
All

For unlimited access to Study Guides, a Grade+ subscription is required.

Document Summary

Your university id number: no calculators are allowed on this exam, please show all your work. You may use backs of pages if necessary. You may not receive full credit for a correct answer if there is no work shown. Part i: (12 pts) compute the following integral: Z ln x x dx: (14 pts) compute the following integral: X x2 dx: (16 pts) suppose you need to evaluate the integral. This cannot be solved using elementary functions, so it has to be done numerically. Use any of the methods we learned (a riemann sum, trapezoidal rule, or simpson"s rule) to estimate the value of the integral. Make sure you indicate which method and which n (your choice!) you are using. You don"t need to simplify your answer, but the nal answer should be a number: (20 pts) superman is trapped in a cell with 16 grams of radioactive kryptonite.

Get access

Grade+
$40 USD/m
Billed monthly
Grade+
Homework Help
Study Guides
Textbook Solutions
Class Notes
Textbook Notes
Booster Class
10 Verified Answers

Related Documents

MAT 127
Final Exam
Study Guide
MAT 127 Midterm: S06mt1
turquoisegnu128
MAT 127
Final Exam
Study Guide
MAT 127 Final: S08final
turquoisegnu128
MAT 127
Final Exam
Study Guide
MAT 127 Midterm: S06mt2
turquoisegnu128

Related Questions

Help
Comments

    please use the following information to answer questions 1-6

    Imagine you have graduated and have just gotten a job in a fictionalized version of Paducah, KY, home of the world famous Dippin' Dots (Links to an external site.)Links to an external site.. You got the job by pitching a truly marvelous idea: The Grand Cone-yan, an ice cream festival as grand as any Court Days (Links to an external site.)Links to an external site. or Apple Festival (Links to an external site.)Links to an external site..

    The centerpiece of the festival is a 10 foot tall ice cream cone filled with local ice cream dots.

    The day before the festival the contractors have brought the truck of ice cream, and begin to fill the cone. After only a single minute, there is a foot of ice cream in your frozen glass cone. Since the entire cone is only 10 feet tall, you decide to come back in 10 minutes to witness the final filling.

    You are shocked when you return to find the cone has only been filled to the 2 foot mark! (The worker politely corrects you to say it is actually 2 feet and 2 inches.) You give it another 10 minutes, but the cone is only 2 foot 9 inches filled.

    Not knowing what else to do, you make a spreadsheet of the progress.

    Time (minutes) 0 1 10 20 30 60 120
    Height (feet, inches) 0' 0" 1' 0" 2' 2" 2' 9" 3' 1" 3' 11" 4' 11"

    You wonder why they have slowed down so much, so you keep checking in every hour.

    Time (hours) 1 2 3 4 5 6
    Height (feet, inches) 3' 11" 4' 11" 5' 8" 6' 3" 6' 6" 6' 11"

    After six hours you are worried the entire festival might fail, but you won't give up! You keep spreadsheeting.

    Time (hours) 7 8 9 10 11 12
    Height (feet, inches) 7' 4" 7' 8" 7' 11" 8' 3" 8' 6" 8' 9"

    After 12 hours, you take a quick trip home to change clothes, and return to your spreadsheeting.

    Time (hours) 13 14 15 16 17 18
    Height (feet, inches) 8' 11" 9' 2" 9' 5" 9' 7" 9' 9" 10' 0"

    Finally, late in the night, around 3am, it is complete. Your masterpiece. The Grand Cone-yan. But why did it take so long? It took a lot longer than 10 minutes. Why did the workers slow down so much? The first minute finished the first foot, but three feet took 30 minutes instead of 3 minutes. And now it's 3am!

    The workers say that they filled at a steady rate of 13 gallons per hour, and that any faster would run the risk of drain freeze.

    Your responses

    1. What is wrong with the following argument?

    If you really did 13 gallons per hour, then the 10 foot cone should have only taken 10 / 13 = 0.7 hours, less than an hour tops.

    2. What is wrong the following question?

    How do you convert gallons into feet?

    3. Find an authoritative source for the volume of a cone. Give the formula and explain what each part of the formula means in this problem.

    4. Most formulas will have both radius and height. Find a reasonable source for the relationship between the radius and height of an ice cream cone. Give an expression like

    R = H

    5. Calculate the volume of the cone using your formula. At a constant rate of 13 gallons per hour, how long should it have taken to fill up?

    You may use the approximate formula V=0.02908882 h3 if the formula you discovered does not match at all.

    6. There should still be a discrepancy between the V=0.02908882 h3 and the spreadsheet. Can you explain what likely happened?