![Math 116 / Final (April 28, 2014) page 8 7. [8 points] Roy the alpaca is designing a pool and a deck for his family. The pool has the shape of a cardioid whose equation is given by r = 4−4sin(θ) where r is in meters and θ is a number. Cranberry juice to detox thc](/img/512x512/800842620324.webp)
University of Michigan Department of Mathematics Winter, 2010 Math 116 Exam 1 Problem 10 Math 116 / Final (April 23, 2010) page 6 4.[8 points] Consider a solid whose base is contained between the curves y = e x , y = 1, andWinter, 2018 Math 116 Exam 1 Problem 6 Solution Author: University of Michigan Department of Mathematics Subject: This is a problem which appeared on a calculus exam at the University of Michigan Created Date: 1/5/2023 12:00:40 AM Math 116 / Exam 2 (November 13, 2017) do not write your name on this exam page 4 3. [12 points] Define a sequence a n for n≥ 1 by a n = 0 if nis odd 1/3 if nis even. Note that this means the first three terms of this sequence are a1 = 0, a2 = 1/3, a3 = 0. Math 116 — Practice for Exam 3 Generated December 10, 2018 Name: SOLUTIONS Instructor: Section Number: 1. This exam has 6 questions. ... University of Michigan Department of Mathematics Fall, 2014 Math 116 Exam 3 Problem 2 Solution. Math 116 / Final (December 19, 2016) DO NOT WRITE YOUR NAME ON THIS PAGE page 7 7. [7 … Math 116 { Calculus II { Section 099 { Winter 2019 Instructor: Harry Richman O ce Hours in EH 1860: (tentative) Email: [email protected] W 2-3pm, Th 2-3pm, by appointment Class: TTh, 6:00-8:00pm, Mason Hall 2449 O ce Hour in the Math Lab: F 11-12 Course Description: The course presents concepts of calculus beyond di erentiation. Topics include Math 116 Calculus II. Math 116 Calculus II Course Outline YourGrade Assignments Exams Notes Parent Directory.Math 116 — Practice for Exam 1 GeneratedFebruary8,2023 Name: SOLUTIONS Instructor: SectionNumber: 1. This exam has 5 questions. Note that the problems are not of equal difficulty, so you may want to skip over and return to a problem on which you are stuck. 2. Do not separate the pages of the exam. If any pages do become separated, write your ... University of Michigan Department of Mathematics Winter, 2018 Math 116 Exam 2 Problem 5 (class time) Solution Math 116 / Exam 1 (February 10, 2020 ) page 12 10. Math 116 — Practice for Exam 1 GeneratedJanuary5,2023 Name: SOLUTIONS Instructor: SectionNumber: 1. This exam has 4 questions. ... University of Michigan Department of Mathematics Winter, 2017 Math 116 Exam 1 Problem 5 (counting money) Solution. Math 116 / Exam 1 (February 5, 2018) page 4 2. [9 points]MATH: Get the latest Dragon Victory International stock price and detailed information including MATH news, historical charts and realtime prices. At first, ChatGPT and AI sent me ...Math 116 / Exam 2 (March 21, 2022 ) do not write your name on this exam page 5 5. [12 points] A tech startup is growing quickly, and the company needs to understand its customers data-storage needs to properly scale its infrastructure. Over the course of each month, the users each store 5 gigabytes of new data. Additionally, because users areMath 116 / Final (December 14, 2022) page 4 2.[15 points] The parts of this problem are unrelated to each other. Be sure to show work for all parts, and circle your final answer. a.[5 points] A leaking bag of sugar is lifted vertically from the ground to a height of 10 feet above the ground. The weight of the bag of sugar is 6− √University of Michigan Department of Mathematics Winter, 2012 Math 116 Exam 2 Problem 9 (wire) Math 116 / Exam 2 (March 19, 2012) page 11 c. [6 points] Find the mean length of wire between two consecutive flaws.University of Michigan Department of Mathematics Winter, 2018 Math 116 Exam 1 Problem 2 (owl and dove) Solution Math 116 / Exam 1 (October 14, 2015) DO NOT WRITE YOUR NAME ON THIS PAGE page 3 2.[7points] SupposeMath 116 — Practice for Exam 3 Generated April 4, 2016 Name: SOLUTIONS Instructor: Section Number: 1. This exam has 10 questions. Note that the problems are not of equal difficulty, so you may want to ... University of Michigan Department of Mathematics Winter, 2010 Math 116 Exam 3 Problem 3 Solution. Math 116 / Final (April 19, 2012) …Math 116 / Exam 2 (November 12, 2014) page 2 1. [12 points] Franklin, your robot, is on the local news. Let R(t) be the number of robots, in millions, that have joined the robot uprising tminutes after the start of the broadcast. 1 P∞ n=1(−1)n n(1+ln(n)) converges conditionally. University of Michigan Department of Mathematics. Winter, 2011 Math 116 Exam 3 Problem 10 Solution. 5. 4. (8 points) The Sierpinski Carpet is an example of a mathematical object called a fractal. It is. We would like to show you a description here but the site won’t allow us.Math 116 – Team Homework #1, Winter 2023 SOLUTIONS Some guidelines for your first assignment • You must read and attempt the problems before meeting with your team. Even if you aren’t able to obtain all the answers, being prepared during the team meetings helps your group work more efficiently during the meeting. Math 116 / Exam 1 (February 7, 2022 ) page 4 Solution: The required labeled values are included in the graph below, and the value at x= −6 should be one less than the value at x= −5. The function should be increasing on [−6,−4.5] and [0,6], decreasing on [−4.5,0], with maximum and minimum at the transition points (Near We would like to show you a description here but the site won’t allow us.One of the central themes in Shakespeare’s “Sonnet 116” is the idea of love as a constant force that cannot waver. The poem also stresses that love is invaluable and challenges the...University of Michigan Department of Mathematics Winter, 2010 Math 116 Exam 1 Problem 8. ... Math 116 / Exam 1 (February 6, 2017) do not write your name on this exam page 2 1. [12 points] Suppose that f is a twice differentiable function … %PDF-1.5 %âãÏÓ 100 0 obj > endobj 120 0 obj >/Filter/FlateDecode/ID[6BC99638CD0083F06ECAA05FCF088A92>20D79659FAC441B286CC35362EAA6005>]/Index[100 50]/Info 99 0 R ... University of Michigan Department of Mathematics Winter, 2018 Math 116 Exam 1 Problem 2 (owl and dove) Solution Math 116 / Exam 1 (October 14, 2015) DO NOT WRITE YOUR NAME ON THIS PAGE page 3 2.[7points] Suppose Math 116 / Exam 2 (November 12, 2018 ) do not write your name on this exam page 2 1.[11 points] For each of parts a-d below: Find the exact value, if possible. Recall that x= p 2 is a solution in exact form to the equation x2 = 2, but x= 1:41421356237 is not. If the given limit or integral either does not exist or diverges, write \does not exist".Math 116 / Exam 1 (February 8, 2016) DO NOT WRITE YOUR NAME ON THIS PAGE page 8 8.[12points] Inthefollowingquestions,circlethecorrectanswer. Youdonotneedtoshowany ... University of Michigan Department of Mathematics Winter, 2018 Math 116 Exam 1 Problem 6. Created Date: 9/26/2018 11:46:19 PM Title: Math 116 Calculus II. Math 116 Calculus II Course Outline YourGrade Assignments Exams Notes Parent Directory. University of Michigan Department of Mathematics Fall, 2019 Math 116 Exam 1 Problem 3 (cave) SolutionUniversity of Michigan Department of Mathematics Winter, 2015 Math 116 Exam 1 Problem 3 Solution. Math 116 / Exam 1 (October 9, 2013) page 10 8.[10points] Letg(x)beanoddcontinuousfunctionandh(x)anantiderivativeofg(x). Find ... Math 116 / Midterm (October 10, 2016) DO NOT WRITE YOUR NAME ON THIS PAGE page 2 1. [13 points] …Math 116 — First Midterm — February 12, 2024 EXAM SOLUTIONS This material is ©2024, University of Michigan Department of Mathematics, and released under a Creative Commons BY-NC-SA 4.0 International License. It is explicitly not for distribution on websites that share course materials. 1.This exam has 16 pages including this cover.Math 116 Masteries Last modified: Tue May 7 09:35:00 EDT 2024 Comments to math-itc(at)umich(dot)edu ©2004-09 Gavin LaRose, UM Math Dept/Regents of UMichMathematics is one of the most precise and versatile human languages. With it, mathematical scientists have described and understood complex physical phenomena, supported the infrastructure of the internet era, optimized production in industrial processes, and cultivated the creativity of young minds. As a language, together with its axiomatic ...Math 116 / Exam 2 (November 14, 2023) page 2 1.[8 points] Ricky’s college has installed a new model of napping pod in the library for students to get some well-deserved rest. Let f(t) be the probability density function (pdf) for the amount of time, t, Ricky sleeps after he falls asleep in a pod, where t is measured in hours.Math 116 / Final (December 14, 2021 ) do not write your name on this exam page 2 1.[9 points] Arnold is building a set for his son Michael’s school play in which Michael will have to climb a very tall beanstalk to fight a giant. a.[4 points] At first, Arnold decides that since the beanstalk is extremely tall, he should Math 116 / Exam 2 (November 13, 2017) do not write your name on this exam page 4 3. [12 points] Define a sequence a n for n≥ 1 by a n = 0 if nis odd 1/3 if nis even. Note that this means the first three terms of this sequence are a1 = 0, a2 = 1/3, a3 = 0. University of Michigan Department of Mathematics Winter, 2015 Math 116 Exam 1 Problem 3 Math 116 / Exam 1 (October 9, 2013) page 10 8.[10points] Letg(x)beanoddcontinuousfunctionandh(x)anantiderivativeofg(x). In order for a course to transfer to the University of Michigan as Math 116, it must thoroughly cover the following topics: Volumes of revolution by slicing. Integration by parts and substitution. Improper integrals. Sequences and series including p-series, ratio test, alt series test, integral test, comparison test, limit comparison test.University of Michigan Department of Mathematics Fall, 2011 Math 116 Exam 1 Problem 1Math 116 — Practice for Exam 3 Generated December 10, 2018 Name: Instructor: Section Number: 1. This exam has 6 questions. Note that the problems are not of equal difficulty, so you may want to skip ... University of Michigan Department of Mathematics Winter, 2016 Math 116 Exam 1 Problem 7 (jewelry) Created Date: 12/10/2018 10:29:12 PM Title: Math 116 { Calculus II { Section 099 { Winter 2019 Instructor: Harry Richman O ce Hours in EH 1860: (tentative) Email: [email protected] W 2-3pm, Th 2-3pm, by appointment Class: TTh, 6:00-8:00pm, Mason Hall 2449 O ce Hour in the Math Lab: F 11-12 Course Description: The course presents concepts of calculus beyond di erentiation. Topics include We would like to show you a description here but the site won’t allow us.Math 116 — Practice for Exam 2 Generated November 7, 2017 Name: Instructor: Section Number: 1. This exam has 12 questions. Note that the problems are not of equal …Math 116 | Second Midterm | November 9, 2020. Do not write your name anywhere on this exam or your submissions. Your submissions must, however, have the correct problem …%PDF-1.5 %âãÏÓ 100 0 obj > endobj 120 0 obj >/Filter/FlateDecode/ID[6BC99638CD0083F06ECAA05FCF088A92>20D79659FAC441B286CC35362EAA6005>]/Index[100 50]/Info 99 0 R ...Math 116 / Exam 1 (February 7, 2022 ) page 4 Solution: The required labeled values are included in the graph below, and the value at x= −6 should be one less than the value at x= −5. The function should be increasing on [−6,−4.5] and [0,6], decreasing on [−4.5,0], with maximum and minimum at the transition points (Near University of Michigan Department of Mathematics Winter, 2018 Math 116 Exam 2 Problem 5 (class time) Solution Math 116 / Exam 1 (February 10, 2020 ) page 12 10. Math 116 / Exam 2 (March 20, 2013) page 13 c. [4 points] i) Find the equation in polar coordinates of the line x = 0. Solution: θ = π 2. ii) Find the equation in polar coordinates of the line y = 4. Solution: y = rsinθ = 4, so r = 4 sinθ. University of Michigan Department of Mathematics Winter, 2013 Math 116 Exam 2 Problem 8 (peanut) SolutionDyscalculia is less studied and diagnosed as dyslexia, but it may be just as common. Maybe your child hates math. Maybe you did, too, when you were a kid, or you got so anxious abo...%PDF-1.5 %âãÏÓ 100 0 obj > endobj 120 0 obj >/Filter/FlateDecode/ID[6BC99638CD0083F06ECAA05FCF088A92>20D79659FAC441B286CC35362EAA6005>]/Index[100 50]/Info 99 0 R ...University of Michigan Department of Mathematics Winter, 2011 Math 116 Exam 1 Problem 7 (paint truck) Math 116 / Exam 1 (October 12, 2011) page 9 7. [13 points] Household electricity in the United States is supplied in the form of an alternating ... Math 116 / Exam 2 (November 12, 2018 ) do not write your name on this exam page 2 …Math 116 — Practice for Exam 2 Generated November 7, 2017 Name: SOLUTIONS Instructor: Section Number: 1. This exam has 12 questions. Note that the problems are not of equal difficulty, so you may want to ... University of Michigan Department of Mathematics Winter, 2015 Math 116 Exam 3 Problem 10 (ladybugs2) Solution. Math …Math 116 — Practice for Exam 2 Generated October 5, 2017 Name: Instructor: Section Number: 1. This exam has 6 questions. Note that the problems are not of equal difficulty, so you may want to skip ... University of Michigan Department of Mathematics Fall, 2010 Math 116 Exam 2 Problem 2 (cardioid) Math 116 / Final (April 28, 2014) page 8 7. [8 ...%PDF-1.5 %âãÏÓ 100 0 obj > endobj 120 0 obj >/Filter/FlateDecode/ID[6BC99638CD0083F06ECAA05FCF088A92>20D79659FAC441B286CC35362EAA6005>]/Index[100 50]/Info 99 0 R ... Math 216 is a 4 credit course on differential equations with supplementary coverage of complex numbers and matrix algebra. It is intended for engineers and scientists who will be using differential equations in their work. Those looking for a more in-depth treatment should consider Math 256 , 286, or 316 instead. Applied Honors Calculus Sequence. (MATH 156-285-286): Applied Honors Calculus II (MATH 156) is designed for engineering and science majors who received a score of 4 or 5 on the AP exam (AB or BC). MATH 156 is an alternative to MATH 116 with more emphasis on science applications and theory. The sequence continues with courses in multivariable ...Math 116 / Final (December 17, 2015) DO NOT WRITE YOUR NAME ON THIS PAGE page 3 2. [8 points] Let f(x) = x2x. The first two derivatives of f are given below. f ... University of Michigan Department of Mathematics Fall, 2017 Math 116 Exam 3 Problem 6. Created Date: 11/14/2018 9:26:58 PMLet L(h) be the number of meters Alejandra is ahead of Brontel when the owl is. meters above ground. Write an expression for L(h) involving integrals and compute L′(2). Answer: L(h) =. L′(2) =. c. [3 points] The next bird to pass is a dove. This time Alejandra runs twice as fast and Brontel runs three times as fast as they did when chasing ... %PDF-1.5 %âãÏÓ 100 0 obj > endobj 120 0 obj >/Filter/FlateDecode/ID[6BC99638CD0083F06ECAA05FCF088A92>20D79659FAC441B286CC35362EAA6005>]/Index[100 50]/Info 99 0 R ... The sequence Math 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to concentrate in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof ... Math 116 / Final (April 22, 2022) do not write your name on this exam page 15 9.[10 points] After a mistake on their last mission, Brad and Angelina must go on the run together, or risk being captured by an opposing agent. Brad and Angelina’s shared position is given by the parametric equations: (f(t),g(t)) = (t2 + 10, 2t2 + 10) %PDF-1.5 %âãÏÓ 100 0 obj > endobj 120 0 obj >/Filter/FlateDecode/ID[6BC99638CD0083F06ECAA05FCF088A92>20D79659FAC441B286CC35362EAA6005>]/Index[100 50]/Info 99 0 R ... Math 116 - Fall 2017. This webpage is used for Math 116 Section 065 in University of Michigan during the fall semester in 2017.We would like to show you a description here but the site won’t allow us.Math 116 / Midterm (November 14, 2016) DO NOT WRITE YOUR NAME ON THIS PAGE page 3 2.[5 points] Find constants Aand Bso that the function h(w), de ned for w>0 by h(w) = Aw3 + 1 w; is a solution to the di erential equation w2 dh dw 3wh+ B= 0 satisfying h(1) = 3 2. Show all your work, and write your nal answers in the spaces provided. Solution: A ... University of Michigan Department of Mathematics Winter, 2017 Math 116 Exam 1 Problem 9 (nano pyramid) Math 116 / Exam 1 (February 5, 2018) do not write your name on this exam page 10 9. The sequence Math 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to concentrate in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof ...Math 116 — Practice for Exam 1 Generated September 30, 2020 Name: Instructor: Section Number: 1. This exam has 12 questions. ... University of Michigan Department of Mathematics Winter, 2018 Math 116 Exam 1 Problem 9 (muck tank) Math 116 / Exam 1 (October 9, 2017) do not write your name on this exam page 5 4. [10 points]Math 116 — Practice for Exam 2 Generated November 7, 2017 Name: Instructor: Section Number: 1. This exam has 12 questions. Note that the problems are not of equal …1 P∞ n=1(−1)n n(1+ln(n)) converges conditionally. University of Michigan Department of Mathematics. Winter, 2011 Math 116 Exam 3 Problem 10 Solution. 5. 4. (8 points) The Sierpinski Carpet is an example of a mathematical object called a fractal. It is.Math 116 / Exam 2 (March 20, 2013) page 13 c. [4 points] i) Find the equation in polar coordinates of the line x = 0. Solution: θ = π 2. ii) Find the equation in polar coordinates of the line y = 4. Solution: y = rsinθ = 4, so r = 4 sinθ. University of Michigan Department of Mathematics Winter, 2013 Math 116 Exam 2 Problem 8 (peanut) SolutionUniversity of Michigan Department of Mathematics Winter, 2012 Math 116 Exam 2 Problem 9 (wire) Math 116 / Exam 2 (March 19, 2012) page 11 c. [6 points] Find the mean length of wire between two consecutive flaws.We would like to show you a description here but the site won’t allow us.University of Michigan Department of Mathematics Winter, 2014 Math 116 Exam 3 Problem 8 Solution Math 116 / Final (December 17, 2015) DO NOT WRITE YOUR NAME ON THIS PAGE page 11 13.Math 116 { Calculus II { Section 020 { Fall 2017. Course Description: The course presents concepts of calculus from four points of view: geometric (graphs), numeric (tables), symbolic (formulas), and verbal descriptions. Students will develop their reading, writing and questioning skills, as well as their ability to work cooperatively.Math 116 Exam 3 Shop Cart is empty. Math 116 Exam 3 Shop Topic 2001–2012 2013–present; TF/Multiple choice ...Math 116 / Exam 2 (March 29, 2021) do not write answers on this page page 4 3.[7 points] Emily is a physics teacher. She is demonstrating the physics of rocket-launching with a water rocket in her class today. The water rocket weighs 3 lbs on the ground, and Emily launches it straight up to 10 ft above the ground. During the launch, the rocket’sUniversity of Michigan Department of Mathematics Winter, 2014 Math 116 Exam 3 Problem 8 Math 116 / Final (April 26, 2013) page 10 8.[8points] Considerthepowerseries University of Michigan Department of Mathematics Winter, 2018 Math 116 Exam 2 Problem 5 (class time) Solution Math 116 / Exam 1 (February 10, 2020 ) page 12 10. The sequence Math 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to concentrate in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof ...
Math 116 — Practice for Exam 2 Generated November 7, 2017 Name: Instructor: Section Number: 1. This exam has 12 questions. Note that the problems are not of equal …. Cookies dispensary az
Math 116 / Final (December 17, 2015) DO NOT WRITE YOUR NAME ON THIS PAGE page 3 2. [8 points] Let f(x) = x2x. The first two derivatives of f are given below. f ... University of Michigan Department of Mathematics Fall, 2017 Math 116 Exam 3 Problem 6. Created Date: 11/14/2018 9:26:58 PMMath 116 / Exam 2 (November 14 , 2012) page 6 b. [1 point] The slope field of the differential equation dP dt = 2(1−2sint)P is shown below. Use it to sketch the graph of P(t), the number of bees (in thousands) in the colony afterMath 116 / Final (April 23, 2015) page 10 ... University of Michigan Department of Mathematics Winter, 2015 Math 116 Exam 3 Problem 10 (ladybugs2) Solution.Math 116 Assessment Proctored Mastery Testing Dates: Assess: Opens: Closes: Proctored Lab Hours: Proctored labs are in East Hall, B069, 722, 723, or 727: Proctored Lab Schedule. Hints and Tips: You login to the system ... ©2004-09 Gavin LaRose, UM Math Dept/Regents of UMich ...The sequence Math 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to concentrate in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof ...Math 116 / Exam 2 (November 9, 2020 ) page 2 1.[8 points] The graph of a piecewise-linear cumulative distribution function P(x) is given below. The function P(x) is de ned for all real numbers xand is constant for x<aand for x>14. a 14 x y a.[3 points] The median value for xis 10. Use this fact, and the fact that P(x) is a cumulativeMath 116 / Midterm (November 14, 2016) DO NOT WRITE YOUR NAME ON THIS PAGE page 3 2.[5 points] Find constants Aand Bso that the function h(w), de ned for w>0 by h(w) = Aw3 + 1 w; is a solution to the di erential equation w2 dh dw 3wh+ B= 0 satisfying h(1) = 3 2. Show all your work, and write your nal answers in the spaces provided. Solution: A ...University of Michigan Department of Mathematics Winter, 2017 Math 116 Exam 1 Problem 9 (nano pyramid) Math 116 / Exam 1 (February 5, 2018) do not write your name on this exam page 10 9. [9 points] ... Math 116 / Exam 1 (February 10, 2020 ) do not write your name on this exam page 5 5. [10 points] After a long day filming a space walk scene ...Math 116 — Practice for Exam 2 Generated November 7, 2017 Name: Instructor: Section Number: 1. This exam has 12 questions. Note that the problems are not of equal …Math 116 / Exam 1 (February 6, 2017) do not write your name on this exam page 6 5. [12 points] Several high-ranking Illuminati officials are relaxing while counting their money. ... University of Michigan Department of Mathematics Winter, 2018 Math 116 Exam 1 Problem 2 (owl and dove) Math 116 / Exam 1 (October 14, 2015) DO NOT WRITE …Math 116 / Exam 1 (February 6, 2017) do not write your name on this exam page 6 5. [12 points] Several high-ranking Illuminati officials are relaxing while counting their money. ... University of Michigan Department of Mathematics Winter, 2018 Math 116 Exam 1 Problem 2 (owl and dove) Math 116 / Exam 1 (October 14, 2015) DO NOT WRITE …Math 116 { Calculus II { Section 099 { Winter 2019 Instructor: Harry Richman O ce Hours in EH 1860: (tentative) Email: [email protected] W 2-3pm, Th 2-3pm, by appointment …Math 116 — Practice for Exam 2 Generated October 22, 2018 Name: Instructor: Section Number: 1. This exam has 3 questions. Note that the problems are not of equal difficulty, so you may want to skip over and return to a problem on which you are stuck. 2. Do not separate the pages of the exam. If any pages do become separated, write your name ...Math 116 - Fall 2017. This webpage is used for Math 116 Section 065 in University of Michigan during the fall semester in 2017.Math 116 / Exam 1 (March 29, 2021) page 3 2.[12 points] In order to build a settlement on the island, intruders start cutting down trees at the forest, cutting the trees into logs, and putting the logs in a pile. Let A nbe the number of logs they have in the pile at noon on the n-th day. The intruders have 100 logs in the pile at1.The government has assigned a team to excavate a buried treasure. The team digs and comes across a box, with the top of the box located 25 meters below ground level. The box is a cube, with side length 3 meters. The team lifts the box to ground level as follows. A rope, of mass 10 kg per meter, is attached to the box..