[MATH 136] - Final Exam Guide - Comprehensive Notes fot the exam (131 pages long!)

Fall 2017 Math 2150 Final Exam Take 1 Part 1 Section 8 osed book, closed notes. No calculators. Show your work. No loitering, no smoking, walking on the grass, no feeding the animals, no parking, no stopping or standing, no mping, no running, no fishing, no vacancy. All problems weighted equally (1) Use Euler's method to estimate y(7) when y, + V-x and y(1) -3. Use step size 3. (2) Solve the differential equation (4xY + 3z2jdz + (3xY + 6y2)dy 0. 3) Is the differential equation y'"-6z3y" cosas linear? why or why not? 4) Tanks T1 and T2 contain 50 gallons and 100 gallons of salt solutions, respectively. A solution with 2 pounds of salt per gallon is pumped into T1 from an external source at 1 gal/min, and a solution with 3 pounds of salt per gallon is pumped into T2 from an external source at 2 gal/min. The solution from T1 is pumped into T2 at 3 gal/min, and the solution from T2 is pumped into T1 at 4 gal/min. T1 is drained at 2 gal/min and T2 is drained at 1 gal/min. Let Q1(t) and Q2(t) be the number of pounds of salt in T1 and T2, respectively, at time t>0. Derive a system of differential equations for Q1 and Q2. Assume that both mixtures are well stirred. guess" method (a kn

Fall 2017 Math 2150 Final Exam Take 1 Part 2 Section 8 Closed book, closed notes. No caleulators. Show your work. No loitering, no smoking, no walking on the grass, no feeding the animals, no parking, no stopping or standing, no dumping, no running, no fishing, no vacancy. All problems weighted equally. (1) Use the power series method to solve (1-z)y" +zy-y = 0. Here's a standard power series that you will find useful in your answer: 23 2 3 4! n! nao (2) A 64 Ib object stretches a spring 4 ft in equilibrium. It is attached to a dashpot with damping constant c-8 lb-sec/ft. The object is initially displaced 18 inches above equilibrium and given a downward velocity of 4 ft/sec. Find its displacement for t>0. Assume the motion is free. Since the weight is 64, for the mass you can use m =64/32 = 2. The following equations will be useful: The equation of motion for this system is my" + c/ + ky= F, where m is the mass of the object, c is the damping constant, k is the spring constant, and F is the forcing function. mg = kar, where g 32n/s2 is the gravitational constant, and Al is the distance by which a spring is stretched from its natural length when the object is attached to it. Remember to convert from inches to feet, so all units are compatible.

Problem: Divisibility and Divisibility Rules There are many rules to determine if a number is divisible by other smaller numbers. In basic arithmetic courses, you learned divisibility and discussed a few common divisibility rules. Your task is to determine if the given number is divisible by 9 but is not divisible by 11 Given number: 7,176,825,942,116,027,211 Note: You want to use divisibility rules. Do not attempt to use long division and do not just use your calculator 1. Research the topic of divisibility 2. Research the divisibility rules for 9 and 11. 3. Using the divisibility rules found, determine how the given number is divisible by 9 and is not divisible by 11. "Note:I am telling you that the number IS divisible by 9 and IS NOT divisible by 11. Do not try to show the opposite of this statement. 4. Include the following information in a report, in this order: a. Explain (in a few sentences) the topic of divisibility, including any correct terms that apply b. Explain in your own words the divisibility rule of 9. C. Give an example using another number to help the explanation. d. Show how the given number is divisible by 9. Work out all your steps. e. Explain in your own words the divisibility rule of 11 f. Give an example using another number to help the explanation. g. Show how the given number is not divisible by 11. Work out all your steps. 5. You must locate a minimum of 2 sources to help you complete this project. More than two sources, though not required, can be used if it helps to give detail to the project. a. You must use at least one book or E-book (other than your textbook). Do not use the dictionary for your definition. b. You must use at least one website. Do not use Wikipedia c. Your sources should explain the topics of the problem (divisibility and divisibility rules) and have examples that help you with the problem. Your sources should be relevant to the project and not just be a math source because it has math in the context d. 6. Correctly cite, in MLA format, the sources that you located to complete the assignment. If you need help for citations in MLA format, you can try using the website EasyBih Be sure to do the entire project typed neatly 7. Papers will be compared for similarity Plagiarism is against the academic honesty policy and will receive a zera. Note: A detailed Grading Rubric is provided on Canvas and on the assignment submission link The due date for the project is listed on Canvas. The Math/Analytical Project must be submitted through Canvas. Directions for submitting can be found in the Course Syllabus and on Canvas.