MATH-205 Midterm: Bates MATH 205 021216jayawant205exam

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turquoisegnu128

7 Mar 2019

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Name: check that you have 7 questions on three pages, show all your work to receive full credit for a problem. Points will be taken o if you do not show how you arrived at your answer, even if the answer is correct: please keep your explanations brief; be clear and to the point. Points will be taken o for incorrect or irrelevant statements: (6 points) consider the following system of equations. x1 + kx2 = 1. 3x1 + 5x2 = 2k (a) find the row echelon form (ref) of the augmented matrix of the system given in the problem. Do this by hand and not with a calculator. State the row operation(s) that you do in your computation. (b) find all real values of k such that the system given in the problem has only one solution: (8 points) a mining company has three mines. One day of operation at the mines produces the following output.

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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.

Show transcribed image text 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.

Math 1113 Fall 2017 . Fulk Project 2 Solve the following problems below individually or in groups of up to three. Each group will submit only one project. Each group member will also submit an explanation their contribution to the group project. Show all work leading to your solutions. To receive credit, you must clearly support you answers. Turn in on Wednesday, November 29 Points may be taken off for sloppy your project at the beginning of class disorganized, or poorly written work 1. (20 points) As viewed from the earth, the angle subtended by the full moon is s 0518Â°. Use this information and the fact that the distance AB from the earth to the moon is 236,900 mi to find the radius of the moon. (20 points) Variable stars are ones whose brightness varies periodically. One of the most visible is R Leonis; its brightness is modeled by the function b) -7.9-2.1 measured in days. a) Find the period of R Leonis. b) Find the maximum and minimum brightness c) Graph the function b. 2. where t is 3. (20 points) A movie theater has a 25-foot-high screen that is 8 feet above eye level. If you sit too close, your viewing angle is too small. If you sit too far back, the image is too small. If you sit x feet back from the screen, your viewing angle, Î¸, is given by Find the viewing angle, in radians, at distances of 5 feet, 10 feet, 15 feet, 20 feet, and 25 feet. Then graph the function in a graphing calculator with a viewing window of [0, 50, 10] by 10, 1, 0.1]. Use the calculator to find the distance at which you have a maximum viewing angle. [Hint: Viewing windows are written as [minmax Xscl by Dmin.Jmax Yscil. These values can be adjusted by pressing the WINDOW button on the calculator. To find a maximum, press 2ND TRACE, choose maximum, move to the left of the maximum and press ENTER, move to the right of the maximum and press ENTER, and then press ENTER again. (x-79j+12, (20 points) The number of hours of daylight in Boston is given by y-3sin where : s he number of days after lanuary 1. Within a year,when does Boston have 13.5 hours of daylight? Give your answer in days after January 1 and round to the nearest day. 4

1. (45 marks) Short-Answer Questions. Put your answer in the box provided but show your work also. Each question is worth 3 marks, but not all questions are of equal difficulty. Full marks will be given for correct answers placed in the box, but at most 1 mark will be given for incorrect answer. Unless otherwise stated, it is not necessary to simplify your answers in this question. a) Find the equation of the tangent plane to the graph of the function z = f(x,y) = sell at (0,1). Answer b) Evaluate (T, 0) if f(x,y) = sin(ry). Answer c) Graph of a function z = f(x,y) is given by: Which of the following level curves correspondes to this function. Answer d) If f(x,y) = e(3x – 2y), find lim - Math)-f(x,y) e) Find % if f(x, y) = x2 - y3 and 2 = r sin(t), y = r cos(t). Answer f) Evaluate the directional derivative of f(x, y) = !at (1, -1) in the direction of u =(2, 1). Answer 8) Does Simono converge? h) Sketch the direction field of the differential equation = 1-2y. i) Consider the differential equation ay = 15 - 31, y(0) = 0, and use Euler's method with step size 0.1 to estimate y(0.1). Answer j) Knowing that (-3,-3) is a critical point of f(x,y) = 2:3 + y2 – 4.cy -3.0, use the second derivative test to find out whether it is a local minimum, local maximum, or a saddle point. Answer k) Solve the initial value problem, dy dt 642 2y + cos(u) y(1) = . Answer 1) Is ū=(2,2, -1) perpendicular to v = (5,-4, 2)? Answer m) Find the area between the graph of y = 1 + sin(x) and y=1-sin(x) from 0 to 7. Answer n) Determine the lentgh of the curve y = 8/2,0 SIS 3. Evaluate and simplify your answer. Answer o) Express the volume of the solid obtained by rotating the bounded region that lies between curves y = (x-2)2 and y=1,150 $4 about the vertical line 2 = 5. Do not evaluate this integral. Answer

MATH-205 Midterm: Bates MATH 205 021216jayawant205exam

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