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MATH 147 Final: Math 147 TAMU Fall 09Final

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turquoisegnu128

31 Jan 2019

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Texas A&M University

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This is the nal exam for m147, fall 2009, and the exam this year will have the same format (ten multiple choice questions and ve problems for which work is to be written out). This exam covered one section that will not be on the nal exam for. In light of this, you should skip problems 9, 10, and 15. On the other hand, you should go back and work problems 7, 8, 9, 10, 14b, and 15 from last year"s exam: (we did not cover the material for problem 14a this year. ) Solutions are given at the end of the exam. Written out work on these problems will not be checked, so take care in marking your answers. Problems 11-15 unjusti ed answers will not receive credit. You may need the following summation formulas. k = n(n + 1)

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INSTRUCTIONS: There are 15 problems on this exam, and each problem is worth 13 points, plus 5 points for writing down an approximate volume of the planet Earth in cubic miles at the bottomleft corner of page 3, for a total possible 200 points. For this exam, you are allowed to use one 8.5"X11" sheet of notes (both sides, in your own handwriting), pencil, eraser, ruler, scratch paper and calculator. Even though the questions are multiple-choice, you need to show enough work to justify your answer in order to receive full credit. After you have determined the correct solution to each problem, write the letter corresponding to your answer in the appropriate space on the right side of the page AND circle your answer. If your answer does not agree with any of the choices, after double-checking your work, choose option E) and prominently mark your answer (box, circle, underline, etc.). Time limit: Two hours. Attach (i.e. staple) any notecard and scratch paper to the rear of this exam paper. Good luck! MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. The northern third of Indiana is a rectangle measuring 96 miles by 132 miles. Thus, let D = [0, 96] times [0,132]. Assuming that the total annual snowfall (in inches), S(x,y), at (x,y) euro D is given by the function S(x,y) = 60e-0.001 (2x + y) with (x,y) euro D, find the average snowfall on D. 51.14 inches 52.06 inches 51.78 inches 52.44 inches Evaluate the work done between point 1 and point 2 for the conservative field F. Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C. Evaluate the surface integral of G over the surface S. S is the portion of the cone Find the flux of the vector field F across the surface S in the indicated direction. Using the Divergence Theorem, find the outward flux of F across the boundary of the region D. Integrate the function f over the given region. f(x,y) = 1/ln x over the region bounded by the x-axis, line x = 9, and curvey y = ln x Reverse the order of integration and then evaluate the integral Use a double integral in polar coordinates to find the area of the region specified in polar coordinates. the region inside both r = 7 sin Theta and r = 7 cos Theta Use spherical coordinates to find the volume of the indicated region. the region bounded above by the sphere x2 + y2 + z2 = 25 and below by the cone z = Find the center of mass of the rectangular solid of density (x,y,z) = xyz defined by 0 LE x LE 8, Use the given transformation to evaluate the integral. where R is the parallelogram bounded by the lines y = 8x + 8, y = 8x +9, y = -6x + 2, y = -6x +7 Evaluate the line integral along the curve C. Find the work done by F over the curve in the direction of increasing t.

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

To find how much each American drove, we divide the total miles driven by the total number of drivers (rounded to the nearest million for simplicity): 4,000,000,000,000 = 4,000,000 = 14, 035 R25 (showing long division work) 285,000,000 285 Supposing that the total of miles driven does not change much from year to year, and rounding to the nearest thousand, we estimate each American drives about 14,000 miles a year.(*) Based on the above (*), estimate how many miles the average American drives per day. Write (and evaluate) the mathematical operation(s) that justify your estimate Compare your estimate to actual US Bureau of Transportation statistics, which indicate that the average person travels 40 miles on a daily basis-most of it in a personal vehicle. What might account for the difference between this data and your estimate? Suppose you drive 40 miles a day. If your car gets 20 miles per gallon, and gasoline costs $3.00 a gallon, how much will you spend on gasoline each day? How much will you spend each week? Each year? To fully charge the battery of an electric car requires about 15 kilowatt hours (kwH) overnight, when electricity prices are about 10 cents per kilowatt-hour. Assume that a fully charged electric car can last for a day. How much would you be paying each week to "fuel" or charge your electric car, in dollars? Based on your answers in (2), how much more would it cost you per year to fuel a gasoline-powered car, instead of an electric car? First figure it out, then write and evaluate all the mathematical operations to justify your reasoning: Sample Problem and Solution: A recycling facility used to pick up 13 pounds of e-waste from each of a hundred residences each day. The waste from 80 of the residences was shipped to China, while half of the remainder was actually unrecyclable and ended up in a landfill. (The other half was recycled). Find the total pounds of waste picked up from a hundred residences in a day. Solution: Since 13 pounds of e-waste was picked up from 100 residences, the total amount of waste picked up in a day is 13 Times 100 = 1300 pounds. Find the total pounds of waste shipped to China from a hundred residences in a day. Solution: The waste from 80 households was shipped to china. Thus the total amount of waste shipped to China in a day is 13 Times 80 = 1040 pounds. Find the total pounds of waste from a hundred residences actually recycled in a day. Solution: The waste from 80 households was shipped to China, so the remaining households are 20. The half of the remainder was unrecyclable and the other half of the remainder was recycled, thus the waste from 10 households was recycled. Hence the amount of wasted recycled in a day is 13 Times 10=130 pounds. Ten years later, the similar pattern holds for the recycling company-they still collect e-waste from 100 residences every day, the waste from 80 of these is still sent to China, and only half of the remainder is recycled-but they collect more waste from each house, 25 pounds of waste is collected from each of 100 residences every day. Find the total pounds of waste collected from a hundred residences in a day. Find the total pounds of waste shipped to China from a hundred residences in a day. Find the total pounds of waste actually recycled from a hundred residences in a day. (Justify your reasoning):