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MATH 251 Midterm: MATH 251 PSU M251Exam 2(su14)

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turquoisegnu128

15 Feb 2019

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This exam has 12 questions for a total of 100 points. In order to obtain full credit for each problems, all work must be shown. Credit will not be given for an answer not supported by work. The point value for each question is in parentheses to the right of the question number. You may not use a calculator on this exam. Please turn off and put away your cell phone. July 24, 2014: (6 points) consider the seventh order linear equation y(7) + 18y(5) + 81y = 0, which has a characteristic equation r7 + 18r5 + 81r3 = r3(r2 + 9)2 = 0. What is its general solution: (6 points) determine whether each pair of functions is linearly independent or linearly depen- dent. Justify your answer. (a) (2 points) t + 1, e2t (b) (2 points) 2 sin( t), cos( t) (c) (2 points) e3t 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

A student she started this process, how much money will she have after 39 weeks a) Write the multiplication expression that modes this situation b) Evaluate the expression to anpwer the question Write your currently works part time and each week puts 525 Inta her If she had no money saved when savings jar in her.coom, if she had no meney .savins answer the question Write your answer in a complete contextual sentence. 7. If you deposit S If you deposit $950into an account and the accouet balance increases by,1.8% each yea. a) Write the exponential expression that Write the exponential expression that Write the exponential expression that Evaluate the expression to determine the a cent. Write your answer in a complete contextual sentence. t models this situstion if you leave the money in the models this stuation if you leave the money in the account for twe years b) c) c) mode's this situation if you leave the money in the account for five years expression that mode's this situation if you leave the money in the account for twelve years the amount you have at the end of the 12 year period. Round answer to the nearest honey bee colonies ina 8. The number of honey bee colonies has been decreasn g by about 8.5% each year. If there were 25,000 Write the exponential expression that models how many c) Write the exponential expression that models how many honey bees there would be after tern d) Evaluate the expression to determine how many haney bees there particuiar region a) Write the exponential b) the exponential expression that models how many honey bees there would be ater two years ion that models how many honey bees there would be afer tour years e years efter ten years. Since we are dealing with bees, round apprepriately. Write your answer in a complete contextual sentence. 9. A group of friends went out on Friday nignt for dinner ane erinks. The total bill without tax was $173.s0. The tax rate on restaurant food and alconoUs 625%. T he service et the restaura rt was great and they were a bg goup, so they crose to leave a 22% tip. a) Determine the amount of money they left for the tip b) Determine the total amount that they had to pay for their bil, tax, and tip. 10, According to the American Cancer Society in 2015 estimates that 40,290 women will die from dimensional analysis determine your final answer in a complete contextual sentence. Remember to round appropriately 11. According to an a n 2015 it estlmates that 40290 women will die from breast cancer. Using how many women will de per hour in 2015 due to breast cancer. Show al of your work and write article on the Global Issues.org web site."At least 80% of humanity Ewes on less than S10 a day." Source The population of the world ls about 7.3 billion people as of June 2015. Use these two pieces of information to complete the foliowing a) Write the population of the earth in standard form b) Estimate the number of people that live on less than $10 per day. Show all of your work for the estimace. Remember to use numbers that are easy to work with and do not use a calculator Now use a calculator to determine the number of people that live on less than $10 per day, 12. A large elephant can weigh up to 6,350 klograms, which is There is the belief that elephants are afraid of mice as often depicted in cartoons. Compare the weight of the mouse to determine how many times heavier the elephant is than the mouse. Show all of your work and answer in a complete contextual sentence. 6,350,000 grams. An adult mouse can weigh up to about 40 grams weight of the elephant to the write your

Show transcribed image text A student she started this process, how much money will she have after 39 weeks a) Write the multiplication expression that modes this situation b) Evaluate the expression to anpwer the question Write your currently works part time and each week puts 525 Inta her If she had no money saved when savings jar in her.coom, if she had no meney .savins answer the question Write your answer in a complete contextual sentence. 7. If you deposit S If you deposit $950into an account and the accouet balance increases by,1.8% each yea. a) Write the exponential expression that Write the exponential expression that Write the exponential expression that Evaluate the expression to determine the a cent. Write your answer in a complete contextual sentence. t models this situstion if you leave the money in the models this stuation if you leave the money in the account for twe years b) c) c) mode's this situation if you leave the money in the account for five years expression that mode's this situation if you leave the money in the account for twelve years the amount you have at the end of the 12 year period. Round answer to the nearest honey bee colonies ina 8. The number of honey bee colonies has been decreasn g by about 8.5% each year. If there were 25,000 Write the exponential expression that models how many c) Write the exponential expression that models how many honey bees there would be after tern d) Evaluate the expression to determine how many haney bees there particuiar region a) Write the exponential b) the exponential expression that models how many honey bees there would be ater two years ion that models how many honey bees there would be afer tour years e years efter ten years. Since we are dealing with bees, round apprepriately. Write your answer in a complete contextual sentence. 9. A group of friends went out on Friday nignt for dinner ane erinks. The total bill without tax was $173.s0. The tax rate on restaurant food and alconoUs 625%. T he service et the restaura rt was great and they were a bg goup, so they crose to leave a 22% tip. a) Determine the amount of money they left for the tip b) Determine the total amount that they had to pay for their bil, tax, and tip. 10, According to the American Cancer Society in 2015 estimates that 40,290 women will die from dimensional analysis determine your final answer in a complete contextual sentence. Remember to round appropriately 11. According to an a n 2015 it estlmates that 40290 women will die from breast cancer. Using how many women will de per hour in 2015 due to breast cancer. Show al of your work and write article on the Global Issues.org web site."At least 80% of humanity Ewes on less than S10 a day." Source The population of the world ls about 7.3 billion people as of June 2015. Use these two pieces of information to complete the foliowing a) Write the population of the earth in standard form b) Estimate the number of people that live on less than $10 per day. Show all of your work for the estimace. Remember to use numbers that are easy to work with and do not use a calculator Now use a calculator to determine the number of people that live on less than $10 per day, 12. A large elephant can weigh up to 6,350 klograms, which is There is the belief that elephants are afraid of mice as often depicted in cartoons. Compare the weight of the mouse to determine how many times heavier the elephant is than the mouse. Show all of your work and answer in a complete contextual sentence. 6,350,000 grams. An adult mouse can weigh up to about 40 grams weight of the elephant to the write your