MATH IN OUR WORLD (LOOSELEAF)-W/ACCESS
3rd Edition
ISBN: 9781259969690
Author: sobecki
Publisher: MCG
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Chapter 6.4, Problem 69E
To determine
Whether the company to cover its start-up cost when the company sells of 18 units and find the profit of a company when it sells 120 units.
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with x(0) = 1, y(0) = -1
(b) Consider the initial value problem corresponding to the given phase portrait.
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Draw two "straight line solutions"
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Chapter 6 Solutions
MATH IN OUR WORLD (LOOSELEAF)-W/ACCESS
Ch. 6.1 - Translate each verbal statement into symbols. (a)...Ch. 6.1 - Prob. 2TTOCh. 6.1 - Prob. 3TTOCh. 6.1 - Prob. 4TTOCh. 6.1 - Prob. 5TTOCh. 6.1 - Prob. 1ECh. 6.1 - Prob. 2ECh. 6.1 - Prob. 3ECh. 6.1 - Prob. 4ECh. 6.1 - Whats the difference between checking your answer...
Ch. 6.1 - Prob. 6ECh. 6.1 - 3 less than a numberCh. 6.1 - A number decreased by 17Ch. 6.1 - A number increased by 9Ch. 6.1 - 6 increased by a numberCh. 6.1 - 11 decreased by a numberCh. 6.1 - 8 more than a numberCh. 6.1 - 6 subtracted from a numberCh. 6.1 - 7 times a numberCh. 6.1 - One-half a number added to that numberCh. 6.1 - 5 more than 3 times a numberCh. 6.1 - The quotient of 3 times a number and 6Ch. 6.1 - 4 less than 6 times a numberCh. 6.1 - The quotient of a number and 14Ch. 6.1 - The product of 7 and a number, all subtracted from...Ch. 6.1 - Triple the sum of a number and pi.Ch. 6.1 - One-fourth the difference of 12 and a number.Ch. 6.1 - Three times a number subtracted from the quotient...Ch. 6.1 - The sum of 146 and the product of a number raised...Ch. 6.1 - The square of the sum formed from adding five...Ch. 6.1 - The square root of the difference between half a...Ch. 6.1 - Six times a certain number plus the number is...Ch. 6.1 - The sum of a number and the number plus 2 is equal...Ch. 6.1 - Twice a number is 32 less than 4 times the number....Ch. 6.1 - The larger of two numbers is 10 more than the...Ch. 6.1 - The difference of two numbers is 6. The sum of the...Ch. 6.1 - Five times a number is equal to the number...Ch. 6.1 - Twice a number is 24 less than 4 times the number....Ch. 6.1 - The difference between one-half a number and the...Ch. 6.1 - Twelve more than a number is divided by 2. The...Ch. 6.1 - Eighteen less than a number is tripled, and the...Ch. 6.1 - A math class containing 57 students was divided...Ch. 6.1 - 38. In 2015, the Coca-Cola company and PepsiCo had...Ch. 6.1 - The cost, including sales tax, of a Ford Focus SE...Ch. 6.1 - During the first day of a heat wave, an emergency...Ch. 6.1 - Prob. 41ECh. 6.1 - If Marita invested half of her money at 8% and...Ch. 6.1 - A basketball team played 32 games and won 4 more...Ch. 6.1 - Prob. 44ECh. 6.1 - If a television set is marked 13 off and sells for...Ch. 6.1 - A carpenter wanted to cut a 6-foot board into...Ch. 6.1 - The Halloween Association reported that last year,...Ch. 6.1 - In a charity triathlon, Mark ran half the distance...Ch. 6.1 - A nurse is told to give a patient recovering from...Ch. 6.1 - Prob. 50ECh. 6.1 - Prob. 51ECh. 6.1 - In 2011, there were 92 female officials in...Ch. 6.1 - Prob. 53ECh. 6.1 - Prob. 54ECh. 6.1 - Prob. 55ECh. 6.1 - If the perimeter of a triangular flower bed is 15...Ch. 6.1 - Prob. 57ECh. 6.1 - Prob. 58ECh. 6.1 - Prob. 59ECh. 6.1 - Prob. 60ECh. 6.1 - Prob. 61ECh. 6.1 - Prob. 62ECh. 6.1 - The temperature and the wind combine to cause body...Ch. 6.1 - Prob. 64ECh. 6.1 - The prevailing winds for air travel in the United...Ch. 6.1 - In an attempt to conserve energy (and, lets be...Ch. 6.1 - Winona has two jobs: one pays 11.25 per hour, and...Ch. 6.1 - Prob. 68ECh. 6.2 - From 1969 through 1977, there were 24 teams in...Ch. 6.2 - Find the ratio of 40 ounces to 2 pounds. (There...Ch. 6.2 - Decide if each proportion is true or false. (a)...Ch. 6.2 - Solve the proportion: x7=2225Ch. 6.2 - Solve the proportion: x+615=x25Ch. 6.2 - Prob. 6TTOCh. 6.2 - The staff biologists at a wildlife preserve tagged...Ch. 6.2 - A 6-month-old Labrador puppy gets 412 cups of food...Ch. 6.2 - Prob. 9TTOCh. 6.2 - Prob. 10TTOCh. 6.2 - Prob. 11TTOCh. 6.2 - Prob. 1ECh. 6.2 - Prob. 2ECh. 6.2 - Prob. 3ECh. 6.2 - Prob. 4ECh. 6.2 - Prob. 5ECh. 6.2 - Prob. 6ECh. 6.2 - Describe the procedure for solving a proportion.Ch. 6.2 - What is the constant of proportionality in a...Ch. 6.2 - For Exercises 716, write each ratio statement as a...Ch. 6.2 - For Exercises 716, write each ratio statement as a...Ch. 6.2 - For Exercises 716, write each ratio statement as a...Ch. 6.2 - For Exercises 716, write each ratio statement as a...Ch. 6.2 - For Exercises 716, write each ratio statement as a...Ch. 6.2 - For Exercises 716, write each ratio statement as a...Ch. 6.2 - For Exercises 716, write each ratio statement as a...Ch. 6.2 - For Exercises 716, write each ratio statement as a...Ch. 6.2 - For Exercises 716, write each ratio statement as a...Ch. 6.2 - For Exercises 716, write each ratio statement as a...Ch. 6.2 - For Exercises 1726, solve each proportion. 17....Ch. 6.2 - For Exercises 1726, solve each proportion. 18....Ch. 6.2 - For Exercises 1726, solve each proportion. 19....Ch. 6.2 - For Exercises 1726, solve each proportion. 20....Ch. 6.2 - For Exercises 1726, solve each proportion. 21....Ch. 6.2 - For Exercises 1726, solve each proportion. 22....Ch. 6.2 - For Exercises 1726, solve each proportion. 23....Ch. 6.2 - For Exercises 1726, solve each proportion. 24....Ch. 6.2 - For Exercises 1726, solve each proportion. 25....Ch. 6.2 - For Exercises 1726, solve each proportion. 26....Ch. 6.2 - The Information Resources Institute reports that...Ch. 6.2 - The U.S. Department of Agriculture reported that...Ch. 6.2 - Under normal conditions, 1.5 feet of snow will...Ch. 6.2 - The Travel Industry Association of America reports...Ch. 6.2 - A gallon of paint will cover 640 square feet of...Ch. 6.2 - The American Dietetic Association reported that 31...Ch. 6.2 - The U.S. Census Bureau reported that 9 out of...Ch. 6.2 - Angel took a 2-year lease on a new car and after 8...Ch. 6.2 - Prob. 37ECh. 6.2 - The American Dietetic Association states that 11...Ch. 6.2 - Mark is interested in measuring the height of a...Ch. 6.2 - An online photo printing service will put any...Ch. 6.2 - A small college has 1,200 students and 80...Ch. 6.2 - Prob. 42ECh. 6.2 - According to a poll conducted by the Pew Research...Ch. 6.2 - Based on a combination of worldwide surveys...Ch. 6.2 - 45. According to a poll conducted by the Gallup...Ch. 6.2 - Prob. 46ECh. 6.2 - The amount of simple interest on a specific amount...Ch. 6.2 - The number of tickets purchased for a prize varies...Ch. 6.2 - Prob. 49ECh. 6.2 - Prob. 50ECh. 6.2 - Prob. 51ECh. 6.2 - Prob. 52ECh. 6.2 - Under certain conditions, the pressure of a gas...Ch. 6.2 - The strength of a particular beam varies inversely...Ch. 6.2 - In karate, the force needed to break a board...Ch. 6.2 - The weight of a body varies inversely with the...Ch. 6.2 - The time to complete a project is inversely...Ch. 6.2 - The intensity of sound varies inversely as the...Ch. 6.2 - Prob. 59ECh. 6.2 - Prob. 60ECh. 6.2 - Prob. 61ECh. 6.2 - Prob. 62ECh. 6.2 - Prob. 63ECh. 6.2 - Prob. 64ECh. 6.2 - Prob. 65ECh. 6.2 - Prob. 66ECh. 6.2 - Prob. 67ECh. 6.2 - Prob. 68ECh. 6.2 - Prob. 69ECh. 6.2 - Prob. 70ECh. 6.2 - Prob. 71ECh. 6.2 - Prob. 72ECh. 6.3 - Plot the points whose coordinates are (5, 3), (1,...Ch. 6.3 - Prob. 2TTOCh. 6.3 - Prob. 3TTOCh. 6.3 - Graph 2x y = 10.Ch. 6.3 - Prob. 5TTOCh. 6.3 - Find the slope of a line passing through the...Ch. 6.3 - Prob. 7TTOCh. 6.3 - Prob. 8TTOCh. 6.3 - Graph each line. (a) x = 7 (b) y = 1Ch. 6.3 - The cost of a medium cheese pizza at Marios Campus...Ch. 6.3 - A contestant on The Biggest Loser starts out...Ch. 6.3 - How can you tell what quadrant a point is in by...Ch. 6.3 - Prob. 2ECh. 6.3 - Prob. 3ECh. 6.3 - Prob. 4ECh. 6.3 - Prob. 5ECh. 6.3 - Prob. 6ECh. 6.3 - Prob. 7ECh. 6.3 - Prob. 8ECh. 6.3 - For Exercises 922, plot each point on the...Ch. 6.3 - Prob. 10ECh. 6.3 - Prob. 11ECh. 6.3 - Prob. 12ECh. 6.3 - Prob. 13ECh. 6.3 - Prob. 14ECh. 6.3 - Prob. 15ECh. 6.3 - Prob. 16ECh. 6.3 - Prob. 17ECh. 6.3 - For Exercises 922, plot each point on the...Ch. 6.3 - Prob. 19ECh. 6.3 - Prob. 20ECh. 6.3 - Prob. 21ECh. 6.3 - Prob. 22ECh. 6.3 - Prob. 23ECh. 6.3 - Prob. 24ECh. 6.3 - Prob. 25ECh. 6.3 - Prob. 26ECh. 6.3 - Prob. 27ECh. 6.3 - Prob. 28ECh. 6.3 - Prob. 29ECh. 6.3 - In Problems 2330, write the coordinates of the...Ch. 6.3 - For Exercises 3140, draw the graph for each...Ch. 6.3 - Prob. 32ECh. 6.3 - Prob. 33ECh. 6.3 - Prob. 34ECh. 6.3 - Prob. 35ECh. 6.3 - Prob. 36ECh. 6.3 - Prob. 37ECh. 6.3 - Prob. 38ECh. 6.3 - Prob. 39ECh. 6.3 - Prob. 40ECh. 6.3 - Prob. 41ECh. 6.3 - Prob. 42ECh. 6.3 - Prob. 43ECh. 6.3 - Prob. 44ECh. 6.3 - For Exercises 4148, find the slope of the line...Ch. 6.3 - Prob. 46ECh. 6.3 - Prob. 47ECh. 6.3 - Prob. 48ECh. 6.3 - For Exercises 4956, find the coordinates of both...Ch. 6.3 - For Exercises 4956, find the coordinates of both...Ch. 6.3 - Prob. 51ECh. 6.3 - Prob. 52ECh. 6.3 - Prob. 53ECh. 6.3 - Prob. 54ECh. 6.3 - Prob. 55ECh. 6.3 - Prob. 56ECh. 6.3 - For Exercises 5764, write the equation in...Ch. 6.3 - Prob. 58ECh. 6.3 - Prob. 59ECh. 6.3 - Prob. 60ECh. 6.3 - Prob. 61ECh. 6.3 - For Exercises 5764, write the equation in...Ch. 6.3 - For Exercises 5764, write the equation in...Ch. 6.3 - For Exercises 5764, write the equation in...Ch. 6.3 - For Exercises 6568, draw the graph for each...Ch. 6.3 - Prob. 66ECh. 6.3 - Prob. 67ECh. 6.3 - Prob. 68ECh. 6.3 - A newspapers website charges 6.50 per week to run...Ch. 6.3 - Prob. 70ECh. 6.3 - Prob. 71ECh. 6.3 - Prob. 72ECh. 6.3 - Prob. 73ECh. 6.3 - Prob. 74ECh. 6.3 - Prob. 75ECh. 6.3 - Prob. 76ECh. 6.3 - Prob. 77ECh. 6.3 - Prob. 78ECh. 6.3 - Prob. 79ECh. 6.3 - Prob. 80ECh. 6.3 - Prob. 81ECh. 6.3 - Prob. 82ECh. 6.3 - Prob. 83ECh. 6.3 - Prob. 84ECh. 6.3 - Prob. 85ECh. 6.3 - Prob. 86ECh. 6.3 - Prob. 87ECh. 6.3 - Prob. 88ECh. 6.3 - Prob. 89ECh. 6.3 - Prob. 90ECh. 6.3 - Prob. 91ECh. 6.3 - Prob. 92ECh. 6.3 - Prob. 93ECh. 6.3 - Prob. 94ECh. 6.3 - Prob. 95ECh. 6.3 - Prob. 96ECh. 6.4 - Which of the following equations represent...Ch. 6.4 - Prob. 2TTOCh. 6.4 - Prob. 3TTOCh. 6.4 - Find the domain and range of the following...Ch. 6.4 - Prob. 5TTOCh. 6.4 - Prob. 6TTOCh. 6.4 - Prob. 1ECh. 6.4 - Prob. 2ECh. 6.4 - Prob. 3ECh. 6.4 - Prob. 4ECh. 6.4 - Prob. 5ECh. 6.4 - Prob. 6ECh. 6.4 - Prob. 7ECh. 6.4 - In the linear function f(x) = ax + b, what is the...Ch. 6.4 - Prob. 9ECh. 6.4 - Prob. 10ECh. 6.4 - Prob. 11ECh. 6.4 - Prob. 12ECh. 6.4 - Prob. 13ECh. 6.4 - For Exercises 922, state whether or not the...Ch. 6.4 - Prob. 15ECh. 6.4 - Prob. 16ECh. 6.4 - Prob. 17ECh. 6.4 - Prob. 18ECh. 6.4 - Prob. 19ECh. 6.4 - Prob. 20ECh. 6.4 - Prob. 21ECh. 6.4 - For Exercises 922, state whether or not the...Ch. 6.4 - Prob. 23ECh. 6.4 - Prob. 24ECh. 6.4 - Prob. 25ECh. 6.4 - Prob. 26ECh. 6.4 - Prob. 27ECh. 6.4 - Prob. 28ECh. 6.4 - Prob. 29ECh. 6.4 - Prob. 30ECh. 6.4 - Prob. 31ECh. 6.4 - Prob. 32ECh. 6.4 - Prob. 33ECh. 6.4 - Prob. 34ECh. 6.4 - Prob. 35ECh. 6.4 - Prob. 36ECh. 6.4 - Prob. 37ECh. 6.4 - Prob. 38ECh. 6.4 - Prob. 39ECh. 6.4 - Prob. 40ECh. 6.4 - Prob. 41ECh. 6.4 - Prob. 42ECh. 6.4 - For Exercises 3546, find the domain and range of...Ch. 6.4 - Prob. 44ECh. 6.4 - Prob. 45ECh. 6.4 - Prob. 46ECh. 6.4 - Prob. 47ECh. 6.4 - Prob. 48ECh. 6.4 - Prob. 49ECh. 6.4 - Prob. 50ECh. 6.4 - Prob. 51ECh. 6.4 - In Exercises 4756, graph each linear function. 52....Ch. 6.4 - Prob. 53ECh. 6.4 - Prob. 54ECh. 6.4 - Prob. 55ECh. 6.4 - Prob. 56ECh. 6.4 - The percentage of the adult population that smokes...Ch. 6.4 - The percentage of the adult population that smokes...Ch. 6.4 - The percentage of the adult population that smokes...Ch. 6.4 - Prob. 60ECh. 6.4 - Prob. 61ECh. 6.4 - Prob. 62ECh. 6.4 - The percentage of the adult population that smokes...Ch. 6.4 - Prob. 64ECh. 6.4 - Prob. 65ECh. 6.4 - Prob. 66ECh. 6.4 - Prob. 67ECh. 6.4 - A realtor makes a commission of 6% of the purchase...Ch. 6.4 - Prob. 69ECh. 6.4 - Prob. 70ECh. 6.4 - Prob. 71ECh. 6.4 - A salesperson earns a base income of 250 a week...Ch. 6.4 - Prob. 73ECh. 6.4 - Prob. 74ECh. 6.4 - Prob. 75ECh. 6.4 - Prob. 76ECh. 6.4 - While Jenny is studying for class, she realizes...Ch. 6.4 - Prob. 78ECh. 6.4 - Prob. 79ECh. 6.4 - Prob. 80ECh. 6.4 - Prob. 81ECh. 6.4 - At a grocery store, the cashier rang up a total of...Ch. 6.4 - Prob. 83ECh. 6.4 - Prob. 84ECh. 6.4 - The manager of a winery found that when the price...Ch. 6.4 - Prob. 86ECh. 6.4 - While traveling across state lines to retrieve an...Ch. 6.4 - Prob. 88ECh. 6.4 - Prob. 89ECh. 6.4 - Prob. 90ECh. 6.4 - An oven is set to 450 degrees when its turned on....Ch. 6.4 - The independent variable of a function is n, the...Ch. 6.4 - Prob. 93ECh. 6.4 - Prob. 94ECh. 6.4 - Prob. 95ECh. 6.4 - Prob. 96ECh. 6.4 - Prob. 97ECh. 6.4 - Prob. 98ECh. 6.4 - Prob. 99ECh. 6.5 - Prob. 1TTOCh. 6.5 - Prob. 2TTOCh. 6.5 - Prob. 3TTOCh. 6.5 - Prob. 4TTOCh. 6.5 - Prob. 5TTOCh. 6.5 - Prob. 6TTOCh. 6.5 - Prob. 7TTOCh. 6.5 - Prob. 8TTOCh. 6.5 - Prob. 9TTOCh. 6.5 - Prob. 1ECh. 6.5 - Prob. 2ECh. 6.5 - Prob. 3ECh. 6.5 - Prob. 4ECh. 6.5 - Prob. 5ECh. 6.5 - Prob. 6ECh. 6.5 - Prob. 7ECh. 6.5 - Prob. 8ECh. 6.5 - Prob. 9ECh. 6.5 - Prob. 10ECh. 6.5 - Prob. 11ECh. 6.5 - Prob. 12ECh. 6.5 - For Exercises 1122, graph each parabola. 11. f(x)...Ch. 6.5 - Prob. 14ECh. 6.5 - Prob. 15ECh. 6.5 - For Exercises 1122, graph each parabola. 14. f(x)...Ch. 6.5 - For Exercises 1122, graph each parabola. 15. f(x)...Ch. 6.5 - For Exercises 1122, graph each parabola. 16. f(x)...Ch. 6.5 - Prob. 19ECh. 6.5 - Prob. 20ECh. 6.5 - Prob. 21ECh. 6.5 - Prob. 22ECh. 6.5 - Prob. 23ECh. 6.5 - Prob. 24ECh. 6.5 - For Exercises 2332, graph each exponential...Ch. 6.5 - For Exercises 2332, graph each exponential...Ch. 6.5 - Prob. 27ECh. 6.5 - For Exercises 2332, graph each exponential...Ch. 6.5 - Prob. 29ECh. 6.5 - Prob. 30ECh. 6.5 - Prob. 31ECh. 6.5 - Prob. 32ECh. 6.5 - Prob. 33ECh. 6.5 - Prob. 34ECh. 6.5 - In Exercises 3336, use the change of base formula...Ch. 6.5 - Prob. 36ECh. 6.5 - In Exercises 3336, use the change of base formula...Ch. 6.5 - Prob. 38ECh. 6.5 - In Exercises 3744, solve the equation. Round your...Ch. 6.5 - Prob. 40ECh. 6.5 - In Exercises 3744, solve the equation. Round your...Ch. 6.5 - Prob. 42ECh. 6.5 - Prob. 43ECh. 6.5 - Prob. 44ECh. 6.5 - In Exercises 3744, solve the equation. Round your...Ch. 6.5 - Prob. 46ECh. 6.5 - Prob. 47ECh. 6.5 - Prob. 48ECh. 6.5 - Prob. 49ECh. 6.5 - Prob. 50ECh. 6.5 - The profit for a company that produces discount...Ch. 6.5 - Prob. 52ECh. 6.5 - Prob. 53ECh. 6.5 - An online vendor that sells boxes of computer...Ch. 6.5 - Prob. 55ECh. 6.5 - Prob. 56ECh. 6.5 - Prob. 57ECh. 6.5 - In a biology experiment, there were 300,000 cells...Ch. 6.5 - Prob. 59ECh. 6.5 - Prob. 60ECh. 6.5 - Prob. 61ECh. 6.5 - Prob. 62ECh. 6.5 - Prob. 63ECh. 6.5 - Prob. 64ECh. 6.5 - Problems 6366 use the carbon dating equation from...Ch. 6.5 - Prob. 66ECh. 6.5 - Prob. 67ECh. 6.5 - Problems 6366 use the carbon dating equation from...Ch. 6.5 - Prob. 69ECh. 6.5 - Prob. 70ECh. 6.5 - Prob. 71ECh. 6.5 - Prob. 72ECh. 6.5 - Prob. 73ECh. 6.5 - Prob. 74ECh. 6.5 - Prob. 75ECh. 6.5 - Prob. 76ECh. 6.5 - Prob. 77ECh. 6.5 - Prob. 78ECh. 6.5 - Prob. 79ECh. 6.5 - Prob. 80ECh. 6.5 - Prob. 81ECh. 6.5 - Prob. 82ECh. 6.5 - Prob. 83ECh. 6.5 - Now lets compare linear, quadratic, and...Ch. 6.5 - The richest family in town hires you to do 2 weeks...Ch. 6.5 - A new resort in Costa Rica is managed by a retired...Ch. 6 - For Exercises 2831, write each statement in...Ch. 6 - Prob. 2RECh. 6 - Prob. 3RECh. 6 - Prob. 4RECh. 6 - Cindy is making the drive home for Thanksgiving,...Ch. 6 - Prob. 6RECh. 6 - Prob. 7RECh. 6 - Prob. 8RECh. 6 - Prob. 9RECh. 6 - At one county detention facility, inmates...Ch. 6 - Prob. 11RECh. 6 - Prob. 12RECh. 6 - For Exercises 3942, write each ratio as a...Ch. 6 - Prob. 14RECh. 6 - Prob. 15RECh. 6 - Prob. 16RECh. 6 - Prob. 17RECh. 6 - Prob. 18RECh. 6 - Prob. 19RECh. 6 - Prob. 20RECh. 6 - Prob. 21RECh. 6 - A professor states that if a student misses a unit...Ch. 6 - Prob. 23RECh. 6 - The amount of paint needed to paint a spherical...Ch. 6 - Prob. 25RECh. 6 - Prob. 26RECh. 6 - What is a rectangular coordinate system? How is it...Ch. 6 - What exactly is the graph of an equation?Ch. 6 - Prob. 29RECh. 6 - Prob. 30RECh. 6 - Prob. 31RECh. 6 - Prob. 32RECh. 6 - Prob. 33RECh. 6 - Prob. 34RECh. 6 - Prob. 35RECh. 6 - Prob. 36RECh. 6 - Prob. 37RECh. 6 - Prob. 38RECh. 6 - Prob. 39RECh. 6 - Prob. 40RECh. 6 - Prob. 41RECh. 6 - Prob. 42RECh. 6 - Prob. 43RECh. 6 - Prob. 44RECh. 6 - Prob. 45RECh. 6 - Prob. 46RECh. 6 - Prob. 47RECh. 6 - Prob. 48RECh. 6 - Prob. 49RECh. 6 - Prob. 50RECh. 6 - Prob. 51RECh. 6 - Prob. 52RECh. 6 - Prob. 53RECh. 6 - Prob. 54RECh. 6 - For Exercises 5254, evaluate each function for the...Ch. 6 - Prob. 56RECh. 6 - Prob. 57RECh. 6 - Prob. 58RECh. 6 - Prob. 59RECh. 6 - Prob. 60RECh. 6 - Prob. 61RECh. 6 - Prob. 62RECh. 6 - Prob. 63RECh. 6 - Prob. 64RECh. 6 - Prob. 65RECh. 6 - Prob. 66RECh. 6 - Prob. 67RECh. 6 - Prob. 68RECh. 6 - Prob. 69RECh. 6 - Prob. 70RECh. 6 - Prob. 71RECh. 6 - Prob. 1CTCh. 6 - Prob. 2CTCh. 6 - Prob. 3CTCh. 6 - A marketing company bought high-capacity flash...Ch. 6 - Prob. 5CTCh. 6 - Prob. 6CTCh. 6 - Prob. 7CTCh. 6 - Prob. 8CTCh. 6 - Prob. 9CTCh. 6 - Prob. 10CTCh. 6 - Prob. 11CTCh. 6 - Prob. 12CTCh. 6 - Prob. 13CTCh. 6 - Prob. 14CTCh. 6 - Prob. 15CTCh. 6 - Prob. 16CTCh. 6 - For Exercises 16 and 17, evaluate each function...Ch. 6 - Prob. 18CTCh. 6 - Prob. 19CTCh. 6 - Prob. 20CTCh. 6 - Prob. 21CTCh. 6 - Prob. 22CTCh. 6 - Prob. 23CTCh. 6 - Prob. 24CTCh. 6 - Prob. 25CT
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- (7) (12 points) Let F(x, y, z) = (y, x+z cos yz, y cos yz). Ꮖ (a) (4 points) Show that V x F = 0. (b) (4 points) Find a potential f for the vector field F. (c) (4 points) Let S be a surface in R3 for which the Stokes' Theorem is valid. Use Stokes' Theorem to calculate the line integral Jos F.ds; as denotes the boundary of S. Explain your answer.arrow_forward(3) (16 points) Consider z = uv, u = x+y, v=x-y. (a) (4 points) Express z in the form z = fog where g: R² R² and f: R² → R. (b) (4 points) Use the chain rule to calculate Vz = (2, 2). Show all intermediate steps otherwise no credit. (c) (4 points) Let S be the surface parametrized by T(x, y) = (x, y, ƒ (g(x, y)) (x, y) = R². Give a parametric description of the tangent plane to S at the point p = T(x, y). (d) (4 points) Calculate the second Taylor polynomial Q(x, y) (i.e. the quadratic approximation) of F = (fog) at a point (a, b). Verify that Q(x,y) F(a+x,b+y). =arrow_forward(6) (8 points) Change the order of integration and evaluate (z +4ry)drdy . So S√ ² 0arrow_forward
- (10) (16 points) Let R>0. Consider the truncated sphere S given as x² + y² + (z = √15R)² = R², z ≥0. where F(x, y, z) = −yi + xj . (a) (8 points) Consider the vector field V (x, y, z) = (▼ × F)(x, y, z) Think of S as a hot-air balloon where the vector field V is the velocity vector field measuring the hot gasses escaping through the porous surface S. The flux of V across S gives the volume flow rate of the gasses through S. Calculate this flux. Hint: Parametrize the boundary OS. Then use Stokes' Theorem. (b) (8 points) Calculate the surface area of the balloon. To calculate the surface area, do the following: Translate the balloon surface S by the vector (-15)k. The translated surface, call it S+ is part of the sphere x² + y²+z² = R². Why do S and S+ have the same area? ⚫ Calculate the area of S+. What is the natural spherical parametrization of S+?arrow_forward(1) (8 points) Let c(t) = (et, et sint, et cost). Reparametrize c as a unit speed curve starting from the point (1,0,1).arrow_forward(9) (16 points) Let F(x, y, z) = (x² + y − 4)i + 3xyj + (2x2 +z²)k = - = (x²+y4,3xy, 2x2 + 2²). (a) (4 points) Calculate the divergence and curl of F. (b) (6 points) Find the flux of V x F across the surface S given by x² + y²+2² = 16, z ≥ 0. (c) (6 points) Find the flux of F across the boundary of the unit cube E = [0,1] × [0,1] x [0,1].arrow_forward
- (8) (12 points) (a) (8 points) Let C be the circle x² + y² = 4. Let F(x, y) = (2y + e²)i + (x + sin(y²))j. Evaluate the line integral JF. F.ds. Hint: First calculate V x F. (b) (4 points) Let S be the surface r² + y² + z² = 4, z ≤0. Calculate the flux integral √(V × F) F).dS. Justify your answer.arrow_forwardDetermine whether the Law of Sines or the Law of Cosines can be used to find another measure of the triangle. a = 13, b = 15, C = 68° Law of Sines Law of Cosines Then solve the triangle. (Round your answers to four decimal places.) C = 15.7449 A = 49.9288 B = 62.0712 × Need Help? Read It Watch Itarrow_forward(4) (10 points) Evaluate √(x² + y² + z²)¹⁄² exp[}(x² + y² + z²)²] dV where D is the region defined by 1< x² + y²+ z² ≤4 and √√3(x² + y²) ≤ z. Note: exp(x² + y²+ 2²)²] means el (x²+ y²+=²)²]¸arrow_forward
- (2) (12 points) Let f(x,y) = x²e¯. (a) (4 points) Calculate Vf. (b) (4 points) Given x directional derivative 0, find the line of vectors u = D₁f(x, y) = 0. (u1, 2) such that the - (c) (4 points) Let u= (1+3√3). Show that Duƒ(1, 0) = ¦|▼ƒ(1,0)| . What is the angle between Vf(1,0) and the vector u? Explain.arrow_forwardFind the missing values by solving the parallelogram shown in the figure. (The lengths of the diagonals are given by c and d. Round your answers to two decimal places.) a b 29 39 66.50 C 17.40 d 0 54.0 126° a Ꮎ b darrow_forwardAnswer the following questions related to the following matrix A = 3 ³).arrow_forward
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