MATH IN OUR WORLD
4th Edition
ISBN: 9781266427183
Author: sobecki
Publisher: MCG
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Chapter 8.3, Problem 77E
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To find: How many ounces of fat did Shirl lose.
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1. Abel's Theorem. The goal in this problem is to prove Abel's theorem by following a series of steps
(each step must be justified).
Theorem 0.1 (Abel's Theorem).
If y1 and y2 are solutions of the differential equation
y" + p(t) y′ + q(t) y = 0,
where p and q are continuous on an open interval, then the Wronskian is given by
W (¥1, v2)(t) = c exp(− [p(t) dt),
where C is a constant that does not depend on t. Moreover, either W (y1, y2)(t) = 0 for every t in I or
W (y1, y2)(t) = 0 for every t in I.
1. (a) From the two equations (which follow from the hypotheses),
show that
y" + p(t) y₁ + q(t) y₁ = 0 and y½ + p(t) y2 + q(t) y2 = 0,
2. (b) Observe that
Hence, conclude that
(YY2 - Y1 y2) + P(t) (y₁ Y2 - Y1 Y2) = 0.
W'(y1, y2)(t) = yY2 - Y1 y2-
W' + p(t) W = 0.
3. (c) Use the result from the previous step to complete the proof of the theorem.
Chapter 8 Solutions
MATH IN OUR WORLD
Ch. 8.1 - Prob. 1TTOCh. 8.1 - Convert 81 feet to yards.Ch. 8.1 - Prob. 3TTOCh. 8.1 - A football field is 100 yards long. How many...Ch. 8.1 - The speed of sound at sea level and room...Ch. 8.1 - Prob. 6TTOCh. 8.1 - Prob. 7TTOCh. 8.1 - Prob. 8TTOCh. 8.1 - Prob. 1ECh. 8.1 - Prob. 2E
Ch. 8.1 - Prob. 3ECh. 8.1 - Prob. 4ECh. 8.1 - Prob. 5ECh. 8.1 - Describe a good rule of thumb for relating inches...Ch. 8.1 - Prob. 7ECh. 8.1 - Writing Exercises
8. Describe the rules for...Ch. 8.1 - Prob. 9ECh. 8.1 - Prob. 10ECh. 8.1 - For Exercises 718, convert each using dimensional...Ch. 8.1 - Prob. 12ECh. 8.1 - Prob. 13ECh. 8.1 - Prob. 14ECh. 8.1 - Prob. 15ECh. 8.1 - Prob. 16ECh. 8.1 - Prob. 17ECh. 8.1 - Prob. 18ECh. 8.1 - Prob. 19ECh. 8.1 - Prob. 20ECh. 8.1 - Prob. 21ECh. 8.1 - Prob. 22ECh. 8.1 - For Exercises 1958, convert each measurement to...Ch. 8.1 - Prob. 24ECh. 8.1 - For Exercises 1958, convert each measurement to...Ch. 8.1 - Prob. 26ECh. 8.1 - For Exercises 1958, convert each measurement to...Ch. 8.1 - For Exercises 1958, convert each measurement to...Ch. 8.1 - Prob. 29ECh. 8.1 - Prob. 30ECh. 8.1 - Prob. 31ECh. 8.1 - For Exercises 1958, convert each measurement to...Ch. 8.1 - For Exercises 1958, convert each measurement to...Ch. 8.1 - Prob. 34ECh. 8.1 - Prob. 35ECh. 8.1 - Prob. 36ECh. 8.1 - Prob. 37ECh. 8.1 - Prob. 38ECh. 8.1 - Prob. 39ECh. 8.1 - Prob. 40ECh. 8.1 - Prob. 41ECh. 8.1 - Prob. 42ECh. 8.1 - Prob. 43ECh. 8.1 - Prob. 44ECh. 8.1 - Prob. 45ECh. 8.1 - Prob. 46ECh. 8.1 - Prob. 47ECh. 8.1 - For Exercises 1958, convert each measurement to...Ch. 8.1 - Prob. 49ECh. 8.1 - Prob. 50ECh. 8.1 - For Exercises 1958, convert each measurement to...Ch. 8.1 - Prob. 52ECh. 8.1 - Prob. 53ECh. 8.1 - Prob. 54ECh. 8.1 - Prob. 55ECh. 8.1 - Prob. 56ECh. 8.1 - Prob. 57ECh. 8.1 - Prob. 58ECh. 8.1 - Prob. 59ECh. 8.1 - Prob. 60ECh. 8.1 - Prob. 61ECh. 8.1 - A professional basketball court is 94 feet long....Ch. 8.1 - Prob. 63ECh. 8.1 - Prob. 64ECh. 8.1 - Prob. 65ECh. 8.1 - Prob. 66ECh. 8.1 - Prob. 67ECh. 8.1 - What are the dimensions of a 6 dm by 5 dm piece of...Ch. 8.1 - Prob. 69ECh. 8.1 - If a millipede has 1,000 legs, how many legs would...Ch. 8.1 - Prob. 71ECh. 8.1 - Prob. 72ECh. 8.1 - Prob. 73ECh. 8.1 - Prob. 74ECh. 8.1 - Prob. 75ECh. 8.1 - Prob. 76ECh. 8.1 - Prob. 77ECh. 8.1 - Prob. 78ECh. 8.1 - Prob. 80ECh. 8.1 - Prob. 81ECh. 8.1 - Prob. 82ECh. 8.1 - A college is building a new basketball court that...Ch. 8.1 - If three servings of ice cream have 20 grams of...Ch. 8.1 - Prob. 85ECh. 8.1 - The campus fitness center is installing an...Ch. 8.1 - Prob. 87ECh. 8.1 - Prob. 88ECh. 8.1 - Prob. 89ECh. 8.1 - Prob. 90ECh. 8.1 - Prob. 91ECh. 8.1 - Prob. 92ECh. 8.1 - Prob. 93ECh. 8.1 - Prob. 94ECh. 8.1 - Prob. 95ECh. 8.1 - Prob. 96ECh. 8.1 - Prob. 97ECh. 8.1 - Prob. 98ECh. 8.1 - Prob. 99ECh. 8.1 - In Problems 95104, decide what units in both the...Ch. 8.1 - Prob. 101ECh. 8.1 - Prob. 102ECh. 8.1 - In Problems 95104, decide what units in both the...Ch. 8.1 - In Problems 95104, decide what units in both the...Ch. 8.1 - Prob. 105ECh. 8.1 - Prob. 106ECh. 8.1 - Prob. 107ECh. 8.1 - Prob. 108ECh. 8.1 - Prob. 109ECh. 8.1 - What units would 7,000 cm have to be converted to...Ch. 8.1 - Prob. 111ECh. 8.2 - Prob. 1TTOCh. 8.2 - A 32-in. wide-screen TV has screen area 3.05 ft2....Ch. 8.2 - Prob. 3TTOCh. 8.2 - Prob. 4TTOCh. 8.2 - Fussy University prohibits any displays on...Ch. 8.2 - Prob. 6TTOCh. 8.2 - Prob. 7TTOCh. 8.2 - Prob. 8TTOCh. 8.2 - Prob. 9TTOCh. 8.2 - Prob. 10TTOCh. 8.2 - Prob. 11TTOCh. 8.2 - Prob. 1ECh. 8.2 - Prob. 2ECh. 8.2 - Prob. 3ECh. 8.2 - Prob. 4ECh. 8.2 - Prob. 5ECh. 8.2 - Prob. 6ECh. 8.2 - Prob. 7ECh. 8.2 - For Exercises 768, convert each measurement to the...Ch. 8.2 - For Exercises 768, convert each measurement to the...Ch. 8.2 - Prob. 10ECh. 8.2 - Prob. 11ECh. 8.2 - Prob. 12ECh. 8.2 - Prob. 13ECh. 8.2 - Prob. 14ECh. 8.2 - Prob. 15ECh. 8.2 - Prob. 16ECh. 8.2 - Prob. 17ECh. 8.2 - Prob. 18ECh. 8.2 - Prob. 19ECh. 8.2 - Prob. 20ECh. 8.2 - Prob. 21ECh. 8.2 - Prob. 22ECh. 8.2 - Prob. 23ECh. 8.2 - Prob. 24ECh. 8.2 - Prob. 25ECh. 8.2 - Prob. 26ECh. 8.2 - Prob. 27ECh. 8.2 - Prob. 28ECh. 8.2 - Prob. 29ECh. 8.2 - Prob. 30ECh. 8.2 - Prob. 31ECh. 8.2 - Prob. 32ECh. 8.2 - Prob. 33ECh. 8.2 - Prob. 34ECh. 8.2 - Prob. 35ECh. 8.2 - Prob. 36ECh. 8.2 - Prob. 37ECh. 8.2 - Prob. 38ECh. 8.2 - Prob. 39ECh. 8.2 - Prob. 40ECh. 8.2 - Prob. 41ECh. 8.2 - Prob. 42ECh. 8.2 - Prob. 43ECh. 8.2 - For Exercises 768, convert each measurement to the...Ch. 8.2 - Prob. 45ECh. 8.2 - Prob. 46ECh. 8.2 - Prob. 47ECh. 8.2 - Prob. 48ECh. 8.2 - Prob. 49ECh. 8.2 - Prob. 50ECh. 8.2 - Prob. 51ECh. 8.2 - Prob. 52ECh. 8.2 - Prob. 53ECh. 8.2 - Prob. 54ECh. 8.2 - Prob. 55ECh. 8.2 - Prob. 56ECh. 8.2 - Prob. 57ECh. 8.2 - Prob. 58ECh. 8.2 - Prob. 59ECh. 8.2 - Prob. 60ECh. 8.2 - Prob. 61ECh. 8.2 - Prob. 62ECh. 8.2 - Prob. 63ECh. 8.2 - Prob. 64ECh. 8.2 - Prob. 65ECh. 8.2 - Prob. 66ECh. 8.2 - Prob. 67ECh. 8.2 - Prob. 68ECh. 8.2 - Prob. 69ECh. 8.2 - Jose has a 15-m2 garden and plans to buy some...Ch. 8.2 - Dan wants to pour a concrete patio in his...Ch. 8.2 - Chloe drank two 20-oz bottles of Diet Pepsi while...Ch. 8.2 - Prob. 73ECh. 8.2 - Prob. 74ECh. 8.2 - Prob. 75ECh. 8.2 - Prob. 76ECh. 8.2 - Prob. 77ECh. 8.2 - Prob. 78ECh. 8.2 - Five cubic feet of seawater have flooded into a...Ch. 8.2 - Prob. 80ECh. 8.2 - Prob. 81ECh. 8.2 - Prob. 82ECh. 8.2 - A search party covered 6 square miles of territory...Ch. 8.2 - A Jacuzzi was filled with 200 gallons of water....Ch. 8.2 - Prob. 85ECh. 8.2 - Prob. 86ECh. 8.2 - Prob. 87ECh. 8.2 - Prob. 88ECh. 8.2 - Prob. 89ECh. 8.2 - In Problems 8590, which unit would be most...Ch. 8.2 - Prob. 91ECh. 8.2 - Prob. 92ECh. 8.2 - Prob. 93ECh. 8.2 - Prob. 94ECh. 8.2 - Prob. 95ECh. 8.2 - Prob. 96ECh. 8.2 - Prob. 97ECh. 8.2 - Prob. 98ECh. 8.2 - Without doing any calculating, which sounds like...Ch. 8.2 - Prob. 102ECh. 8.2 - Prob. 104ECh. 8.2 - As a general rule, there are about 20 drops of...Ch. 8.3 - Prob. 1TTOCh. 8.3 - Prob. 2TTOCh. 8.3 - Prob. 3TTOCh. 8.3 - (a) One of the weight classes in Olympic boxing is...Ch. 8.3 - Barts football coach tells him that hell start...Ch. 8.3 - Prob. 6TTOCh. 8.3 - Prob. 7TTOCh. 8.3 - Prob. 1ECh. 8.3 - In most applications, weight and mass are treated...Ch. 8.3 - Even though the base unit of mass/weight in the...Ch. 8.3 - Measuring temperatures in metric units is...Ch. 8.3 - How do powers of 10 fit into the metric system of...Ch. 8.3 - Prob. 6ECh. 8.3 - For Exercises 716, convert to the indicated unit....Ch. 8.3 - For Exercises 716, convert to the indicated unit....Ch. 8.3 - For Exercises 716, convert to the indicated unit....Ch. 8.3 - For Exercises 716, convert to the indicated unit....Ch. 8.3 - Prob. 11ECh. 8.3 - Prob. 12ECh. 8.3 - Prob. 13ECh. 8.3 - Prob. 14ECh. 8.3 - For Exercises 716, convert to the indicated unit....Ch. 8.3 - For Exercises 716, convert to the indicated unit....Ch. 8.3 - For Exercises 1730, convert each metric weight to...Ch. 8.3 - For Exercises 1730, convert each metric weight to...Ch. 8.3 - For Exercises 1730, convert each metric weight to...Ch. 8.3 - For Exercises 1730, convert each metric weight to...Ch. 8.3 - For Exercises 1730, convert each metric weight to...Ch. 8.3 - For Exercises 1730, convert each metric weight to...Ch. 8.3 - For Exercises 1730, convert each metric weight to...Ch. 8.3 - For Exercises 1730, convert each metric weight to...Ch. 8.3 - For Exercises 1730, convert each metric weight to...Ch. 8.3 - For Exercises 1730, convert each metric weight to...Ch. 8.3 - For Exercises 1730, convert each metric weight to...Ch. 8.3 - For Exercises 1730, convert each metric weight to...Ch. 8.3 - For Exercises 1730, convert each metric weight to...Ch. 8.3 - For Exercises 1730, convert each metric weight to...Ch. 8.3 - For Exercises 3146, convert each amount to the...Ch. 8.3 - For Exercises 3146, convert each amount to the...Ch. 8.3 - For Exercises 3146, convert each amount to the...Ch. 8.3 - For Exercises 3146, convert each amount to the...Ch. 8.3 - For Exercises 3146, convert each amount to the...Ch. 8.3 - For Exercises 3146, convert each amount to the...Ch. 8.3 - For Exercises 3146, convert each amount to the...Ch. 8.3 - For Exercises 3146, convert each amount to the...Ch. 8.3 - For Exercises 3146, convert each amount to the...Ch. 8.3 - For Exercises 3146, convert each amount to the...Ch. 8.3 - For Exercises 3146, convert each amount to the...Ch. 8.3 - For Exercises 3146, convert each amount to the...Ch. 8.3 - For Exercises 3146, convert each amount to the...Ch. 8.3 - For Exercises 3146, convert each amount to the...Ch. 8.3 - For Exercises 3146, convert each amount to the...Ch. 8.3 - For Exercises 3146, convert each amount to the...Ch. 8.3 - For Exercises 4752, convert each Celsius...Ch. 8.3 - For Exercises 4752, convert each Celsius...Ch. 8.3 - For Exercises 4752, convert each Celsius...Ch. 8.3 - For Exercises 4752, convert each Celsius...Ch. 8.3 - For Exercises 4752, convert each Celsius...Ch. 8.3 - For Exercises 4752, convert each Celsius...Ch. 8.3 - For Exercises 5358, convert each Fahrenheit...Ch. 8.3 - Prob. 54ECh. 8.3 - Prob. 55ECh. 8.3 - For Exercises 5358, convert each Fahrenheit...Ch. 8.3 - Prob. 57ECh. 8.3 - Prob. 58ECh. 8.3 - Prob. 59ECh. 8.3 - Prob. 60ECh. 8.3 - Prob. 61ECh. 8.3 - Prob. 62ECh. 8.3 - Prob. 63ECh. 8.3 - Prob. 64ECh. 8.3 - Prob. 65ECh. 8.3 - Prob. 66ECh. 8.3 - Prob. 67ECh. 8.3 - Prob. 68ECh. 8.3 - Prob. 69ECh. 8.3 - For a chicken Marsala recipe, Janine needed 24 oz...Ch. 8.3 - Prob. 71ECh. 8.3 - Prob. 72ECh. 8.3 - Prob. 73ECh. 8.3 - Prob. 74ECh. 8.3 - Prob. 75ECh. 8.3 - While building a new playground at the city...Ch. 8.3 - Prob. 77ECh. 8.3 - During a dinner at Outback Steakhouse, a family of...Ch. 8.3 - An elevator says the maximum capacity is 1,000 kg....Ch. 8.3 - Prob. 80ECh. 8.3 - If the temperature goes down by 7 degrees Celsius...Ch. 8.3 - Between 8 A.M. and noon, the temperature rose by...Ch. 8.3 - Prob. 83ECh. 8.3 - A 1.7-ton truck crosses the border into Canada....Ch. 8.3 - Prob. 85ECh. 8.3 - Prob. 86ECh. 8.3 - Prob. 87ECh. 8.3 - 88.
According to the Guinness Book of World...Ch. 8.3 - Prob. 89ECh. 8.3 - In Exercises 90–93, which would be the most...Ch. 8.3 - Prob. 91ECh. 8.3 - In Exercises 90–93, which would be the most...Ch. 8.3 - In Exercises 90–93, which would be the most...Ch. 8.3 - Prob. 94ECh. 8.3 - (a) The bar graph shows the average monthly high...Ch. 8.3 - Australia is one of the worlds leading producers...Ch. 8.3 - Prob. 101ECh. 8.3 - Prob. 102ECh. 8.3 - Prob. 103ECh. 8.3 - Prob. 104ECh. 8.3 - Prob. 105ECh. 8 - For Exercises 116, convert each of the following...Ch. 8 - Prob. 2RECh. 8 - Prob. 3RECh. 8 - Prob. 4RECh. 8 - Prob. 5RECh. 8 - Prob. 6RECh. 8 - Prob. 7RECh. 8 - Prob. 8RECh. 8 - Prob. 9RECh. 8 - Prob. 10RECh. 8 - Prob. 11RECh. 8 - Prob. 12RECh. 8 - Prob. 13RECh. 8 - Prob. 14RECh. 8 - Prob. 15RECh. 8 - For Exercises 116, convert each of the following...Ch. 8 - Prob. 17RECh. 8 - Prob. 18RECh. 8 - Prob. 19RECh. 8 - Prob. 20RECh. 8 - Prob. 21RECh. 8 - Prob. 22RECh. 8 - Prob. 23RECh. 8 - Prob. 24RECh. 8 - Prob. 25RECh. 8 - Prob. 26RECh. 8 - Prob. 27RECh. 8 - Prob. 28RECh. 8 - Prob. 29RECh. 8 - Prob. 30RECh. 8 - Prob. 31RECh. 8 - Prob. 32RECh. 8 - For Exercises 2341, convert each of the following...Ch. 8 - Prob. 34RECh. 8 - Prob. 35RECh. 8 - Prob. 36RECh. 8 - Prob. 37RECh. 8 - Prob. 38RECh. 8 - Prob. 39RECh. 8 - Prob. 40RECh. 8 - Prob. 41RECh. 8 - Prob. 42RECh. 8 - Prob. 43RECh. 8 - Prob. 44RECh. 8 - Prob. 45RECh. 8 - Prob. 46RECh. 8 - Prob. 47RECh. 8 - Prob. 48RECh. 8 - Prob. 49RECh. 8 - Prob. 50RECh. 8 - Prob. 51RECh. 8 - Prob. 52RECh. 8 - Prob. 53RECh. 8 - Prob. 54RECh. 8 - Prob. 55RECh. 8 - Prob. 56RECh. 8 - Prob. 57RECh. 8 - Prob. 58RECh. 8 - Prob. 59RECh. 8 - Prob. 60RECh. 8 - For Exercises 4962, convert each of the following...Ch. 8 - Prob. 62RECh. 8 - Prob. 63RECh. 8 - Prob. 64RECh. 8 - Prob. 65RECh. 8 - Prob. 66RECh. 8 - Prob. 67RECh. 8 - Prob. 68RECh. 8 - How many pounds is a baby who weighs 3,200 g?Ch. 8 - Heinrichs temperature is 38.5C. A person is...Ch. 8 - Prob. 71RECh. 8 - Prob. 72RECh. 8 - Prob. 73RECh. 8 - Prob. 1CTCh. 8 - Prob. 2CTCh. 8 - Prob. 3CTCh. 8 - Prob. 4CTCh. 8 - Prob. 5CTCh. 8 - Prob. 6CTCh. 8 - Prob. 7CTCh. 8 - Prob. 8CTCh. 8 - Prob. 9CTCh. 8 - Prob. 10CTCh. 8 - Prob. 11CTCh. 8 - For Exercises 121, convert each of the following:...Ch. 8 - Prob. 13CTCh. 8 - Prob. 14CTCh. 8 - Prob. 15CTCh. 8 - Prob. 16CTCh. 8 - Prob. 17CTCh. 8 - Prob. 18CTCh. 8 - Prob. 19CTCh. 8 - Prob. 20CTCh. 8 - Prob. 21CTCh. 8 - Prob. 22CTCh. 8 - If a runner averages 5.9 feet per second, how long...Ch. 8 - Prob. 24CTCh. 8 - Prob. 25CTCh. 8 - Prob. 26CTCh. 8 - Prob. 27CTCh. 8 - Prob. 28CTCh. 8 - Prob. 29CTCh. 8 - Prob. 30CTCh. 8 - A young family is looking to buy a house and...Ch. 8 - Prob. 32CTCh. 8 - Prob. 33CT
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