EBK MULTIVARIABLE CALCULUS
EBK MULTIVARIABLE CALCULUS
11th Edition
ISBN: 8220103600781
Author: Edwards
Publisher: YUZU
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Chapter 16.2, Problem 24E
To determine

To calculate:

The general solution of the given linear differential equation y''4y'+21y=0.

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Question 1: If a barometer were built using oil (p = 0.92 g/cm³) instead of mercury (p = 13.6 g/cm³), would the column of oil be higher than, lower than, or the same as the column of mercury at 1.00 atm? If the level is different, by what factor? Explain. (5 pts) Solution: A barometer works based on the principle that the pressure exerted by the liquid column balances atmospheric pressure. The pressure is given by: P = pgh Since the atmospheric pressure remains constant (P = 1.00 atm), the height of the liquid column is inversely proportional to its density: Step 1: Given Data PHg hol=hgx Poil • Density of mercury: PHg = 13.6 g/cm³ Density of oil: Poil = 0.92 g/cm³ • Standard height of mercury at 1.00 atm: hμg Step 2: Compute Height of Oil = 760 mm = 0.760 m 13.6 hoil = 0.760 x 0.92 hoil = 0.760 × 14.78 hoil = 11.23 m Step 3: Compare Heights Since oil is less dense than mercury, the column of oil must be much taller than that of mercury. The factor by which it is taller is: Final…
Question 3: A sealed flask at room temperature contains a mixture of neon (Ne) and nitrogen (N2) gases. Ne has a mass of 3.25 g and exerts a pressure of 48.2 torr. . N2 contributes a pressure of 142 torr. • What is the mass of the N2 in the flask? • Atomic mass of Ne = 20.1797 g/mol • Atomic mass of N = 14.0067 g/mol Solution: We will use the Ideal Gas Law to determine the number of moles of each gas and calculate the mass of N2. PV = nRT where: • P = total pressure • V volume of the flask (same for both gases) n = number of moles of gas • R 0.0821 L atm/mol K • T = Room temperature (assume 298 K) Since both gases are in the same flask, their partial pressures correspond to their mole fractions. Step 1: Convert Pressures to Atmospheres 48.2 PNe = 0.0634 atm 760 142 PN2 = = 0.1868 atm 760 Step 2: Determine Moles of Ne nNe = mass molar mass 3.25 nNe 20.1797 nne 0.1611 mol Step 3: Use Partial Pressure Ratio to Find n
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Chapter 16 Solutions

EBK MULTIVARIABLE CALCULUS

Ch. 16.1 - Prob. 11ECh. 16.1 - Prob. 12ECh. 16.1 - Prob. 13ECh. 16.1 - Prob. 14ECh. 16.1 - Prob. 15ECh. 16.1 - Graphical and Analytic AnalysisIn Exercises 15 and...Ch. 16.1 - Prob. 17ECh. 16.1 - Prob. 18ECh. 16.1 - Prob. 19ECh. 16.1 - Finding a Particular SolutionIn Exercises 17-22,...Ch. 16.1 - Prob. 21ECh. 16.1 - Prob. 22ECh. 16.1 - Prob. 23ECh. 16.1 - Prob. 24ECh. 16.1 - Prob. 25ECh. 16.1 - Prob. 26ECh. 16.1 - Prob. 27ECh. 16.1 - Finding an Integrating Factor In Exercises 23-32,...Ch. 16.1 - Prob. 29ECh. 16.1 - Prob. 30ECh. 16.1 - Prob. 31ECh. 16.1 - Prob. 32ECh. 16.1 - Prob. 33ECh. 16.1 - Using an Integrating Factor In Exercises 33-36,...Ch. 16.1 - Prob. 35ECh. 16.1 - Prob. 36ECh. 16.1 - Prob. 37ECh. 16.1 - Prob. 38ECh. 16.1 - Tangent Curves In Exercises 39-42, use agraphing...Ch. 16.1 - Prob. 40ECh. 16.1 - Prob. 41ECh. 16.1 - Prob. 42ECh. 16.1 - Prob. 43ECh. 16.1 - Finding an Equation of a Curve In Exercises 43 and...Ch. 16.1 - Cost In a manufacturing process where y=C(x)...Ch. 16.1 - HOW DO YOU SEE? The graph shows several...Ch. 16.1 - Prob. 47ECh. 16.1 - Prob. 48ECh. 16.1 - Prob. 49ECh. 16.1 - Prob. 50ECh. 16.1 - Prob. 51ECh. 16.1 - Prob. 52ECh. 16.1 - Prob. 53ECh. 16.1 - Prob. 54ECh. 16.1 - Prob. 55ECh. 16.1 - Prob. 56ECh. 16.1 - Prob. 57ECh. 16.1 - Prob. 58ECh. 16.2 - Prob. 1ECh. 16.2 - Prob. 2ECh. 16.2 - Prob. 3ECh. 16.2 - Prob. 4ECh. 16.2 - Prob. 5ECh. 16.2 - Prob. 6ECh. 16.2 - Prob. 7ECh. 16.2 - Prob. 8ECh. 16.2 - Prob. 9ECh. 16.2 - Prob. 10ECh. 16.2 - Prob. 11ECh. 16.2 - Prob. 12ECh. 16.2 - Prob. 13ECh. 16.2 - Prob. 14ECh. 16.2 - Prob. 15ECh. 16.2 - Prob. 16ECh. 16.2 - Prob. 17ECh. 16.2 - Prob. 18ECh. 16.2 - Prob. 19ECh. 16.2 - Prob. 20ECh. 16.2 - Prob. 21ECh. 16.2 - Prob. 22ECh. 16.2 - Prob. 23ECh. 16.2 - Prob. 24ECh. 16.2 - Prob. 25ECh. 16.2 - Prob. 26ECh. 16.2 - Prob. 27ECh. 16.2 - Prob. 28ECh. 16.2 - Prob. 29ECh. 16.2 - Prob. 30ECh. 16.2 - Prob. 31ECh. 16.2 - Finding a General Solution In exercises 9-36, find...Ch. 16.2 - Prob. 33ECh. 16.2 - Prob. 34ECh. 16.2 - Prob. 35ECh. 16.2 - Prob. 36ECh. 16.2 - Prob. 37ECh. 16.2 - Finding a Particular Solution Determine C and ...Ch. 16.2 - Prob. 39ECh. 16.2 - Prob. 40ECh. 16.2 - Prob. 41ECh. 16.2 - Find a Particular Solution: Initial ConditionsIn...Ch. 16.2 - Prob. 43ECh. 16.2 - Prob. 44ECh. 16.2 - Prob. 45ECh. 16.2 - Prob. 46ECh. 16.2 - Prob. 47ECh. 16.2 - Finding a Particular Solution: Boundary...Ch. 16.2 - Prob. 49ECh. 16.2 - Prob. 50ECh. 16.2 - Prob. 51ECh. 16.2 - Prob. 52ECh. 16.2 - Several shock absorbers are shown at the right. Do...Ch. 16.2 - Prob. 54ECh. 16.2 - Prob. 55ECh. 16.2 - Prob. 56ECh. 16.2 - Motion of a Spring In Exercise 55-58, match the...Ch. 16.2 - Prob. 58ECh. 16.2 - Prob. 59ECh. 16.2 - Prob. 60ECh. 16.2 - Prob. 61ECh. 16.2 - Prob. 62ECh. 16.2 - Prob. 63ECh. 16.2 - Prob. 64ECh. 16.2 - Prob. 65ECh. 16.2 - Prob. 66ECh. 16.2 - Prob. 67ECh. 16.2 - True or False? In exercises 67-70, determine...Ch. 16.2 - Prob. 69ECh. 16.2 - Prob. 70ECh. 16.2 - Wronskian The Wronskian of two differentiable...Ch. 16.2 - Prob. 72ECh. 16.2 - Prob. 73ECh. 16.2 - Prob. 74ECh. 16.3 - Prob. 1ECh. 16.3 - Choosing a MethodDetermine whether you woulduse...Ch. 16.3 - Prob. 3ECh. 16.3 - Prob. 4ECh. 16.3 - Prob. 5ECh. 16.3 - Prob. 6ECh. 16.3 - Prob. 7ECh. 16.3 - Prob. 8ECh. 16.3 - Prob. 9ECh. 16.3 - Prob. 10ECh. 16.3 - Prob. 11ECh. 16.3 - Prob. 12ECh. 16.3 - Prob. 13ECh. 16.3 - Method of Undetermined CoefficientsIn Exercises...Ch. 16.3 - Prob. 15ECh. 16.3 - Prob. 16ECh. 16.3 - Prob. 17ECh. 16.3 - Prob. 18ECh. 16.3 - Prob. 19ECh. 16.3 - Using Initial Conditions In Exercises 17-22, solve...Ch. 16.3 - Prob. 21ECh. 16.3 - Prob. 22ECh. 16.3 - Prob. 23ECh. 16.3 - Prob. 24ECh. 16.3 - Prob. 25ECh. 16.3 - Prob. 26ECh. 16.3 - Prob. 27ECh. 16.3 - Method of Variation of Parameters In Exercises...Ch. 16.3 - Prob. 29ECh. 16.3 - Electrical Circuits In Exercises 29 and 30, use...Ch. 16.3 - Prob. 31ECh. 16.3 - Prob. 32ECh. 16.3 - Prob. 33ECh. 16.3 - Prob. 34ECh. 16.3 - Prob. 35ECh. 16.3 - Prob. 36ECh. 16.3 - Prob. 37ECh. 16.3 - Prob. 38ECh. 16.3 - Prob. 39ECh. 16.3 - Prob. 40ECh. 16.3 - Prob. 41ECh. 16.4 - Prob. 1ECh. 16.4 - Prob. 2ECh. 16.4 - Prob. 3ECh. 16.4 - Power Series Solution In Exercises 3-6, use a...Ch. 16.4 - Prob. 5ECh. 16.4 - Prob. 6ECh. 16.4 - Prob. 7ECh. 16.4 - Prob. 8ECh. 16.4 - Prob. 9ECh. 16.4 - Prob. 10ECh. 16.4 - Prob. 11ECh. 16.4 - Prob. 12ECh. 16.4 - Prob. 13ECh. 16.4 - Prob. 14ECh. 16.4 - Prob. 15ECh. 16.4 - Prob. 16ECh. 16.4 - Prob. 17ECh. 16.4 - Prob. 18ECh. 16.4 - Prob. 19ECh. 16.4 - Prob. 20ECh. 16.4 - Prob. 21ECh. 16.4 - Prob. 22ECh. 16.4 - Prob. 23ECh. 16.4 - Prob. 24ECh. 16.4 - Airys Equation Find the first six terms of the...Ch. 16 - Prob. 1RECh. 16 - Prob. 2RECh. 16 - Prob. 3RECh. 16 - Prob. 4RECh. 16 - Prob. 5RECh. 16 - Solving an Exact Differential Equation In...Ch. 16 - Prob. 7RECh. 16 - Prob. 8RECh. 16 - Prob. 9RECh. 16 - Prob. 10RECh. 16 - Prob. 11RECh. 16 - Prob. 12RECh. 16 - Prob. 13RECh. 16 - Prob. 14RECh. 16 - Prob. 15RECh. 16 - Prob. 16RECh. 16 - Prob. 17RECh. 16 - Prob. 18RECh. 16 - Prob. 19RECh. 16 - Prob. 20RECh. 16 - Prob. 21RECh. 16 - Prob. 22RECh. 16 - Prob. 23RECh. 16 - Prob. 24RECh. 16 - Prob. 25RECh. 16 - Prob. 26RECh. 16 - Prob. 27RECh. 16 - Prob. 28RECh. 16 - Prob. 29RECh. 16 - Prob. 30RECh. 16 - Prob. 31RECh. 16 - Prob. 32RECh. 16 - Prob. 33RECh. 16 - Prob. 34RECh. 16 - Prob. 35RECh. 16 - Motion of a SpringIn Exercise 35-36, a 64-pound...Ch. 16 - Prob. 37RECh. 16 - Prob. 38RECh. 16 - Prob. 39RECh. 16 - Prob. 40RECh. 16 - Prob. 41RECh. 16 - Prob. 42RECh. 16 - Prob. 43RECh. 16 - Prob. 44RECh. 16 - Prob. 45RECh. 16 - Using Initial Conditions In Exercises 45-50, solve...Ch. 16 - Prob. 47RECh. 16 - Prob. 48RECh. 16 - Prob. 49RECh. 16 - Prob. 50RECh. 16 - Method of Variation of Parameters In Exercises...Ch. 16 - Prob. 52RECh. 16 - Prob. 53RECh. 16 - Prob. 54RECh. 16 - Prob. 55RECh. 16 - Prob. 56RECh. 16 - Prob. 57RECh. 16 - Prob. 58RECh. 16 - Prob. 59RECh. 16 - Prob. 60RECh. 16 - Prob. 61RECh. 16 - Prob. 62RECh. 16 - Prob. 1PSCh. 16 - Prob. 2PSCh. 16 - Prob. 3PSCh. 16 - Prob. 4PSCh. 16 - Prob. 5PSCh. 16 - Prob. 6PSCh. 16 - Prob. 7PSCh. 16 - Prob. 8PSCh. 16 - Pendulum Consider a pendulum of length L that...Ch. 16 - Prob. 10PSCh. 16 - Prob. 11PSCh. 16 - Prob. 12PSCh. 16 - Prob. 13PSCh. 16 - Prob. 14PSCh. 16 - Prob. 15PSCh. 16 - ChebyshevsEquation ConsiderChebyshevs equation...Ch. 16 - Prob. 17PSCh. 16 - Prob. 18PSCh. 16 - Prob. 19PSCh. 16 - Laguerres Equation Consider Laguerres Equation...
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