
Calculus Volume 2
17th Edition
ISBN: 9781938168062
Author: Gilbert Strang, Edwin Jed Herman
Publisher: OpenStax
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Textbook Question
Chapter 4.3, Problem 156E
For the following problems, use Newton’s law of cooling.
156. The liquid base of an ice cream has an initial temperature of 200° F before it is placed in a freezer with a constant temperature of 0°F. After 1 hour, the temperature of the ice-cream base has decreased to 140°F. Formulate and solve the initial-value problem to determine the temperature of the ice cream.
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Chapter 4 Solutions
Calculus Volume 2
Ch. 4.1 - Determine the order of the following differential...Ch. 4.1 - Determine the order of the following differential...Ch. 4.1 - Determine the order of the following differential...Ch. 4.1 - Determine the order of the following differential...Ch. 4.1 - Determine the order of the following differential...Ch. 4.1 - Determine the order of the following differential...Ch. 4.1 - Determine the order of the following differential...Ch. 4.1 - Verify that the following functions are solutions...Ch. 4.1 - Verify that the following functions are solutions...Ch. 4.1 - Verify that the following functions are solutions...
Ch. 4.1 - Verify that the following functions are solutions...Ch. 4.1 - Verify that the following functions are solutions...Ch. 4.1 - Verify that the following functions are solutions...Ch. 4.1 - Verify that the following functions are solutions...Ch. 4.1 - Verify that the following functions are solutions...Ch. 4.1 - Verify that the following functions are solutions...Ch. 4.1 - Verify that the following functions are solutions...Ch. 4.1 - Verify the following general solutions and find...Ch. 4.1 - Verify the following general solutions and find...Ch. 4.1 - Verify the following general solutions and find...Ch. 4.1 - Verify the following general solutions and find...Ch. 4.1 - Verify the following general solutions and find...Ch. 4.1 - Verify the following general solutions and find...Ch. 4.1 - Verify the following general solutions and find...Ch. 4.1 - Verify the following general solutions and find...Ch. 4.1 - Verify the following general solutions and find...Ch. 4.1 - Verify the following general solutions and find...Ch. 4.1 - For the following problems, find the general...Ch. 4.1 - For the following problems, find the general...Ch. 4.1 - For the following problems, find the general...Ch. 4.1 - For the following problems, find the general...Ch. 4.1 - For the following problems, find the general...Ch. 4.1 - For the following problems, find the general...Ch. 4.1 - For the following problems, find the general...Ch. 4.1 - For the following problems, find the general...Ch. 4.1 - For the following problems, find the general...Ch. 4.1 - For the following problems, find the general...Ch. 4.1 - Solve the following initial-value problems...Ch. 4.1 - Solve the following initial-value problems...Ch. 4.1 - Solve the following initial-value problems...Ch. 4.1 - Solve the following initial-value problems...Ch. 4.1 - Solve the following initial-value problems...Ch. 4.1 - Solve the following initial-value problems...Ch. 4.1 - Solve the following initial-value problems...Ch. 4.1 - Solve the following initial-value problems...Ch. 4.1 - Solve the following initial-value problems...Ch. 4.1 - Solve the following initial-value problems...Ch. 4.1 - Recall that a family of solutions includes...Ch. 4.1 - Recall that a family of solutions includes...Ch. 4.1 - Recall that a family of solutions includes...Ch. 4.1 - Recall that a family of solutions includes...Ch. 4.1 - Recall that a family of solutions includes...Ch. 4.1 - Recall that a family of solutions includes...Ch. 4.1 - Recall that a family of solutions includes...Ch. 4.1 - Recall that a family of solutions includes...Ch. 4.1 - Recall that a family of solutions includes...Ch. 4.1 - Recall that a family of solutions includes...Ch. 4.1 - Recall that a family of solutions includes...Ch. 4.1 - Recall that a family of solutions includes...Ch. 4.1 - Recall that a family of solutions includes...Ch. 4.1 - Recall that a family of solutions includes...Ch. 4.1 - Recall that a family of solutions includes...Ch. 4.1 - Recall that a family of solutions includes...Ch. 4.1 - Recall that a family of solutions includes...Ch. 4.1 - Recall that a family of solutions includes...Ch. 4.2 - For the following problems, use the direction...Ch. 4.2 - For the following problems, use the direction...Ch. 4.2 - For the following problems, use the direction...Ch. 4.2 - For the following problems, use the direction...Ch. 4.2 - For the following problems, use the direction...Ch. 4.2 - For the following problems, use the direction...Ch. 4.2 - For the following problems, use the direction...Ch. 4.2 - For the following problems, use the direction...Ch. 4.2 - Draw the direction field for the following...Ch. 4.2 - Draw the direction field for the following...Ch. 4.2 - Draw the direction field for the following...Ch. 4.2 - Draw the direction field for the following...Ch. 4.2 - Draw the direction field for the following...Ch. 4.2 - Draw the directional field for the following...Ch. 4.2 - Draw the directional field for the following...Ch. 4.2 - Draw the directional field for the following...Ch. 4.2 - Draw the directional field for the following...Ch. 4.2 - Draw the directional field for the following...Ch. 4.2 - Match the direction field with the given...Ch. 4.2 - Match the direction field with the given...Ch. 4.2 - Match the direction field with the given...Ch. 4.2 - Match the direction field with the given...Ch. 4.2 - Match the direction field with the given...Ch. 4.2 - Match the direction field with the given...Ch. 4.2 - Match the direction field with the given...Ch. 4.2 - Match the direction field with the given...Ch. 4.2 - Match the direction field with the given...Ch. 4.2 - Match the direction field with the given...Ch. 4.2 - Estimate the following solutions using Euler’s...Ch. 4.2 - Estimate the following solutions using Euler’s...Ch. 4.2 - WEstimate the following solutions using Euler’s...Ch. 4.2 - Estimate the following solutions using Euler’s...Ch. 4.2 - Estimate the following solutions using Euler’s...Ch. 4.2 - Estimate the following solutions using Euler’s...Ch. 4.2 - Estimate the following solutions using Euler’s...Ch. 4.2 - Estimate the following solutions using Euler’s...Ch. 4.2 - Estimate the following solutions using Euler’s...Ch. 4.2 - Estimate the following solutions using Euler’s...Ch. 4.2 - Differential equations can be used to model...Ch. 4.2 - Differential equations can be used to model...Ch. 4.2 - Differential equations can be used to model...Ch. 4.2 - Differential equations can be used to model...Ch. 4.2 - Differential equations can be used to model...Ch. 4.2 - Differential equations can be used to model...Ch. 4.2 - Differential equations can be used to model...Ch. 4.2 - Differential equations can be used to model...Ch. 4.2 - Differential equations can be used to model...Ch. 4.2 - Differential equations can be used to model...Ch. 4.2 - Consider the initial-value problem y' = 2y, y(0) =...Ch. 4.2 - Consider the initial-value problem y' = 2y, y(0) =...Ch. 4.2 - Consider the initial-value problem y' = 2y, y(0) =...Ch. 4.2 - Consider the initial-value problem y' = 2y, y(0) =...Ch. 4.2 - Consider the initial-value problem y' = 2y, y(0) =...Ch. 4.3 - Solve the following initial-value problems with...Ch. 4.3 - Solve the following initial-value problems with...Ch. 4.3 - Solve the following initial-value problems with...Ch. 4.3 - Solve the following initial-value problems with...Ch. 4.3 - Find the general solution to the differential...Ch. 4.3 - Find the general solution to the differential...Ch. 4.3 - Find the general solution to the differential...Ch. 4.3 - Find the general solution to the differential...Ch. 4.3 - Find the general solution to the differential...Ch. 4.3 - Find the general solution to the differential...Ch. 4.3 - Find the general solution to the differential...Ch. 4.3 - Find the general solution to the differential...Ch. 4.3 - Find the general solution to the differential...Ch. 4.3 - Find the general solution to the differential...Ch. 4.3 - Find the solution to the initial-value problem....Ch. 4.3 - Find the solution to the initial-value problem....Ch. 4.3 - Find the solution to the initial-value problem....Ch. 4.3 - Find the solution to the initial-value problem....Ch. 4.3 - Find the solution to the initial-value problem....Ch. 4.3 - Find the solution to the initial-value problem....Ch. 4.3 - Find the solution to the initial-value problem....Ch. 4.3 - Find the solution to the initial-value problem....Ch. 4.3 - Find the solution to the initial-value problem....Ch. 4.3 - Find the solution to the initial-value problem....Ch. 4.3 - For the following problems, use a software program...Ch. 4.3 - For the following problems, use a software program...Ch. 4.3 - For the following problems, use a software program...Ch. 4.3 - For the following problems, use a software program...Ch. 4.3 - For the following problems, use a software program...Ch. 4.3 - Most drugs in the bloodstream decay according to...Ch. 4.3 - A drug is administered intravenously to a patient...Ch. 4.3 - [T] How often should a drug be taken if its dose...Ch. 4.3 - A tank contains 1 kilogram of salt dissolved in...Ch. 4.3 - A tank containing 10 kilograms of salt dissolved...Ch. 4.3 - [T] For the preceding problem, find flow much salt...Ch. 4.3 - Torricelli’s law states that for a water tank with...Ch. 4.3 - For the preceding problem, determine how long it...Ch. 4.3 - For the following problems, use Newton’s law of...Ch. 4.3 - For the following problems, use Newton’s law of...Ch. 4.3 - For the following problems, use Newton’s law of...Ch. 4.3 - For the following problems, use Newton’s law of...Ch. 4.3 - For the following problems, use Newton’s law of...Ch. 4.3 - For the following problems, use Newton’s law of...Ch. 4.3 - For the following problems, use Newton’s law of...Ch. 4.3 - For the following problems, use Newton’s law of...Ch. 4.3 - For the following problems, use Newton’s law of...Ch. 4.3 - For the following problems, use Newton’s law of...Ch. 4.3 - For the following problems, use Newton’s law of...Ch. 4.3 - For the following problems, use Newton’s law of...Ch. 4.4 - Student Project: Logistic Equation with a...Ch. 4.4 - Student Project: Logistic Equation with a...Ch. 4.4 - Student Project: Logistic Equation with a...Ch. 4.4 - Student Project: Logistic Equation with a...Ch. 4.4 - For the following problems, consider the logistic...Ch. 4.4 - For the following problems, consider the logistic...Ch. 4.4 - For the following problems, consider the logistic...Ch. 4.4 - For the following problems, consider the logistic...Ch. 4.4 - For the following problems, consider the logistic...Ch. 4.4 - A population of deer inside a park has a carrying...Ch. 4.4 - A population of frogs in a pond has a growth rate...Ch. 4.4 - [T] Bacteria grow at a rate of 2O per hour in a...Ch. 4.4 - [T] Rabbits in a park have an initial population...Ch. 4.4 - [T] Two monkeys are placed on an island. After 5...Ch. 4.4 - [T] A butterfly sanctuary is built that can hold...Ch. 4.4 - The following problems consider the logistic...Ch. 4.4 - The following problems consider the logistic...Ch. 4.4 - The following problems consider the logistic...Ch. 4.4 - The following problems consider the logistic...Ch. 4.4 - The following problems consider the logistic...Ch. 4.4 - It is more likely that the amount of fishing is...Ch. 4.4 - It is more likely that the amount of fishing is...Ch. 4.4 - It is more likely that the amount of fishing is...Ch. 4.4 - It is more likely that the amount of fishing is...Ch. 4.4 - It is more likely that the amount of fishing is...Ch. 4.4 - The following problems add in a minimal threshold...Ch. 4.4 - The following problems add in a minimal threshold...Ch. 4.4 - The following problems add in a minimal threshold...Ch. 4.4 - The following problems add in a minimal threshold...Ch. 4.4 - The following problems add in a minimal threshold...Ch. 4.4 - The following questions consider the Gompertz...Ch. 4.4 - The following questions consider the Gompertz...Ch. 4.4 - The following questions consider the Gompertz...Ch. 4.4 - The following questions consider the Gompertz...Ch. 4.4 - The following questions consider the Gompertz...Ch. 4.4 - The following questions consider the Gompertz...Ch. 4.4 - The following questions consider the Gompertz...Ch. 4.4 - The following questions consider the Gompertz...Ch. 4.4 - The following questions consider the Gompertz...Ch. 4.4 - Below is a table of the populations of whooping...Ch. 4.4 - Below is a table of the populations of whooping...Ch. 4.4 - Below is a table of the populations of whooping...Ch. 4.4 - Below is a table of the populations of whooping...Ch. 4.4 - Below is a table of the populations of whooping...Ch. 4.5 - Are the following differential equations linear?...Ch. 4.5 - Are the following differential equations linear?...Ch. 4.5 - Are the following differential equations linear?...Ch. 4.5 - Are the following differential equations linear?...Ch. 4.5 - Are the following differential equations linear?...Ch. 4.5 - Write the following first-order differential...Ch. 4.5 - Write the following first-order differential...Ch. 4.5 - Write the following first-order differential...Ch. 4.5 - Write the following first-order differential...Ch. 4.5 - Write the following first-order differential...Ch. 4.5 - What are the integrating factors for the following...Ch. 4.5 - What are the integrating factors for the following...Ch. 4.5 - What are the integrating factors for the following...Ch. 4.5 - What are the integrating factors for the following...Ch. 4.5 - What are the integrating factors for the following...Ch. 4.5 - Solve the following differential equations by...Ch. 4.5 - Solve the following differential equations by...Ch. 4.5 - Solve the following differential equations by...Ch. 4.5 - Solve the following differential equations by...Ch. 4.5 - Solve the following differential equations by...Ch. 4.5 - Solve the following differential equations by...Ch. 4.5 - Solve the following differential equations by...Ch. 4.5 - Solve the following differential equations by...Ch. 4.5 - Solve the following differential equations by...Ch. 4.5 - Solve the following differential equations by...Ch. 4.5 - Solve the following differential equations. Use...Ch. 4.5 - Solve the following differential equations. Use...Ch. 4.5 - Solve the following differential equations. Use...Ch. 4.5 - Solve the following differential equations. Use...Ch. 4.5 - Solve the following differential equations. Use...Ch. 4.5 - Solve the following differential equations. Use...Ch. 4.5 - Solve the following differential equations. Use...Ch. 4.5 - Solve the following differential equations. Use...Ch. 4.5 - Solve the following initial-value problems by...Ch. 4.5 - Solve the following initial-value problems by...Ch. 4.5 - Solve the following initial-value problems by...Ch. 4.5 - Solve the following initial-value problems by...Ch. 4.5 - Solve the following initial-value problems by...Ch. 4.5 - Solve the following initial-value problems by...Ch. 4.5 - Solve the following initial-value problems by...Ch. 4.5 - Solve the following initial-value problems by...Ch. 4.5 - Solve the following initial-value problems by...Ch. 4.5 - Solve the following initial-value problems by...Ch. 4.5 - A falling object of mass m can reach terminal...Ch. 4.5 - Using your expression from the preceding problem,...Ch. 4.5 - [T] Using your equation for terminal velocity,...Ch. 4.5 - A more accurate way to describe terminal velocity...Ch. 4.5 - Using your expression from the preceding problem,...Ch. 4.5 - [T] Using your equation for terminal velocity,...Ch. 4.5 - For the following problems, determine how...Ch. 4.5 - For the following problems, determine how...Ch. 4.5 - For the following problems, determine how...Ch. 4.5 - For the following problems, determine how...Ch. 4.5 - For the following problems, determine how...Ch. 4 - True or False? Justify your answer with a proof or...Ch. 4 - True or False? Justify your answer with a proof or...Ch. 4 - True or False? Justify your answer with a proof or...Ch. 4 - True or False? Justify your answer with a proof or...Ch. 4 - For the following problems, find the general...Ch. 4 - For the following problems, find the general...Ch. 4 - For the following problems, find the general...Ch. 4 - For the following problems, find the general...Ch. 4 - For the following problems, find the general...Ch. 4 - For the following problems, find the general...Ch. 4 - For the following problems, find the solution to...Ch. 4 - For the following problems, find the solution to...Ch. 4 - For the following problems, find the solution to...Ch. 4 - For the following problems, find the solution to...Ch. 4 - For the following problems, find the solution to...Ch. 4 - For the following problems, find the solution to...Ch. 4 - For the following problems, draw the directional...Ch. 4 - For the following problems, draw the directional...Ch. 4 - For the following problems, use Euler’s Method...Ch. 4 - For the following problems, use Euler’s Method...Ch. 4 - For the following problems, set up and solve the...Ch. 4 - For the following problems, set up and solve the...Ch. 4 - For the following problems, set up and solve the...Ch. 4 - For the following problems, set up and solve the...Ch. 4 - For the following problems, set up and solve the...Ch. 4 - For the following problems, set up and solve the...Ch. 4 - For the following problems, set up and solve the...Ch. 4 - For the following problems, set up and solve the...Ch. 4 - For the following problems, set up and solve the...
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- R₂ = X2 2) slots per pole per phase 3/31 msl 180 60 Kd Ka Sin (1) Isin (6) sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed, 120*50 1000 6 S = 1000-950 1000 Copper bosses: 5kw Rotor input 5 0.05 : loo kw 6) 1 اذا ميريد شرح الكتب فقط 100 7) rotor DC ined sove in peaper I need a detailed solution on paper please Find the general solution of the following equations: Q2lyl-4y+13y=esinx. Find the general solution of the following equations: " Qly (49) - 16y= 0. 151arrow_forward۳/۱ R₂ = X2 2) slots per pole per phase = 3/31 B-18060 msl kd Kasi Sin (1) I sin (6) sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed s = 1000-950 1000 Copper losses: 5kw Rotor input 5 0.05 6) 1 120 x 50 G loo kw اذا میرید شرح الكتب فقط look 7) rotor DC ined sove in peaper I need a detailed solution on paper dy please 04 12=-cosx.y + 2cosx with y(x) = 1 か 'Oy + xlny + xe")dx + (xsiny + xlnx +*dy=0. 01arrow_forward٣/١ R2X2 2) slots per pole per phase = 3/31 B, 18060 msl kd Kas Sin (1) 1sin() sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speeds S = 1000-950 1000 Copper bosses 5kw 120*50 loca G Rotor input 5 loo kw 0.05 6) 1 اذا ميريد شرح الكتب فقط lookw 7) rotor ined sove in peaper I need a detailed solution on paper please DC 口 04 on its wheels as shown in figure. The the door is 8 m below the free surface o is located at the center of the d no water leaks an accident and lands at the bottom of the lake 12m high and I m wide, and the top edge of water Determine the hydrostatic force on the discuss if the driver can open the door, if ong person can lift 100 kg, the passenger The door can be approximated as a vertical rec | 279|-|(23+2+12+20=2) AA Find the general solution of the following equations: 11 - 1/4+xy/-(1-x²³)= 0. 2arrow_forward
- ۳/۱ : +0 العنوان I need a detailed drawing with explanation R₂ = X2 2) slots per pole per phase 3/31 Le msl 180 60 Kd Ka Sin (1) Isin (6) sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed, 120*50 1000 6 S = 1000-950 1000 Copper bosses: 5kw Rotor input 5 loo kw 0.05 6) 1 اذا ميريد شرح الكتب فقط ١٥٠ 7) rotov DC ined sove in peaper I need a detailed solution on paper please 064 Q1// Find the solution of: ( texty Q1// Find the solution of: '' y' -2y= 22% √y³arrow_forwardR2X2 2) slots per pole per phase = 3/31 B-180-60 msl kd Ka, Sin (1) I sin (6) sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed s = 1000-950 1000 Copper losses 5kw 120 50 G Rotor input 5 loo kw 6) 1 ۳/۱ 0.05 إذا ميريد شرح الكتب فقط look 7) rotov DC ined sove in peaper I need a detailed solution on paper please Find the general solution of the following equations: " yll + 4y = tan2x. Find the general solution of the following equations: 01-24+7=0 T el [A] G ха =T Marrow_forwardR₂ = X2 2) slots per pole per phase = 3/31 B-18060 msl kd Kasi Sin (1) I sin (6) sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed s = 1000-950 1000 Copper losses: 5kw Rotor input 5 0.05 6) 1 120 x 50 G loo kw اذا میرید شرح الكتب فقط look 7) rotor DC ined sove in peaper I need a detailed solution on paper please 0 64 Solve the following equations: = dx x²+y2 with y(0) = 1. 7357 Solve the following equations: dy x³+3xy² Q1// = dx 3x²y+y³° 01arrow_forward
- ٣/١ R2X2 2) slots per pole per phase = 3/3 1 B18060 msl Kd 3 Kol Sin (1) 1sin() sin(30) Sin (30) اذا میرید شرح الكتب بس 0 بالفراغ 3) cos (30) 0.866 4) Rotating 5) Synchronous speeds 120*50 G looo 1000-950 1000 50:05 Copper losses: 5kw Rotor input 5 loo kw 0.05 6) 1 اذا ميريد شرح الكتب فقط look 7) rotor DC ined sove in peaper I need a detailed solution on paper please 0 64 (Find the solution of the initial-valued problems: xy' + 2y = x³e* ;y(1) = 0 Q1// Find the solution of: (1) y' + ytqpx = see²x y³arrow_forwardA fluid has density 800 kg/m³ and flows with velocity v = xi + yj + zk, where x, y, and z are measured in meters, and the components of u are measured in meters per second. Find the rate of flow outward through the part of the paraboloid z = 64 - x² - y² that lies above the xy plane.arrow_forward۳/۱ : +0 العنوان I need a detailed drawing with explanation R₂ = X2 2) slots per pole per phase 3/31 Le msl 180 60 Kd Ka Sin (1) Isin (6) sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed, 120 x 50 S = 1000-950 1000 Copper bosses: 5kw Rotor input 5 6 : loo kw 6) 1 0.05 اذا ميريد شرح الكتب فقط 100 7) rotor DC 1000 ined sove in peaper I need a detailed solution on paper please // Find the solution of: |(2xy³ + 4x)y' = x²y² + y² 351 // Find the solution of: (1) 2xyy' = 1+ y² 01 175 T Τ Marrow_forward
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