تكلم مع الذكاء الاصطناعي
Deck 8: Mathematical Modeling With Differential Equations
ملء الشاشة (f)
سؤال
Solve the differential equation. 
سؤال
What is the solution to the following differential equation? 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Suppose 
, find the value of the slope field at 
.
A)
B)
C)
D)
E)
, find the value of the slope field at .A)
B)
C)
D)
E)
سؤال
Solve the differential equation. 
سؤال
What is the solution to the following differential equation? 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
A tank is filled with 
gallons of water with 
oz of salt dissolved in it. At t = 0, salt solution containing 
oz/gal enters the tank at a rate of 
gal/min. Well-mixed solution leaves at the same rate. Write down an expression that gives the amount of salt S, in the tank at any time t.
gallons of water with oz of salt dissolved in it. At t = 0, salt solution containing oz/gal enters the tank at a rate of gal/min. Well-mixed solution leaves at the same rate. Write down an expression that gives the amount of salt S, in the tank at any time t. سؤال
Use Euler's method with the step size of 
to approximate solution to the initial-value problem 
at 
.
A)
B)
C)
D)
E)
to approximate solution to the initial-value problem at .A)
B)
C)
D)
E)
سؤال
Solve the following differential equation. 
سؤال
Solve the following differential equation. 
سؤال
What is the solution to the following differential equation? 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Solve the following differential equation. 
سؤال
Suppose 
, find the value of the slope field at 
.
A)
B)
C)
D)
E)
, find the value of the slope field at .A)
B)
C)
D)
E)
سؤال
A tank is filled with 
gallons of water in which 
oz of salt is dissolved. At t = 0, salt solution containing 
oz/gal enters the tank at a rate of 
gal/min. Well mixed solution leaves at the same rate. Write down an expression that gives the amount of salt S, in the tank at any time t.
gallons of water in which oz of salt is dissolved. At t = 0, salt solution containing oz/gal enters the tank at a rate of gal/min. Well mixed solution leaves at the same rate. Write down an expression that gives the amount of salt S, in the tank at any time t. سؤال
Suppose 
, find the value of the slope field at 
.
A)
B)
C)
D)
E)
, find the value of the slope field at .A)
B)
C)
D)
E)
سؤال
Suppose 
, find the value of the slope field at 
.
A)
B)
C)
D)
E)
, find the value of the slope field at .A)
B)
C)
D)
E)
سؤال
Solve the differential equation by separation of variables. 
سؤال
Suppose 
. Find the value of the slope field at 
.
A)
B)
C)
D)
E)
. Find the value of the slope field at .A)
B)
C)
D)
E)
سؤال
Solve the following initial-value problem. 
سؤال
A tank initially contains 
gal of pure water. At time 
a solution containing 
oz of dissolved salt per gal flows into the tank at 
gal/min. The well stirred mixture is pumped out of the tank at the same rate. Write down an expression for the amount of salt in the tank at any time. How much salt is present at the end of 
minutes?
gal of pure water. At time a solution containing oz of dissolved salt per gal flows into the tank at gal/min. The well stirred mixture is pumped out of the tank at the same rate. Write down an expression for the amount of salt in the tank at any time. How much salt is present at the end of minutes? سؤال
Solve the differential equation using any method you wish. 
سؤال
Use Euler's method with the step size of 
to compute the approximate solution to the initial-value problem 
at 
.
to compute the approximate solution to the initial-value problem at . سؤال
What is the solution to the following differential equation? 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use Euler's method with the step size of 
to compute the approximate solution to the initial-value problem 
at 
. Round your answer to six decimal places if need be.
to compute the approximate solution to the initial-value problem at . Round your answer to six decimal places if need be. سؤال
Solve the differential equation using any method you wish. 
سؤال
What is the solution to the following differential equation? 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use Euler's method with the step size of 
to approximate solution to the initial-value problem 
at 
.
A)
B)
C)
D)
E)
to approximate solution to the initial-value problem at .A)
B)
C)
D)
E)
سؤال
Use Euler's method with the step size of 
to compute the approximate solution to the initial-valued problem 
at 
. Round your answer to six decimal places if need be.
to compute the approximate solution to the initial-valued problem at . Round your answer to six decimal places if need be. سؤال
What is the solution to the following differential equation? 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
What is the solution to the following differential equation? 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use Euler's method with the step size of 
to approximate solution to the initial-value problem 
at 
.
A)
B)
C)
D)
E)
to approximate solution to the initial-value problem at .A)
B)
C)
D)
E)
سؤال
What is the solution to the following initial-value problem? (Use separation of variables!) 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
What is the solution to the following differential equation? 
سؤال
Use Euler's method with the step size of 
to approximate solution to the initial-value problem 
at 
. You will need to take two steps here!
A)
B)
C)
D)
E)
to approximate solution to the initial-value problem at . You will need to take two steps here!A)
B)
C)
D)
E)
سؤال
Solve the differential equation by separation of variables. 
سؤال
Use Euler's method with the step size of 
to approximate solution to the initial-value problem 
at 
.
A)
B)
C)
D)
E)
to approximate solution to the initial-value problem at .A)
B)
C)
D)
E)
سؤال
What is the solution to the following differential equation? (Use separation of variables!) 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Solve the differential equation by separation of variables. 
سؤال
Use Euler's method with the step size of 
to approximate solution to the initial-value problem 
at 
.
A)
B)
C)
D)
E)
to approximate solution to the initial-value problem at .A)
B)
C)
D)
E)
سؤال
What is the solution to the following differential equation? (Use separation of variables!) 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Solve the differential equation by separation of variables. 
سؤال
Solve the initial-value problem. 
سؤال
Find the exponential decay model 
that satisfies 
, if the halving time is 
years. Round any numerical quantities to 6 decimal places if need be.
A)
B)
C)
D)
E)
that satisfies , if the halving time is years. Round any numerical quantities to 6 decimal places if need be.A)
B)
C)
D)
E)
سؤال
Find the exponential decay model 
that satisfies 
, if the halving time is 
years.
A)
B)
C)
D)
E)
that satisfies , if the halving time is years.A)
B)
C)
D)
E)
سؤال
Solve the initial-value problem. 
سؤال
For radioactive carbon-14, 
If 330 g of carbon exist today in a sealed container, how many grams of carbon-14 will be left after 
years? Round your answer to 6 decimal places.
If 330 g of carbon exist today in a sealed container, how many grams of carbon-14 will be left after years? Round your answer to 6 decimal places. سؤال
A particle moving along the x-axis encounters a resisting force that results in an acceleration of 
Given that 
cm and v = 
cm/s at t = 0, find the velocity v as a function of t.
Given that cm and v = cm/s at t = 0, find the velocity v as a function of t. سؤال
If 
the situation modeled is
A) increasing
B) decreasing
C) remaining constant
D) More information is needed.
E) Cannot be determined.
the situation modeled isA) increasing
B) decreasing
C) remaining constant
D) More information is needed.
E) Cannot be determined.
سؤال
Suppose that a radioactive substance decays with a half-life of 
years. Find a function that expresses the amount of substance present at time t if there are 
g of the substance initially present. Round answers to 3 decimal places if need be.
A)
B)
C)
D)
E)
years. Find a function that expresses the amount of substance present at time t if there are g of the substance initially present. Round answers to 3 decimal places if need be.A)
B)
C)
D)
E)
سؤال
A particle moving along the x-axis encounters a resisting force that results in an acceleration of 
Given that 
cm and v = 35 cm/s at t = 0, find the position x as a function of t.
Given that cm and v = 35 cm/s at t = 0, find the position x as a function of t. سؤال
Solve the initial-value problem. 
سؤال
Find the exponential growth model 
that satisfies 
, if the doubling time is 
years.
A)
B)
C)
D)
E)
that satisfies , if the doubling time is years.A)
B)
C)
D)
E)
سؤال
A cup of water with a temperature of 
C is placed in a room at constant temperature 
C. It takes 
minutes for the cup to cool to 
. Assuming Newton's Law of Cooling applies, find the temperature, T, of the cup of water at any time t. Express all numerical quantities in exact form.
C is placed in a room at constant temperature C. It takes minutes for the cup to cool to . Assuming Newton's Law of Cooling applies, find the temperature, T, of the cup of water at any time t. Express all numerical quantities in exact form. سؤال
Solve the initial-value problem. 
سؤال
Find the exponential growth model 
that satisfies 
, if the doubling time is 
years. Round any numerical quantities to 6 decimal places if need be.
A)
B)
C)
D)
E)
that satisfies , if the doubling time is years. Round any numerical quantities to 6 decimal places if need be.A)
B)
C)
D)
E)
سؤال
Solve the initial-value problem. 
سؤال
If 
the situation modeled is
A) increasing
B) decreasing
C) remaining constant
D) More information is needed.
E) Cannot be determined.
the situation modeled isA) increasing
B) decreasing
C) remaining constant
D) More information is needed.
E) Cannot be determined.
سؤال
If 
the situation modeled is
A) increasing
B) decreasing
C) remaining constant
D) More information is needed.
E) Cannot be determined.
the situation modeled isA) increasing
B) decreasing
C) remaining constant
D) More information is needed.
E) Cannot be determined.
سؤال
A cup of water with a temperature of 
C is placed in a room with constant temperature 
C. It takes 
minutes for the cup to cool to 
. Assuming Newton's Law of Cooling applies, find the temperature, T, of the cup of water at any time t. Express all numerical quantities in exact form.
C is placed in a room with constant temperature C. It takes minutes for the cup to cool to . Assuming Newton's Law of Cooling applies, find the temperature, T, of the cup of water at any time t. Express all numerical quantities in exact form. سؤال
A certain radioactive substance has a half-life of 
years. Approximately how many years will it take so that only 
of the original amount remains? Round your answers to six decimal places.
years. Approximately how many years will it take so that only of the original amount remains? Round your answers to six decimal places. سؤال
Suppose 5 grams of a radioactive substance decays according to the equation 
If it takes 
years for the substance to reduce to 
of its original mass, write an equation for the amount of the substance present as a function of time.
If it takes years for the substance to reduce to of its original mass, write an equation for the amount of the substance present as a function of time. سؤال
State the order of the differential equation, and decide which family of functions is a solution. 
A)
; 2nd order
B)
; 1st order
C)
; 1st order
D)
; 2nd order
E)
; 2nd order
A)
; 2nd orderB)
; 1st orderC)
; 1st orderD)
; 2nd orderE)
; 2nd order سؤال
Solve the initial-value problem. 
سؤال
State the order of the differential equation, and decide which family of functions is a solution. 
A)
; 2nd order
B)
; 1st order
C)
; 1st order
D)
; 2nd order
E)
; 2nd order
A)
; 2nd orderB)
; 1st orderC)
; 1st orderD)
; 2nd orderE)
; 2nd order سؤال
Solve the initial-value problem. 
سؤال
If 
the situation modeled is
A) increasing
B) decreasing
C) remaining constant
D) More information is needed.
E) Cannot be determined.
the situation modeled isA) increasing
B) decreasing
C) remaining constant
D) More information is needed.
E) Cannot be determined.
سؤال
Solve the initial-value problem. 
سؤال
Solve the initial-value problem. 
سؤال
Suppose that an initial population of 
bacteria dies exponentially at a rate of 
% per hour. How many bacteria are present after t hours?
A)
B)
C)
D)
E)
bacteria dies exponentially at a rate of % per hour. How many bacteria are present after t hours?A)
B)
C)
D)
E)
سؤال
Suppose that an initial population of 
bacteria grows exponentially at a rate of 
% per hour. How many bacteria are present after t hours?
A)
B)
C)
D)
E)
bacteria grows exponentially at a rate of % per hour. How many bacteria are present after t hours?A)
B)
C)
D)
E)
سؤال
Solve the initial-value problem. 
سؤال
State the order of the differential equation, and decide which family of functions is a solution. 
A)
; 1st order
B)
; 1st order
C)
; 2nd order
D)
; 2nd order
E)
; 2nd order
A)
; 1st orderB)
; 1st orderC)
; 2nd orderD)
; 2nd orderE)
; 2nd order سؤال
If 
the situation modeled is
A) increasing
B) decreasing
C) remaining constant
D) More information is needed.
E) Cannot be determined.
the situation modeled isA) increasing
B) decreasing
C) remaining constant
D) More information is needed.
E) Cannot be determined.
سؤال
If 
the situation modeled is
A) increasing
B) decreasing
C) remaining constant
D) More information is needed.
E) Cannot be determined.
the situation modeled isA) increasing
B) decreasing
C) remaining constant
D) More information is needed.
E) Cannot be determined.
سؤال
Solve the initial-value problem. 
سؤال
State the order of the differential equation, and decide which family of functions is a solution. 
A)
; 1st order
B)
; 1st order
C)
; 2nd order
D)
; 1st order
E)
; 2nd order
A)
; 1st orderB)
; 1st orderC)
; 2nd orderD)
; 1st orderE)
; 2nd order سؤال
Solve the initial-value problem. 
سؤال
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ملء الشاشة (f)
Deck 8: Mathematical Modeling With Differential Equations
1
Solve the differential equation.
2
What is the solution to the following differential equation?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
3
Suppose , find the value of the slope field at .
A)
B)
C)
D)
E)
, find the value of the slope field at .A)
B)
C)
D)
E)
4
Solve the differential equation.
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 77 في هذه المجموعة.
فتح الحزمة
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5
What is the solution to the following differential equation?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 77 في هذه المجموعة.
فتح الحزمة
k this deck
6
A tank is filled with gallons of water with oz of salt dissolved in it. At t = 0, salt solution containing oz/gal enters the tank at a rate of gal/min. Well-mixed solution leaves at the same rate. Write down an expression that gives the amount of salt S, in the tank at any time t.
gallons of water with oz of salt dissolved in it. At t = 0, salt solution containing oz/gal enters the tank at a rate of gal/min. Well-mixed solution leaves at the same rate. Write down an expression that gives the amount of salt S, in the tank at any time t. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 77 في هذه المجموعة.
فتح الحزمة
k this deck
7
Use Euler's method with the step size of to approximate solution to the initial-value problem at .
A)
B)
C)
D)
E)
to approximate solution to the initial-value problem at .A)
B)
C)
D)
E)
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 77 في هذه المجموعة.
فتح الحزمة
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8
Solve the following differential equation.
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 77 في هذه المجموعة.
فتح الحزمة
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9
Solve the following differential equation.
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 77 في هذه المجموعة.
فتح الحزمة
k this deck
10
What is the solution to the following differential equation?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 77 في هذه المجموعة.
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11
Solve the following differential equation.
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 77 في هذه المجموعة.
فتح الحزمة
k this deck
12
Suppose , find the value of the slope field at .
A)
B)
C)
D)
E)
, find the value of the slope field at .A)
B)
C)
D)
E)
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 77 في هذه المجموعة.
فتح الحزمة
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13
A tank is filled with gallons of water in which oz of salt is dissolved. At t = 0, salt solution containing oz/gal enters the tank at a rate of gal/min. Well mixed solution leaves at the same rate. Write down an expression that gives the amount of salt S, in the tank at any time t.
gallons of water in which oz of salt is dissolved. At t = 0, salt solution containing oz/gal enters the tank at a rate of gal/min. Well mixed solution leaves at the same rate. Write down an expression that gives the amount of salt S, in the tank at any time t. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 77 في هذه المجموعة.
فتح الحزمة
k this deck
14
Suppose , find the value of the slope field at .
A)
B)
C)
D)
E)
, find the value of the slope field at .A)
B)
C)
D)
E)
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 77 في هذه المجموعة.
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15
Suppose , find the value of the slope field at .
A)
B)
C)
D)
E)
, find the value of the slope field at .A)
B)
C)
D)
E)
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 77 في هذه المجموعة.
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16
Solve the differential equation by separation of variables.
فتح الحزمة
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فتح الحزمة
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17
Suppose . Find the value of the slope field at .
A)
B)
C)
D)
E)
. Find the value of the slope field at .A)
B)
C)
D)
E)
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 77 في هذه المجموعة.
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18
Solve the following initial-value problem.
فتح الحزمة
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فتح الحزمة
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19
A tank initially contains gal of pure water. At time a solution containing oz of dissolved salt per gal flows into the tank at gal/min. The well stirred mixture is pumped out of the tank at the same rate. Write down an expression for the amount of salt in the tank at any time. How much salt is present at the end of minutes?
gal of pure water. At time a solution containing oz of dissolved salt per gal flows into the tank at gal/min. The well stirred mixture is pumped out of the tank at the same rate. Write down an expression for the amount of salt in the tank at any time. How much salt is present at the end of minutes? فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 77 في هذه المجموعة.
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20
Solve the differential equation using any method you wish.
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 77 في هذه المجموعة.
فتح الحزمة
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21
Use Euler's method with the step size of to compute the approximate solution to the initial-value problem at .
to compute the approximate solution to the initial-value problem at . فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 77 في هذه المجموعة.
فتح الحزمة
k this deck
22
What is the solution to the following differential equation?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 77 في هذه المجموعة.
فتح الحزمة
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23
Use Euler's method with the step size of to compute the approximate solution to the initial-value problem at . Round your answer to six decimal places if need be.
to compute the approximate solution to the initial-value problem at . Round your answer to six decimal places if need be. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 77 في هذه المجموعة.
فتح الحزمة
k this deck
24
Solve the differential equation using any method you wish.
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 77 في هذه المجموعة.
فتح الحزمة
k this deck
25
What is the solution to the following differential equation?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 77 في هذه المجموعة.
فتح الحزمة
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26
Use Euler's method with the step size of to approximate solution to the initial-value problem at .
A)
B)
C)
D)
E)
to approximate solution to the initial-value problem at .A)
B)
C)
D)
E)
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 77 في هذه المجموعة.
فتح الحزمة
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27
Use Euler's method with the step size of to compute the approximate solution to the initial-valued problem at . Round your answer to six decimal places if need be.
to compute the approximate solution to the initial-valued problem at . Round your answer to six decimal places if need be. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 77 في هذه المجموعة.
فتح الحزمة
k this deck
28
What is the solution to the following differential equation?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 77 في هذه المجموعة.
فتح الحزمة
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29
What is the solution to the following differential equation?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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30
Use Euler's method with the step size of to approximate solution to the initial-value problem at .
A)
B)
C)
D)
E)
to approximate solution to the initial-value problem at .A)
B)
C)
D)
E)
فتح الحزمة
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31
What is the solution to the following initial-value problem? (Use separation of variables!)
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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32
What is the solution to the following differential equation?
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33
Use Euler's method with the step size of to approximate solution to the initial-value problem at . You will need to take two steps here!
A)
B)
C)
D)
E)
to approximate solution to the initial-value problem at . You will need to take two steps here!A)
B)
C)
D)
E)
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34
Solve the differential equation by separation of variables.
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35
Use Euler's method with the step size of to approximate solution to the initial-value problem at .
A)
B)
C)
D)
E)
to approximate solution to the initial-value problem at .A)
B)
C)
D)
E)
فتح الحزمة
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36
What is the solution to the following differential equation? (Use separation of variables!)
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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37
Solve the differential equation by separation of variables.
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38
Use Euler's method with the step size of to approximate solution to the initial-value problem at .
A)
B)
C)
D)
E)
to approximate solution to the initial-value problem at .A)
B)
C)
D)
E)
فتح الحزمة
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39
What is the solution to the following differential equation? (Use separation of variables!)
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
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40
Solve the differential equation by separation of variables.
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41
Solve the initial-value problem.
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42
Find the exponential decay model that satisfies , if the halving time is years. Round any numerical quantities to 6 decimal places if need be.
A)
B)
C)
D)
E)
that satisfies , if the halving time is years. Round any numerical quantities to 6 decimal places if need be.A)
B)
C)
D)
E)
فتح الحزمة
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43
Find the exponential decay model that satisfies , if the halving time is years.
A)
B)
C)
D)
E)
that satisfies , if the halving time is years.A)
B)
C)
D)
E)
فتح الحزمة
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44
Solve the initial-value problem.
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45
For radioactive carbon-14, If 330 g of carbon exist today in a sealed container, how many grams of carbon-14 will be left after years? Round your answer to 6 decimal places.
If 330 g of carbon exist today in a sealed container, how many grams of carbon-14 will be left after years? Round your answer to 6 decimal places. فتح الحزمة
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46
A particle moving along the x-axis encounters a resisting force that results in an acceleration of Given that cm and v = cm/s at t = 0, find the velocity v as a function of t.
Given that cm and v = cm/s at t = 0, find the velocity v as a function of t. فتح الحزمة
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47
If the situation modeled is
A) increasing
B) decreasing
C) remaining constant
D) More information is needed.
E) Cannot be determined.
the situation modeled isA) increasing
B) decreasing
C) remaining constant
D) More information is needed.
E) Cannot be determined.
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48
Suppose that a radioactive substance decays with a half-life of years. Find a function that expresses the amount of substance present at time t if there are g of the substance initially present. Round answers to 3 decimal places if need be.
A)
B)
C)
D)
E)
years. Find a function that expresses the amount of substance present at time t if there are g of the substance initially present. Round answers to 3 decimal places if need be.A)
B)
C)
D)
E)
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49
A particle moving along the x-axis encounters a resisting force that results in an acceleration of Given that cm and v = 35 cm/s at t = 0, find the position x as a function of t.
Given that cm and v = 35 cm/s at t = 0, find the position x as a function of t. فتح الحزمة
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50
Solve the initial-value problem.
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51
Find the exponential growth model that satisfies , if the doubling time is years.
A)
B)
C)
D)
E)
that satisfies , if the doubling time is years.A)
B)
C)
D)
E)
فتح الحزمة
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52
A cup of water with a temperature of C is placed in a room at constant temperature C. It takes minutes for the cup to cool to . Assuming Newton's Law of Cooling applies, find the temperature, T, of the cup of water at any time t. Express all numerical quantities in exact form.
C is placed in a room at constant temperature C. It takes minutes for the cup to cool to . Assuming Newton's Law of Cooling applies, find the temperature, T, of the cup of water at any time t. Express all numerical quantities in exact form. فتح الحزمة
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53
Solve the initial-value problem.
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54
Find the exponential growth model that satisfies , if the doubling time is years. Round any numerical quantities to 6 decimal places if need be.
A)
B)
C)
D)
E)
that satisfies , if the doubling time is years. Round any numerical quantities to 6 decimal places if need be.A)
B)
C)
D)
E)
فتح الحزمة
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55
Solve the initial-value problem.
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56
If the situation modeled is
A) increasing
B) decreasing
C) remaining constant
D) More information is needed.
E) Cannot be determined.
the situation modeled isA) increasing
B) decreasing
C) remaining constant
D) More information is needed.
E) Cannot be determined.
فتح الحزمة
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57
If the situation modeled is
A) increasing
B) decreasing
C) remaining constant
D) More information is needed.
E) Cannot be determined.
the situation modeled isA) increasing
B) decreasing
C) remaining constant
D) More information is needed.
E) Cannot be determined.
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 77 في هذه المجموعة.
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58
A cup of water with a temperature of C is placed in a room with constant temperature C. It takes minutes for the cup to cool to . Assuming Newton's Law of Cooling applies, find the temperature, T, of the cup of water at any time t. Express all numerical quantities in exact form.
C is placed in a room with constant temperature C. It takes minutes for the cup to cool to . Assuming Newton's Law of Cooling applies, find the temperature, T, of the cup of water at any time t. Express all numerical quantities in exact form. فتح الحزمة
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59
A certain radioactive substance has a half-life of years. Approximately how many years will it take so that only of the original amount remains? Round your answers to six decimal places.
years. Approximately how many years will it take so that only of the original amount remains? Round your answers to six decimal places. فتح الحزمة
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60
Suppose 5 grams of a radioactive substance decays according to the equation If it takes years for the substance to reduce to of its original mass, write an equation for the amount of the substance present as a function of time.
If it takes years for the substance to reduce to of its original mass, write an equation for the amount of the substance present as a function of time. فتح الحزمة
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61
State the order of the differential equation, and decide which family of functions is a solution.
A) ; 2nd order
B) ; 1st order
C) ; 1st order
D) ; 2nd order
E) ; 2nd order
A)
; 2nd orderB)
; 1st orderC)
; 1st orderD)
; 2nd orderE)
; 2nd order فتح الحزمة
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62
Solve the initial-value problem.
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63
State the order of the differential equation, and decide which family of functions is a solution.
A) ; 2nd order
B) ; 1st order
C) ; 1st order
D) ; 2nd order
E) ; 2nd order
A)
; 2nd orderB)
; 1st orderC)
; 1st orderD)
; 2nd orderE)
; 2nd order فتح الحزمة
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64
Solve the initial-value problem.
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65
If the situation modeled is
A) increasing
B) decreasing
C) remaining constant
D) More information is needed.
E) Cannot be determined.
the situation modeled isA) increasing
B) decreasing
C) remaining constant
D) More information is needed.
E) Cannot be determined.
فتح الحزمة
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66
Solve the initial-value problem.
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67
Solve the initial-value problem.
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68
Suppose that an initial population of bacteria dies exponentially at a rate of % per hour. How many bacteria are present after t hours?
A)
B)
C)
D)
E)
bacteria dies exponentially at a rate of % per hour. How many bacteria are present after t hours?A)
B)
C)
D)
E)
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69
Suppose that an initial population of bacteria grows exponentially at a rate of % per hour. How many bacteria are present after t hours?
A)
B)
C)
D)
E)
bacteria grows exponentially at a rate of % per hour. How many bacteria are present after t hours?A)
B)
C)
D)
E)
فتح الحزمة
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70
Solve the initial-value problem.
فتح الحزمة
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71
State the order of the differential equation, and decide which family of functions is a solution.
A) ; 1st order
B) ; 1st order
C) ; 2nd order
D) ; 2nd order
E) ; 2nd order
A)
; 1st orderB)
; 1st orderC)
; 2nd orderD)
; 2nd orderE)
; 2nd order فتح الحزمة
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72
If the situation modeled is
A) increasing
B) decreasing
C) remaining constant
D) More information is needed.
E) Cannot be determined.
the situation modeled isA) increasing
B) decreasing
C) remaining constant
D) More information is needed.
E) Cannot be determined.
فتح الحزمة
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73
If the situation modeled is
A) increasing
B) decreasing
C) remaining constant
D) More information is needed.
E) Cannot be determined.
the situation modeled isA) increasing
B) decreasing
C) remaining constant
D) More information is needed.
E) Cannot be determined.
فتح الحزمة
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74
Solve the initial-value problem.
فتح الحزمة
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75
State the order of the differential equation, and decide which family of functions is a solution.
A) ; 1st order
B) ; 1st order
C) ; 2nd order
D) ; 1st order
E) ; 2nd order
A)
; 1st orderB)
; 1st orderC)
; 2nd orderD)
; 1st orderE)
; 2nd order فتح الحزمة
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76
Solve the initial-value problem.
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77
A 100-kg block stretches a spring 0.05 m from its initial position. If the spring is then stretched 0.2 m and released, write an equation for its position relative to its equilibrium position.
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