Question 1

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line

Accepted Answer

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E)  None 
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E)  None

Question 2

Set up,but do not evaluate,an integral for the area of the surface obtained by rotating the curve about the given axis.   y-axis

Accepted Answer

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Question 3

Solve the differential equation.

Accepted Answer

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E)  None of these 
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E)  None of these

Question 4

A certain small country has $20 billion in paper currency in circulation,and each day $70 million comes into the country's banks.The government decides to introduce new currency by having the banks replace old bills with new ones whenever old currency comes into the banks.Let   denote the amount of new currency in circulation at time t with   .Formulate and solve a mathematical model in the form of an initial-value problem that represents the "flow" of the new currency into circulation (in billions per day).

Accepted Answer

The answer of A certain small country has $20 billion...

Question 5

Find the area of the surface obtained by rotating the circle   about the line   .

Accepted Answer

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D)    
E)    
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E)

Question 6

Find the center of mass of the system comprising masses mk located at the points Pk in a coordinate plane.Assume that mass is measured in grams and distance is measured in centimeters.
m1 = 3 , m2 = 4, m3 = 5
P1 (-3,5), P2 (3,4), P3 (-4,1)

Accepted Answer

The answer of Find the center of mass of the...

Question 7

Choose the differential equation corresponding to this direction field.

Accepted Answer

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C)    
D)    
E)    
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E)

Question 8

Find the centroid of the region bounded by the graphs of the given equations.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 9

Find the area of the surface obtained by revolving the graph of y =   on [0,1] about the x-axis.

Accepted Answer

The answer of Find the area of the surface obtained...

Question 10

Find the area of the region bounded by the given curves.

Accepted Answer

A)    
B)    
C)    
D)    
E)  None of these 
A)    
B)    
C)    
D)    
E)  None of these

Question 11

Find the number b such that the line   divides the region bounded by the curves   and   into two regions with equal area.

Accepted Answer

A)    
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E)    
A)    
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E)

Question 12

Find the center of mass of a lamina in the shape of a quarter-circle with radius 9 with density

Accepted Answer

The answer of Find the center of mass of a...

Question 13

Find the centroid of the region bounded by the given curves.

Accepted Answer

A)    
B)    
C)    
D)    
E)  None of these 
A)    
B)    
C)    
D)    
E)  None of these

Question 14

Find the volume of the solid obtained by rotating the region bounded by   about the line

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 15

The base of S is a circular region with boundary curve   Cross-sections perpendicular to the x axis are isosceles right triangles with hypotenuse in the base. Find the volume of S.

Accepted Answer

The answer of The base of S is a circular...

Question 16

Find the volume of the frustum of a pyramid with square base of side  b = 17, square top of side a = 5, and height h = 19.

Accepted Answer

The answer of Find the volume of the frustum of...

Question 17

Find the volume of the solid obtained by rotating the region bounded by   and   about the y-axis.

Accepted Answer

The answer of Find the volume of the solid obtained...

Question 18

The volume of a solid torus (the donut-shaped solid shown in the figure)with r = 5 and R = 15 is

Accepted Answer

A) True 
 B)False

Question 19

Set up,but do not evaluate,an integral for the length of the curve

Accepted Answer

The answer of Set up,but do not evaluate,an integral for...

Question 20

A tank contains 1050 L of brine with 20 kg of dissolved salt.Pure water enters the tank at a rate of 16 L/min.The solution is kept thoroughly mixed and drains from the tank at the same rate.How much salt is in the tank after 20 minutes?

Accepted Answer

The answer of A tank contains 1050 L of brine...

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line

Set up,but do not evaluate,an integral for the area of the surface obtained by rotating the curve about the given axis. y-axis

Solve the differential equation.

Find the area of the surface obtained by rotating the circle about the line .

Find the center of mass of the system comprising masses m_k located at the points P_k in a coordinate plane.Assume that mass is measured in grams and distance is measured in centimeters. m₁ = 3 , m₂ = 4, m₃ = 5 P₁(-3,5), P₂(3,4), P₃(-4,1)

Choose the differential equation corresponding to this direction field.

Find the centroid of the region bounded by the graphs of the given equations.

Find the area of the surface obtained by revolving the graph of y = on [0,1] about the x-axis.

Find the area of the region bounded by the given curves.

Find the number b such that the line divides the region bounded by the curves and into two regions with equal area.

Find the center of mass of a lamina in the shape of a quarter-circle with radius 9 with density

Find the centroid of the region bounded by the given curves.

Find the volume of the solid obtained by rotating the region bounded by about the line

The base of S is a circular region with boundary curve Cross-sections perpendicular to the x axis are isosceles right triangles with hypotenuse in the base. Find the volume of S.

Find the volume of the frustum of a pyramid with square base of side b = 17, square top of side a = 5, and height h = 19.

Find the volume of the solid obtained by rotating the region bounded by and about the y-axis.

The volume of a solid torus (the donut-shaped solid shown in the figure)with r = 5 and R = 15 is

Set up,but do not evaluate,an integral for the length of the curve

A tank contains 1050 L of brine with 20 kg of dissolved salt.Pure water enters the tank at a rate of 16 L/min.The solution is kept thoroughly mixed and drains from the tank at the same rate.How much salt is in the tank after 20 minutes?

Functions and Limits

Derivatives

Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

Applications of Differentiation

Integrals

Techniques of Integration

Series

Parametric Equations and Polar Coordinates

Ectors and the Geometry of Space

Partial Derivatives

Multiple Integrals

Vector Calculus

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Exam 7: Applications of Integration

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line

Set up,but do not evaluate,an integral for the area of the surface obtained by rotating the curve about the given axis. y-axis

Solve the differential equation.

Find the area of the surface obtained by rotating the circle about the line .

Find the center of mass of the system comprising masses mk located at the points Pk in a coordinate plane.Assume that mass is measured in grams and distance is measured in centimeters. m1 = 3 , m2 = 4, m3 = 5 P1 (-3,5), P2 (3,4), P3 (-4,1)

Choose the differential equation corresponding to this direction field.

Find the centroid of the region bounded by the graphs of the given equations.

Find the area of the surface obtained by revolving the graph of y = on [0,1] about the x-axis.

Find the area of the region bounded by the given curves.

Find the number b such that the line divides the region bounded by the curves and into two regions with equal area.

Find the center of mass of a lamina in the shape of a quarter-circle with radius 9 with density

Find the centroid of the region bounded by the given curves.

Find the volume of the solid obtained by rotating the region bounded by about the line

The base of S is a circular region with boundary curve Cross-sections perpendicular to the x axis are isosceles right triangles with hypotenuse in the base. Find the volume of S.

Find the volume of the frustum of a pyramid with square base of side b = 17, square top of side a = 5, and height h = 19.

Find the volume of the solid obtained by rotating the region bounded by and about the y-axis.

The volume of a solid torus (the donut-shaped solid shown in the figure)with r = 5 and R = 15 is

Set up,but do not evaluate,an integral for the length of the curve

A tank contains 1050 L of brine with 20 kg of dissolved salt.Pure water enters the tank at a rate of 16 L/min.The solution is kept thoroughly mixed and drains from the tank at the same rate.How much salt is in the tank after 20 minutes?

Functions and Limits

Derivatives

Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

Applications of Differentiation

Integrals

Techniques of Integration

Series

Parametric Equations and Polar Coordinates

Ectors and the Geometry of Space

Partial Derivatives

Multiple Integrals

Vector Calculus

Filters

Find the center of mass of the system comprising masses m_k located at the points P_k in a coordinate plane.Assume that mass is measured in grams and distance is measured in centimeters. m₁ = 3 , m₂ = 4, m₃ = 5 P₁(-3,5), P₂(3,4), P₃(-4,1)