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Deck 12: Extension D: Multiple Integrals
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Question
Find the mass and the center of mass of the lamina occupying the region R,where R is the triangular region with vertices 
and 
,and having the mass density 
A)
, 
B)
, 
C)
, 
D)
, 
and ,and having the mass density A)
, B)
, C)
, D)
, 
Question
An electric charge is spread over a rectangular region 
Find the total charge on R if the charge density at a point 
in R (measured in coulombs per square meter)is 
A)
coulombs
B)
coulombs
C)
coulombs
D)
coulombs
Find the total charge on R if the charge density at a point in R (measured in coulombs per square meter)is A)
coulombsB)
coulombsC)
coulombsD)
coulombs Question
Find the center of mass of a lamina in the shape of an isosceles right triangle with equal sides of length 
if the density at any point is proportional to the square of the distance from the vertex opposite the hypotenuse.Assume the vertex opposite the hypotenuse is located at 
,and that the sides are along the positive axes.
A)
B)
C)
D)
E) None of these
if the density at any point is proportional to the square of the distance from the vertex opposite the hypotenuse.Assume the vertex opposite the hypotenuse is located at ,and that the sides are along the positive axes.A)
B)
C)
D)
E) None of these
Question
Find the mass of the lamina that occupies the region 
and has the given density function.Round your answer to two decimal places. 
and has the given density function.Round your answer to two decimal places. Question
A lamina occupies the part of the disk 
in the first quadrant.Find its center of mass if the density at any point is proportional to its distance from the x-axis.
in the first quadrant.Find its center of mass if the density at any point is proportional to its distance from the x-axis.
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Deck 12: Extension D: Multiple Integrals
1
Find the mass and the center of mass of the lamina occupying the region R,where R is the triangular region with vertices and ,and having the mass density
A) ,
B) ,
C) ,
D) ,
and ,and having the mass density A)
, B)
, C)
, D)
, , 2
An electric charge is spread over a rectangular region Find the total charge on R if the charge density at a point in R (measured in coulombs per square meter)is
A) coulombs
B) coulombs
C) coulombs
D) coulombs
Find the total charge on R if the charge density at a point in R (measured in coulombs per square meter)is A)
coulombsB)
coulombsC)
coulombsD)
coulombs coulombs 3
Find the center of mass of a lamina in the shape of an isosceles right triangle with equal sides of length if the density at any point is proportional to the square of the distance from the vertex opposite the hypotenuse.Assume the vertex opposite the hypotenuse is located at ,and that the sides are along the positive axes.
A)
B)
C)
D)
E) None of these
if the density at any point is proportional to the square of the distance from the vertex opposite the hypotenuse.Assume the vertex opposite the hypotenuse is located at ,and that the sides are along the positive axes.A)
B)
C)
D)
E) None of these
4
Find the mass of the lamina that occupies the region and has the given density function.Round your answer to two decimal places.
and has the given density function.Round your answer to two decimal places. Unlock Deck
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5
A lamina occupies the part of the disk in the first quadrant.Find its center of mass if the density at any point is proportional to its distance from the x-axis.
in the first quadrant.Find its center of mass if the density at any point is proportional to its distance from the x-axis. Unlock Deck
Unlock for access to all 5 flashcards in this deck.
Unlock Deck
k this deck
Unlock Deck
Unlock for access to all 5 flashcards in this deck.
