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![SO m=$(55-34-22)dx = [52- »m = £[55. – 2co? che ] m= (550-150 – 10007 >> m=K(159.34) This is the required mass, where, K=Cons](http://img.homeworklib.com/questions/d9310850-240a-11eb-96d5-ef03262603e2.png?x-oss-process=image/resize,w_560)
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Let R be the shaded region below. (0,8) D1(10,8) (0,3) Suppose aty are in cm, density...
(1 point) Find the center of mass (r, of the lamina which occupies the region if the density at a...
how is this done? urgent.
(1 point) Find the center of mass (r, of the lamina which occupies the region if the density at any point is proportional to the distance from the origin x= 0
(1 point) Find the center of mass (r, of the lamina which occupies the region if the density at any point is proportional to the distance from the origin x= 0
please check your answer x,y and z are measured in cm Let W be the solid between a hemisphere of radi us 3 and a hem...
please check your answer
x,y and z are measured in cm
Let W be the solid between a hemisphere of radi us 3 and a hemisphere of radius 6, but not in the first octant (a) Suppose the density at a point (x, y, z) is proportional to the distance from the origin. Find a formula P(x,y, z) = (b) Use spherical coordinates to set up the integral to find the mass of W For instructor's notes only. Do not...
Problem 2. (a) Let Di be a disc of radius 1 centred around the point (1,3),...
Problem 2. (a) Let Di be a disc of radius 1 centred around the point (1,3), and suppose there is a lamina occupying D1. Assume that the mass density of the lamina at a point (x, y) E Di is given by p(, y) exp-K1 (y 3], where K is a positive constant. What is the total mass and what is the centre of mass of the lamina? Hint. You may use Formula (1) from Problem 1 if you want...
Let W be the sold prism shown below (not drawn to scale). This prism has sides on the three coordinate planes with...
Let W be the sold prism shown below (not drawn to scale). This prism has sides on the three coordinate planes with 0 sxs 8, 0sys 11, and 0szs 24. (a) When setting up a triple integral to find the volume of the solid, what is the shape of the "shadow" f we integrate in the order dy dz de -Select- (b) What is the equation of the diagonal plane that forms the slanted surface? and x, y, and z...
(8) Let E C R" and G C R" be open. Suppose that f E G and g G R', so that h = go f : E → R. Prove that if f is differentiable at a point x E E, and if g is differentiable at f (x) E G, th...
(8) Let E C R" and G C R" be open. Suppose that f E G and g G R', so that h = go f : E → R. Prove that if f is differentiable at a point x E E, and if g is differentiable at f (x) E G, then the partial derivatives Dihj(x) exist, for all and j - ...., and 7m に! (The subscripts hi. g. fk denote the coordinates of the functions h, g....
1 Let R be a region bounded between two curves on the r, y-plane. Suppose that you are asked to find the volume of the...
1 Let R be a region bounded between two curves on the r, y-plane. Suppose that you are asked to find the volume of the solid obtained by revolving the region R about the r-axis If you slice the region R into thin horizontal slices, i.e., parallel to the r-axis, in setting up the Riemann sum, then which method will come into play? A. Disc method B. Washer method C. Either disc or a washer method depending on the shape...
Please Answer 135 Below Completely: Definition Let E-R and f : E-+ R be a function....
Please Answer 135 Below Completely:
Definition Let E-R and f : E-+ R be a function. For some p E E' we say that f is continuous at p if for any ε > 0, there exists a δ > 0 (which depends on ε) such that for any x E E with |x-Pl < δ we have If(x) -f(p)le KE. This is often called the rigorous δ-ε definition of continuity. A couple of things to note about this definition....
(8) Let E c R" and G C Rm be open. Suppose that f E -G and g:GR', so that h -gof:E R'. Prove that if f is differentiable at a point x E E and if g is differentiable at f(x) є G, then the...
(8) Let E c R" and G C Rm be open. Suppose that f E -G and g:GR', so that h -gof:E R'. Prove that if f is differentiable at a point x E E and if g is differentiable at f(x) є G, then the partial derivatives Dh,(x) exist, for all , SO , . . . , n, and and J-: に1 The subscripts hi, 9i, k denote the coordinates of the functions h, g, f relative to...
(1 point) The region W is the cone shown below. The angle at the vertex is...
(1 point) The region W is the cone shown below. The angle at the vertex is #/3, and the top is flat and at a height of 3v3. Write the limits of integration for wdV in the following coordinates (do not reduce the domain of integration by taking advantage of symmetry): (a) Cartesian: With a = .b = .d = and f = e = Volume = / ddd (b) Cylindrical: With a = CE and f = ddd e...
3.1. Two metallic rods of length L = 40 cm and unknown linear mass density A...
3.1. Two metallic rods of length L = 40 cm and unknown linear mass density A are suspended from a support using lightweight strings of length s = 8 cm, as shown in the diagram (a) below. The rods are then connected to a circuit in such a way that same current I = 20 A passes through both rods, but flows in opposite directions. When connected in such a way, the rods move away from each other and at...
how is this done? urgent.
(1 point) Find the center of mass (r, of the lamina which occupies the region if the density at any point is proportional to the distance from the origin x= 0
(1 point) Find the center of mass (r, of the lamina which occupies the region if the density at any point is proportional to the distance from the origin x= 0
please check your answer
x,y and z are measured in cm
Let W be the solid between a hemisphere of radi us 3 and a hemisphere of radius 6, but not in the first octant (a) Suppose the density at a point (x, y, z) is proportional to the distance from the origin. Find a formula P(x,y, z) = (b) Use spherical coordinates to set up the integral to find the mass of W For instructor's notes only. Do not...
Problem 2. (a) Let Di be a disc of radius 1 centred around the point (1,3), and suppose there is a lamina occupying D1. Assume that the mass density of the lamina at a point (x, y) E Di is given by p(, y) exp-K1 (y 3], where K is a positive constant. What is the total mass and what is the centre of mass of the lamina? Hint. You may use Formula (1) from Problem 1 if you want...
Let W be the sold prism shown below (not drawn to scale). This prism has sides on the three coordinate planes with 0 sxs 8, 0sys 11, and 0szs 24. (a) When setting up a triple integral to find the volume of the solid, what is the shape of the "shadow" f we integrate in the order dy dz de -Select- (b) What is the equation of the diagonal plane that forms the slanted surface? and x, y, and z...
(8) Let E C R" and G C R" be open. Suppose that f E G and g G R', so that h = go f : E → R. Prove that if f is differentiable at a point x E E, and if g is differentiable at f (x) E G, then the partial derivatives Dihj(x) exist, for all and j - ...., and 7m に! (The subscripts hi. g. fk denote the coordinates of the functions h, g....
1 Let R be a region bounded between two curves on the r, y-plane. Suppose that you are asked to find the volume of the solid obtained by revolving the region R about the r-axis If you slice the region R into thin horizontal slices, i.e., parallel to the r-axis, in setting up the Riemann sum, then which method will come into play? A. Disc method B. Washer method C. Either disc or a washer method depending on the shape...
Please Answer 135 Below Completely:
Definition Let E-R and f : E-+ R be a function. For some p E E' we say that f is continuous at p if for any ε > 0, there exists a δ > 0 (which depends on ε) such that for any x E E with |x-Pl < δ we have If(x) -f(p)le KE. This is often called the rigorous δ-ε definition of continuity. A couple of things to note about this definition....
(8) Let E c R" and G C Rm be open. Suppose that f E -G and g:GR', so that h -gof:E R'. Prove that if f is differentiable at a point x E E and if g is differentiable at f(x) є G, then the partial derivatives Dh,(x) exist, for all , SO , . . . , n, and and J-: に1 The subscripts hi, 9i, k denote the coordinates of the functions h, g, f relative to...
(1 point) The region W is the cone shown below. The angle at the vertex is #/3, and the top is flat and at a height of 3v3. Write the limits of integration for wdV in the following coordinates (do not reduce the domain of integration by taking advantage of symmetry): (a) Cartesian: With a = .b = .d = and f = e = Volume = / ddd (b) Cylindrical: With a = CE and f = ddd e...
3.1. Two metallic rods of length L = 40 cm and unknown linear mass density A are suspended from a support using lightweight strings of length s = 8 cm, as shown in the diagram (a) below. The rods are then connected to a circuit in such a way that same current I = 20 A passes through both rods, but flows in opposite directions. When connected in such a way, the rods move away from each other and at...
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