3) (11 points) Consider the vector field Use the Fundamental Theorem of Line Integrals to find the work done by F along any curve from A(l,1, e) to B(2, el) The Debate Club 4) (10 points) Consider the vector field Fx.)-yi) and the cirele C .Verify Green's Theorem by caleulating the ourward fux of Facrossc.
Homework Answers
Add Answer to:
2) (27 points) Let D be the region bounded from below by the plane : 0, from above by the plane z-2J3 and laterally by the hyperboloid of one sheet x2 + y2-1-24. a) (3 points) Draw the region...
7/10 324-x and the cone 5) (27 points) Let D be the solid region bounded by the paraboloid a) (8 points) Sketch D and set up triple integrals in rectangular coordinates representing th...
7/10 324-x and the cone 5) (27 points) Let D be the solid region bounded by the paraboloid a) (8 points) Sketch D and set up triple integrals in rectangular coordinates representing the dzdyda volume of D according to the order of integration dedyd Open with (9 points) Set up triple integrals in rectangular coordinates representing the volume of D b) according to the order of integration drdedy 8/10 (4 points) Set up triple integrals in cylindrical coordinates representing the...
Let D be the region bounded below by the cone z=x2+y2−−−−−−√ and above by the parabola z=2−x2−y2. Set up the triple integrals in cylindrical coordinates that give the volume of D using the following orders of integration: dzdrdθdzdrdθ.
Let D be the region bounded below by the cone z=x2+y2−−−−−−√ and above by the parabola z=2−x2−y2. Set up the triple integrals in cylindrical coordinates that give the volume of D using the following orders of integration: dzdrdθdzdrdθ.
1. (20 points) Suppose B is the solid region inside the sphere 2+ y2 +2 4, above the plane = 1, a...
Please show all steps. Thank you, need to verify what I'm doing
wrong.
1. (20 points) Suppose B is the solid region inside the sphere 2+ y2 +2 4, above the plane = 1, and in the first octant (z, y, z 0)、z, y and z are measured in meters and the density over B is given by the function p(z, y, z)-(12 + y2 + ?)-1 kg/m3 (a) Set up and write the triple integral that gives the mass...
Use rectangular, cylindrical and spherical coordinates to set up the triple integrals representing the volume of the region bounded below by the xy plane, bounded above by the sphere with radius and...
Use rectangular, cylindrical and spherical coordinates to set up the triple integrals representing the volume of the region bounded below by the xy plane, bounded above by the sphere with radius and centered at the origin the equation of the sphere is x2 + y2 + z2-R2), and outside the cylinder with the equation (x - 1)2 +y2-1 (5 pts each) Find the volume by solving one of the triple integrals from above.( 5 pts) Total of 20 pts)
Use...
(a) Let R be the solid in the first octant which is bounded above by the sphere 22 + y2+2 2 and bounded below by the cone z- r2+ y2. Sketch a diagram of intersection of the solid with the rz plane...
(a) Let R be the solid in the first octant which is bounded above by the sphere 22 + y2+2 2 and bounded below by the cone z- r2+ y2. Sketch a diagram of intersection of the solid with the rz plane (that is, the plane y 0). / 10. (b) Set up three triple integrals for the volume of the solid in part (a): one each using rectangular, cylindrical and spherical coordinates. (c) Use one of the three integrals...
Q4 only: Question 3. Consider the region of R3 given by V is bounded by three surfaces. Si is a disc of radius 1 in the plane z -0. S3 is a disc of radius 2 in the plane z 3 and a) Make a clear sketc...
Q4 only:
Question 3. Consider the region of R3 given by V is bounded by three surfaces. Si is a disc of radius 1 in the plane z -0. S3 is a disc of radius 2 in the plane z 3 and a) Make a clear sketch of V. (Hint: You could consider the cross-section of S2 with y-0, and then use the circular symmetry. (b) Express V in cylindrical coordinates. (c) Calculate the volume of V, working in cylindrical...
Problem 5 [10 points] Set up integrals for both orders of integration. Use the more convenient order to evaluate the integral over the plane region R: A R region bounded by y 0, y x, x 4 R 1+x2 a...
Problem 5 [10 points] Set up integrals for both orders of integration. Use the more convenient order to evaluate the integral over the plane region R: A R region bounded by y 0, y x, x 4 R 1+x2 a) [2 points] First order b) [2 points] Second order c) [6 points] Evaluate the integral using the more convenient order
Problem 5 [10 points] Set up integrals for both orders of integration. Use the more convenient order to evaluate the...
6) Consider the solid region E bounded by x-0, x-2, 2-y, 2-y-1, 2-0, and 24, set up a triple inte...
6) Consider the solid region E bounded by x-0, x-2, 2-y, 2-y-1, 2-0, and 24, set up a triple integral and write it as an iterated integral in the indicated order of integration that represents the volume of the solid bounded by E. (Sometimes you need to use more than one integral.) (a) da dy dz (projecti (b) dy dz dr (projection on rz-plane) (c) dz dy dx (projection on ry-plane) (d) Calculate the volume of the solid E on...
4. (14 points) Using polar coordinates, set up, but DO NOT EVALUATE, a double integral to find the volume of the solid region inside the cylinder x2 +(y-1)2-1 bounded above by the surface z=e-/-/...
4. (14 points) Using polar coordinates, set up, but DO NOT EVALUATE, a double integral to find the volume of the solid region inside the cylinder x2 +(y-1)2-1 bounded above by the surface z=e-/-/ and bounded below by the xy-plane.
4. (14 points) Using polar coordinates, set up, but DO NOT EVALUATE, a double integral to find the volume of the solid region inside the cylinder x2 +(y-1)2-1 bounded above by the surface z=e-/-/ and bounded below by the xy-plane.
12. Consider the region bounded above by the function ?=1/(?+2)2(?+6)^2 and below by the xy-plane for...
12. Consider the region bounded above by the function
?=1/(?+2)2(?+6)^2 and below by the xy-plane for x≥0 and ?≥0.
(1 point) Consider the region bounded above by the function z = - "2" (x + 2)2(y + 62 an and below by the xy-plane for x > 0 and y 2 0. On a piece of paper, sketch the shadow of the region in the xy-plane. Set up double integrals to compute the volume of the solid region in two...
7/10 324-x and the cone 5) (27 points) Let D be the solid region bounded by the paraboloid a) (8 points) Sketch D and set up triple integrals in rectangular coordinates representing the dzdyda volume of D according to the order of integration dedyd Open with (9 points) Set up triple integrals in rectangular coordinates representing the volume of D b) according to the order of integration drdedy 8/10 (4 points) Set up triple integrals in cylindrical coordinates representing the...
Please show all steps. Thank you, need to verify what I'm doing
wrong.
1. (20 points) Suppose B is the solid region inside the sphere 2+ y2 +2 4, above the plane = 1, and in the first octant (z, y, z 0)、z, y and z are measured in meters and the density over B is given by the function p(z, y, z)-(12 + y2 + ?)-1 kg/m3 (a) Set up and write the triple integral that gives the mass...
Use rectangular, cylindrical and spherical coordinates to set up the triple integrals representing the volume of the region bounded below by the xy plane, bounded above by the sphere with radius and centered at the origin the equation of the sphere is x2 + y2 + z2-R2), and outside the cylinder with the equation (x - 1)2 +y2-1 (5 pts each) Find the volume by solving one of the triple integrals from above.( 5 pts) Total of 20 pts)
Use...
(a) Let R be the solid in the first octant which is bounded above by the sphere 22 + y2+2 2 and bounded below by the cone z- r2+ y2. Sketch a diagram of intersection of the solid with the rz plane (that is, the plane y 0). / 10. (b) Set up three triple integrals for the volume of the solid in part (a): one each using rectangular, cylindrical and spherical coordinates. (c) Use one of the three integrals...
Q4 only:
Question 3. Consider the region of R3 given by V is bounded by three surfaces. Si is a disc of radius 1 in the plane z -0. S3 is a disc of radius 2 in the plane z 3 and a) Make a clear sketch of V. (Hint: You could consider the cross-section of S2 with y-0, and then use the circular symmetry. (b) Express V in cylindrical coordinates. (c) Calculate the volume of V, working in cylindrical...
Problem 5 [10 points] Set up integrals for both orders of integration. Use the more convenient order to evaluate the integral over the plane region R: A R region bounded by y 0, y x, x 4 R 1+x2 a) [2 points] First order b) [2 points] Second order c) [6 points] Evaluate the integral using the more convenient order
Problem 5 [10 points] Set up integrals for both orders of integration. Use the more convenient order to evaluate the...
6) Consider the solid region E bounded by x-0, x-2, 2-y, 2-y-1, 2-0, and 24, set up a triple integral and write it as an iterated integral in the indicated order of integration that represents the volume of the solid bounded by E. (Sometimes you need to use more than one integral.) (a) da dy dz (projecti (b) dy dz dr (projection on rz-plane) (c) dz dy dx (projection on ry-plane) (d) Calculate the volume of the solid E on...
4. (14 points) Using polar coordinates, set up, but DO NOT EVALUATE, a double integral to find the volume of the solid region inside the cylinder x2 +(y-1)2-1 bounded above by the surface z=e-/-/ and bounded below by the xy-plane.
4. (14 points) Using polar coordinates, set up, but DO NOT EVALUATE, a double integral to find the volume of the solid region inside the cylinder x2 +(y-1)2-1 bounded above by the surface z=e-/-/ and bounded below by the xy-plane.
12. Consider the region bounded above by the function
?=1/(?+2)2(?+6)^2 and below by the xy-plane for x≥0 and ?≥0.
(1 point) Consider the region bounded above by the function z = - "2" (x + 2)2(y + 62 an and below by the xy-plane for x > 0 and y 2 0. On a piece of paper, sketch the shadow of the region in the xy-plane. Set up double integrals to compute the volume of the solid region in two...
Most questions answered within 3 hours.
-
Which combination of statements is most accurate, if you think
options A, D, and E are...
asked 4 minutes ago -
What volume of oxygen gas at 423 K and pressure of 750 mm Hg is
produced...
asked 1 minute ago -
The NCAA uses an academic standard policy for initial
eligibility and continuing eligibility, along with the...
asked 3 minutes ago -
A survey of 1282 student loan borrowers found that 431 had loans
totaling more than $20,000...
asked 1 hour ago -
1.a) Balance the following half-reactions by the ion-electron
half-reaction method:
(i) (acid solution) NO2 (g) →...
asked 1 hour ago -
A reversible reaction that occurs in a single step has ΔH =
-47.2 kJ/mol and Ea...
asked 23 minutes ago -
What are some Limitations for affinity purification of a GST-GFP
protein? (also used 3 techniques to...
asked 22 minutes ago -
Magnus has reached the finals of a strength competition. In the
first round, he has to...
asked 20 minutes ago -
A wireless company claims that the average of the customers cell
phone bill is less than...
asked 25 minutes ago -
The reaction
C2H4(g) +
N2O(g)
--------> CH3CHO(g)
+NO(g)
is first order in both
C2H4 and
N2O, with...
asked 1 hour ago -
The Arrhenius equation shows the relationship between the rate
constant k and the temperature T in...
asked 35 minutes ago -
1.
if given unlabeled samples of glucose, malfose and lactose how
could you identify each of...
asked 1 hour ago