can y'all help with with these 3 please!! Thank you!! Question 1 Find the volume beneath...
can y'all help with with these 3 please!! Thank you!!
Question 1
Find the volume beneath z = f(x,y) and above the region described by the triangle with vertices (0,0), (4,0), and (0,4).
f(x,y)= -x-y+c ; use c = 7.
Hint: compute the double integral required to find the volume under
f(x,y) using the limits of integration given by the region on the
x-y plane.
Question 2
Prove that F is a gradient field and determine the work of F to
go from point A: (1 , 3, 2) to point B: (4 , 2 , 4) along any
trajectory.
F=[2xyz x2z+2e(-2y) x2y]
Question 5
Determine the line integral along the curve C from A to B. Find
the parametric form of the curve C. Use the vector field:
Use the following values: a=5; b=2; and c=6.
Homework Answers
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can y'all help with with these 3 please!! Thank
you!!
Question 1
Find the volume beneath...
Question 4 Find the volume beneath z=f(x,y) and above the region described by the rectangle with...
Question 4 Find the volume beneath z=f(x,y) and above the region described by the rectangle with vertices (0,0), (3,0), (3,4), and (0,4). f(x, y) = 4x +9y2 Hint: compute the double integral required to find the volume under f(x,y) using the limits of integration given by the region on the x-y plane.
(1) Integrate f(x, y,z)+Vy - z2 over the straight line segment path from (0,0,0) to (1,1,1) (2) Consider the field F (2xyz+2,x2z, x2y), (a) (b) (c) Show that the field is conservative. Find a pot...
(1) Integrate f(x, y,z)+Vy - z2 over the straight line segment path from (0,0,0) to (1,1,1) (2) Consider the field F (2xyz+2,x2z, x2y), (a) (b) (c) Show that the field is conservative. Find a potential function for the field. Find the work the field does on an object that follows the path consisting of the line segment from (0,0,0) to (1,2,2), followed by the line segment from (1,2,2) to (2,4,3) Find the work done by the field ß-(x, 3y,-5z) along...
Find the volume beneath z = f(x,y) and above the region described by the rectangle with...
Find the volume beneath z = f(x,y) and above the region described by the rectangle with vertices (0,0), (2,0), (2,3), and (0,3). f(x,y)=4x^2+9y^2 Hint: compute the double integral required to find the volume under f(x,y) using the limits of integration given by the region on the x-y plane.
(1 point) Suppose F(x, y) = xyi + (x – y)j and C is the triangle...
(1 point) Suppose F(x, y) = xyi + (x – y)j and C is the triangle from (4,0) to (-4,0) to (0,4) to (4,0). (a) Find the line integral of Ể along each segment of the triangle. Along C1, the line segment from (4,0) to (-4,0), the line integral is Along C2, the line segment from (-4,0) to (0,4), the line integral is Along C3, the line segment from (0,4) to (4,0), the line integral is (b) Find the circulation...
please give the final answer in cubic Find the volume of the solid generated by revolving...
please give the final answer in cubic
Find the volume of the solid generated by revolving the region enclosed by the triangle with vertices (4,0), (5,1), and (4,1) about the y-axis. Use the washer method to set up the integral that gives the volume of the solid.
All of 10 questions, please. 1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the...
All of 10 questions, please.
1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
Line Integral & Path Independency Problem 1 Prove that the vector field = (2x-3yz)i +(2-3x-2) 1-6xyzk...
Line Integral & Path Independency Problem 1 Prove that the vector field = (2x-3yz)i +(2-3x-2) 1-6xyzk is the gradient of a scalar function f(x,y,z). Hint: find the curl of F, is it a zero vector? Integrate and find f(x,y,z), called a potential, like from potential energy? Show all your work, Then, use f(x,y,z) to compute the line integral, or work of the force F: Work of F= di from A:(-1,0, 2) to B:(3,-4,0) along any curve that goes from A...
Find the volume of the solid enclosed by the paraboloid z = 5x2 + 5y 2...
Find the volume of the solid enclosed by the paraboloid z = 5x2 + 5y 2 and the planes x = 0, y = 3, y = x, z = 1225 3 Evaluate the double integral. SS 9. y2 - xdA, D = {lar,y) |0<y< 4,0 <r<y} 24 Evaluate the double integral. I, 4xy dA, D is the triangular region with vertices (0,0), (1, 2), and (0,
1. 5 marks] Find the work done by the force F(x, y) =-ri+yj applied to an...
1. 5 marks] Find the work done by the force F(x, y) =-ri+yj applied to an object that moves along the quarter circle from (2, 0) to (0, 2) 2. [6 marks Find the volume of the region beneath z (0,0), (1,0), and (1,2) y and the triangle with vertices
please solve all with detailed steps. thank you! Find the mass, and the center of mass...
please solve all with detailed steps. thank you!
Find the mass, and the center of mass of the solid cone D with density p(x, y, z) = 1 bounded by the surface z = 4- x2 + y2 and z = 0 1) 2) Evaluate dA where R is the square with vertices (0,0), (1,–1), (2,0), and (1,1) x+y+1 (Hint: use a convenient change of variables) 3) Evaluate the line integral (x - y+ 2z)ds where C is the circle...
Question 4 Find the volume beneath z=f(x,y) and above the region described by the rectangle with vertices (0,0), (3,0), (3,4), and (0,4). f(x, y) = 4x +9y2 Hint: compute the double integral required to find the volume under f(x,y) using the limits of integration given by the region on the x-y plane.
(1) Integrate f(x, y,z)+Vy - z2 over the straight line segment path from (0,0,0) to (1,1,1) (2) Consider the field F (2xyz+2,x2z, x2y), (a) (b) (c) Show that the field is conservative. Find a potential function for the field. Find the work the field does on an object that follows the path consisting of the line segment from (0,0,0) to (1,2,2), followed by the line segment from (1,2,2) to (2,4,3) Find the work done by the field ß-(x, 3y,-5z) along...
(1 point) Suppose F(x, y) = xyi + (x – y)j and C is the triangle from (4,0) to (-4,0) to (0,4) to (4,0). (a) Find the line integral of Ể along each segment of the triangle. Along C1, the line segment from (4,0) to (-4,0), the line integral is Along C2, the line segment from (-4,0) to (0,4), the line integral is Along C3, the line segment from (0,4) to (4,0), the line integral is (b) Find the circulation...
please give the final answer in cubic
Find the volume of the solid generated by revolving the region enclosed by the triangle with vertices (4,0), (5,1), and (4,1) about the y-axis. Use the washer method to set up the integral that gives the volume of the solid.
All of 10 questions, please.
1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
Line Integral & Path Independency Problem 1 Prove that the vector field = (2x-3yz)i +(2-3x-2) 1-6xyzk is the gradient of a scalar function f(x,y,z). Hint: find the curl of F, is it a zero vector? Integrate and find f(x,y,z), called a potential, like from potential energy? Show all your work, Then, use f(x,y,z) to compute the line integral, or work of the force F: Work of F= di from A:(-1,0, 2) to B:(3,-4,0) along any curve that goes from A...
Find the volume of the solid enclosed by the paraboloid z = 5x2 + 5y 2 and the planes x = 0, y = 3, y = x, z = 1225 3 Evaluate the double integral. SS 9. y2 - xdA, D = {lar,y) |0<y< 4,0 <r<y} 24 Evaluate the double integral. I, 4xy dA, D is the triangular region with vertices (0,0), (1, 2), and (0,
1. 5 marks] Find the work done by the force F(x, y) =-ri+yj applied to an object that moves along the quarter circle from (2, 0) to (0, 2) 2. [6 marks Find the volume of the region beneath z (0,0), (1,0), and (1,2) y and the triangle with vertices
please solve all with detailed steps. thank you!
Find the mass, and the center of mass of the solid cone D with density p(x, y, z) = 1 bounded by the surface z = 4- x2 + y2 and z = 0 1) 2) Evaluate dA where R is the square with vertices (0,0), (1,–1), (2,0), and (1,1) x+y+1 (Hint: use a convenient change of variables) 3) Evaluate the line integral (x - y+ 2z)ds where C is the circle...
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