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need help with #8 and #13. w praxe ved at the way from the w orse...
Find the area of the portion of the plane 2x+3y+4z=28 lying above the rectangle 1≤x≤3,2≤y≤5 in the xy -plane. (1 poimi) Find the surface area of the portion S of the cone 22y, where z 20, contained within the cylinder y2 +22 < 36 Area(S)- (1 poimi) Find the surface area of the portion S of the cone 22y, where z 20, contained within the cylinder y2 +22
Hi, I need help solving number 13. Please show all the steps, thank you. :) Consider the solid Q bounded by z-2-y2;z-tx at each point Р (x, y, z) is given by mass of Q [15 pts] 9. x-4. The density Z/m 3 . Find the center of (x, y, z) [15 pts] 10. Evaluate the following integral: ee' dy dzdx [15 pts] 11. Use spherical coordinates to find the mass m of a solid Q that lies between the...
5. Calculate the surface area of the portion of the sphere x2+y2+12-4 between the planes z-1 and z ะไ 6. Evaluate (xyz) dS, where S is the portion of the plane 2x+2y+z-2 that lies in the first octant. 7. Evaluate F. ds. a) F = yli + xzj-k through the cone z = VF+ア0s z 4 with normal pointing away from the z-axis. b) F-yi+xj+ek where S is the portion of the cylinder+y9, 0szs3, 0s r and O s y...
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...
Solve c and d Please. Find the area of the following surfaces. a) The part of the plane 3z + 2y +z 6 that lies in the first octant. b) The part of the cone zVy that lies between the plane y z and the cylinder y-x c) The surface with vector equation r(u, u) = (u . cos(v), u . sin(v), u) , where 0 u 1, 0 v S T. d) The portion of the unit sphere that...
need 1-5 Midterm #3, Math 228 Each question is worth five points. 1. Let F(r.yzy). Let C be any curve that goes from A(-1,3,9) to B(1,6,-4). a) Show that F is conservative. b) Find a function φ such that ▽φ = F c) Use the result of b) to find Ic F Tds 2. Let F(z, y)-(2), and let C be the boundary of the square with vertices (1, 1). (-1,1). (-1,-1 traced out in the counter-clockwise direction. Find Jc...
U Question 15 "C 7 pts "С If S is the surface of the cylinder E= {(x,y,z) : 32 + y < 4,1523}, oriented outwards, which of the following (after applying the Divergence Theorem) will compute zyz) - dS? 40 O (1 + y2 cos & sin 6)r dr de dz REC O 1988 6%" /*(1 + == sin ®)r dr do dz %%% %%% %%% (r cos 0 + 32 + y2 z cos ( sin 0), dr do...
find the surface area of that portion of the sphere x^2+y^2+z^2 = 25 that is below the xy-plane and within the cylinder x^2+y^2=4 5. [10 Marks] Find the surface area of that portion of the sphere x2 + y2 2-25 that is below the ry-plane and within the cylinder 2 -4
I will rate your answer so please make sure the answer is accurate. The following question is a Calculus 3 problem, please answer 2) in the picture shown below, please show all the steps (step by step) and write out nicely and clearly: 1. Use Stokes, Theorem to find ls (curlF): ndS where F(x, y, z) = (y2z,zz, x2y2) and s is the portion of the paraboloid z x2 + y2 that lies inside the cylinder x2 +y-1. Use the...
can you show me the work for 2,3,4,5, thank you 2. Evaluate ff curl F n dS, where F = (a2yz, yz2, 23e#v), and S is the part of the sphere a2 + y2+225 that lies above the plane z 1, oriented upwards. - Solution: -4T 3. A metal sheet is bent into the shape of the parabaloid r = y2+ 2 where 0 (r, y, z) is 6(x, y, z) = z. Find the mass of the resulting metal...