Let W be the region under the plane z = 4 – 2x- – y and within the x 2 0, y > 0, z > 0 octant. Find U : 4 U 4–2x-y Sllw a? + y? + z² dV = § § S æ² + y² + 2² dz dx dy. 0 0 A) 2 - 2 В) 4 — 2а C) z – 4x D) 2 E) Not enough information. O E O A C В

Q: Write the coordinates for the center of the hyperbola: A/ (x-2) (y + 1)² 64 36

A: given  (x-2)236-(y+1)264=1standard form of hyperbola is  (x-h)2a2-(y-k)2b2=1hwer centre is  (h,k)

Q: c) Calculate (x+y + 2) dV, where E is the region bounded by r2 + y +z s 25 and above the E xy-plane.

A:

Q: 9. Let E be the tetrahedron with vertices: (0,0,0), (3,2,0), (0,3,0), (0, 0, 2). E is bounded by…

A:

Q: The volume of the solid bounded by the plane 3x+6y-2z=12 and the coordinate planes is O A. 2-2y+4 1…

A: We need to find the volume of the solid bounded by the plane 3x+6y-2z=12. Now,…

Q: F = (x² – y²,x, 2yz); C is the boundary of the plane z = 6 – 2x – y in the first octant.

A: Given, F=x2-y2,x,2yz Find the line integral ∮CF·dr in the following. Here C is the boundary of the…

Q: In V=R3 Let W1 be the xy-plane and  let W2 be the z-zxis:             W1={(x,y,0):x,y∈R}  and…

A: Let (x,y,z)∈V, then this element can be written as the sum of an element of W1 and an element of W2…

Q: Let h=f∘g where f:R2→R and g:R2→R2 is defined by g(x,y)=(−3x2y,3x+3y). Find the derivative h′(1,2)…

A:

Q: Consider the equation in x, y, z: : y² + z² = 1, x = [0, 2], y ≥ 0, z ≥ 0 Note the domain conditions…

A: Note the following fact : The equation y2+z2=1 is a circular cylinder having its axis x-axis in the…

Q: Use Stokes' Theorem to evaluate fF.dr where F(x, y, z) = zi − 3yzj+ xk and C is the boundary of the…

A:

Q: 9.) Let E be the tetrahedron with vertices: (0,0,0), (3, 2,0), (0,3,0), (0, 0,2). E is bounded by…

A: The tetrahedron bounded by the planes              from the plane…

Q: 12. Let R be the region of the plane R= {(r, y) : # 2 0 and ²+ y? < 2}. Describe R using polar…

A: Here, the given region is: R=(x,y):x≥0 &amp; x2+y2≤2

Q: . Evaluate || (2- 1) do, where S is the part of the cone z = Vr + y² which lies under the plane z =…

A:

Q: 9.) Let E be the tetrahedron with vertices: (0,0,0), E is bounded by four planes: z = 0, x=0, 2 3…

A: Volume of tetrahedron