Consider the solid generated by the surfaces octant the 1st in

Q: In AABC, X is the centroid. If CW = 15 , find XW. %3D

A: Given,           In △ABC, X is the centroid and CW¯=15

Q: Let D be the solid region in space bounded below by p = 1 and above by cosp = Then the region D is…

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Q: 1. The solid in the first octant bounded by the coordinate planes and the surface z = 1- y – x2.

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Q: A solid dome is to be constructed with the ellipse x^2+3y^2=6 as a base. Using infinitely many…

A: Given that the solid dome is to be constructed with the ellipse x2+3y2=6 as a base. We have to…

Q: 7. In AVYX, the centroid is Z. Use the diagram to solve the problems. If VP = 51, find VZ and ZP.

A: We use the property ,the centroid divides each medians in the ratio 2:1.

Q: 6. Find the volumes of the solids in the following figure z =-VI - r?

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Q: Evaluate 3zdV E where E is the solid enclosed by z = 1 and z = x + y

A: we need to evaluate the given integral about the solid E . first we will find the limit of the…

Q: Evaluate the double integral 8xy dA, where D is the triangular region with vertices (0, 0), (1, 2),…

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Q: Evaluate / / /3zdV E where E is the solid enclosed by z = | and z = = x² + y?

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Q: Find the volume of the solid enclosed by the coordinate plane and the plane 2x + 3y + 6z = 6 using…

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Q: Evaluate the triple integral, 2x2 dV, where T is the solid tetrahedron with verticies (0, 0, 0), (1,…

A: Consider the given triple integral:

Q: Let R be the trapezoid with vertices (1,-1), (3,3), (3,-3) and (9,9). Give a change of variables to…

A: Given that ,  R be the trapezoid with vertices (1,-1) , (3,3) ,(3,-3) and (9,9) . Let , the vertices…

Q: 5. Find the surface area of the portion of the surface z = 2x + y? that is above the triangular…

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Q: Find the volume of the given solid. Under the surface  z = 9xy  and above the triangle with…

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Q: find fvelume of Solid f in the octant that is below porabalord そこ16-メ-9 planes X:0,9:0I and Z=0. and…

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Q: Let D be the region in xy-plane enclosed by the Trapezoid with vertices at the points (1, 1) , (7 ,…

A: We need to use double integral across given trapezium

Q: Evaluate the triple integral ryd xydV where E is the solid tetrahedon with vertices (0,0,0), (10, 0,…

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Q: vo ume of the solid in the litoctanit bounded by the plan 2x+3u +62=12

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Q: What is the region of the solid generated by the graphs of a = y – 4y and a = -y ?

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Q: Evaluate the double integral || 8xy dA, where D is the triangular region with vertices (0, 0), (1,…

A: Given data: The first vertex is O=(0, 0). The second vertex is B=(1, 2). The third vertex is A=(0,…

Q: egral dS over the su 9, where n is th surface element

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Q: Find the volume of the given solid. Under the surface z = 6xy and above the triangle with vertices…

A: Given: z=6xy A triangle with vertices (1,1),(4,1),(1,2)

Q: Let D be the solid region in space bounded below by p = and above by cosp p = ". Then the region D…

A: The solid region is bounded by the surfaces ρ=-1cosϕ and ϕ=3π4. In spherical coordinates,…

Q: Consider the solid whose base is the region bounded by 4x? + 9y? = 36. Y 3 -3 -2 -1 -1 2 3 2 -3 1.

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Q: Suppose that a region R has area A and lies above the x-axis. When R is rotated about the x-axis, it…

A: Use the disc method to find the W in terms of V, k and A.

Q: 4. A 5m x 5cm is cut from a corner of 20cm x 30cm. cardboard, find the centroid from the longest…

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Q: 4. Locate the centroid (x, y)of the following composite areas:

A: The centroid of rectangle is given by x2,y2 where x, y are the length and width respectively. The…

Q: Find the areas of the regions Inside one loop of the lemniscate r2 = 4 sin 2θ

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Q: The simple solid Q, drawn in the first octant and generated by the surfaces y – 1 = (x – 2)² 3x + 2z…

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Q: Let C be the cubic region delimited by the coordinate planes and by the planes x = 2 y=2 and z=2 in…

A: the planes x = 2 y=2 and z=2 in the first octant.

Q: z dV, where E is the solid tetrahedron with vertices (0,0,0), (2,0,0), E Find (0,6,0), and (0,0,3)

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Q: Integrate g(x, y, z) = x + y + z over the portion of the plan 2x + 2y + z = 2 that lies in the first…

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Q: Evaluate the double integral || 8xydA, where Dis the triangular region with vertices (0,0), (1,2),…

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Q: Find the area of the part of the plane 4x + 3y + z = 12 that lies in the first octant.

A: to find:- surface area, A.

Q: A rectangle ℛ with sides a and b is divided into two parts ℛ1 and ℛ2 by an arc of a parabola that…

A: A rectangle ℛ with sides a and b is divided into two parts ℛ1 and ℛ2 by an arc of a parabola that…

Q: Find the volume of the given solid. Under the surface z = 7xy and above the triangle with vertices…

A: Given surface is z = 7xy  And region is above the triangle with vertices (1, 1), (4, 1) and (1, 2).…

Q: Evaluate the triple integral. JUr ryz dV where Tis the solid tetrahedron with vertices (0,0,0),…

A: Find: ∭Txyz dV Obtain the equation of the plane that contains the points 0, 0, 0, 1, 1, 0 and 1, 0,…

Q: Evaluate the double integral. 8y2 dA, D is the triangular region with vertices (0, 1), (1, 2), (4,…

A: we have to find given double integral

Q: Let T be the tetrahedron with vertices (5, 0, 0), (0, 2, 0), (0, 0, 5) and the origin. Write II|…

A: Given T is a tetrahedron with vertices (5,0,0) , (0,2,0), (0,0,5) and  (0,0,0)…

Q: Consider the solid bounded by surfaces S1, S2, S3, S4, S5, and S6 with vertices A, B, C, D, E and O,…

A: In this question, we use the given sketch of the surface and find the parametrization for each…

Q: Consider the solid Q, in the first octant, which is generated by the surfaces: S1 : x2 = −(z − 3),…

A: Given:  S1 : x2 = −(z − 3), S2 : y + z = 3, S3 : z = 2, S4 : z = 0, S5 : y = 0 and S6 : x = 0  The…

Q: Let D be the solid region in the first octant bonded above by z-3 and below by 2= 2++y. Then the…

A: Here we will have to project the 3-dimensional solid regions on a 2-dimensional plane. Hence, we…

Q: Evaluate the double integral / ydrdy where T is the triangle with vertices (0,-1), (0, 5), (4, 3).

A: First, draw the region of integration. Then, use the region to setup the double integral.

Q: Evaluate || 4.nds , where A=zi+xj – 3y°zk and S is the surface of the cylinder x² + y =4 included in…

A: Let ∅=x2+y2-4  Then the normal to the surface S is ∇∅=2xi+2yj The unit normal is…

Q: Calculate (x+ y)dA, where Ris a triangular region with vertices (0,0), (3,0) and (3,3).

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Q: Q1- Determine the coordinates of the centroid of the area.: (1, 1)

A: We need to find the x coordinate and y coordinate of the shaded region which is bounded by two…

Q: Evaluate the double integral. 6y? dA, D is the triangular region with vertices (0, 1), (1, 2), (4,…

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Q: Find ff -6xydA over the D triangular region D with vertices (0,0) (2, 0), (0, 4)

A: problem is related to double integration

Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (5,0,0), (0,6,0), and (0,0,3)

A: This question is related to triple integral, We will solve it using given information.

Q: 2. Find the volume of the wedge cut from the 1-st octant in R³ by the surface z = 4-1 - y.

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