(b) Calculate the volume of the tetrahedron in the first octant bounded by the plane x + 2y + 3z = Q using triple integral. Q- The last digit of your matrix number For example, a student with the matrix number CD150079 will have the values of Q = 9. Use 1 if the last digit is of your matrix number is 0.

Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (1,0,0), E (0,4,0), and (0,0,2)

A: The vertices of the tetrahedron are (0,0,0),(1,0,0),(0,4,0),(0,0,2).  x varies from x:0→1y varies…

Q: Evaluate the triple integral |// xy dV where E is the solid tetrahedon with vertices (0,0,0), (7, 0,…

A: Consider the following: Equation of plane passing through 7,0,0,0,5,0,0,0,10x7+y5+z10=1x ​ranges…

Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (5,0,0), (0,2,0), and (0,0,4)

A: # Given integral is      ∫∫E∫ zdv

Q: Find the center of Center of Mass of a Linear System mass of the given system of point masses lying…

A:

Q: Q3. Consider the homogeneous CLTI system i = Ax where 01 -1 2 1 A -1 a) Is A diagonalizable? If not,…

A: Given that A=2100-12-101.  To check the matrix A is in diagonalizable form or not, first we will…

Q: =) Solve . 3x² + 3y²dV by using cylindrical coordinates, where G is a solid in the first octant that…

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Q: A two-ply laminate composite has the top and bottom ply orientations of 45 and 0° and thicknesses of…

A: Given: Here the given thickness is 2 mm and 4 mm respectively. Let us take k1=2 mm and t2 = 4 mm.…

Q: EXAMPLE 2 to evaluate the Use the change of variables x = u² - v², y = auv integral SSR y dA, where…

A: The objective is to evaluate the integral using change of variable. x=u2-v2, y=2uvy2=4-4x, y2=4+4x,…

Q: (b) Calculate the volume of the tetrahedron in the first octant bounded by the plane x + 2y + 3z = Q…

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Q: Calculate the double integral Sle (x² + 2y) dA, where R is the triangular region with vertices 8/3…

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Q: Find the y coordinate of the centroid of the region shaded in the following diagram. 9 in. -27 in.

A: Here the figure has drawn for our convenience.  To find the centroid, the rectangle indicated in x…

Q: -JIL e √x² + y² dv, where E is the region that lies inside the cylinder x² + y² = 4 and between the…

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Q: Adam has created a triangular table, as shown. Because his table will have only one pedestal leg, he…

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Q: Find the extremum of z =x + y subject to x + 5y = 4. Set up the Bordered Hessian matrix to determine…

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Q: Evaluate the triple integral ∭ExydV where E is the solid tetrahedon with vertices…

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Q: The solid bounded by the paraboloids 2= - 8+z²+ y² and z -3-32²-3y² has volume:

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Q: 1) Find the outward flux of F across the region D where F= (6x² + 2xy, 2y + x²z, 4x² y³ ) and the…

A: The vector field is,F¯=6x2+2xy, 2y+x2z, 4x2y3The region D is cut from the first octant by the…

Q: (2) Find the integral (0,2,0) and (0,0,1). where D is the tetrahedron with vertices (0,0,0),…

A: Given : ∬∫x+2y+z dV             where D is  tetrahedron with vertices 0 ,0 ,0  , 1 , 0 , 0  , 0, 2 ,…

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: Evaluate the triple integral xy dV where E is the solid tetrahedon with vertices (0, 0,0), (6, 0,…

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Q: Evaluate the triple integral // x dV, where T is the solid tetrahedron with vertices T (0,0, 0),…

A: Here we have to evaluate the triple integral , where T is the solid tetrahedron with vertices…

Q: Evaluate the triple integral. 6xyz dV, where T is the solid tetrahedron with vertices (0, 0,0), (1,…

A:

Q: 2. In A ABC, X is the centroid. A A If CW = 15, find cx and XW. W, B. If BX = 8, find BY and XY.

A: we know that  centroid is located 23 of the distance from the vertex along the segment that connects…

Q: Integrate Xy ed २ over the triangular region with vertices: (0,0), ), (0,8) (0,16)

A:

Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (1,0,0), (0,2,0), and (0,0,4)

A: x varies from 0 to 1& y varies from 0 to 2 and z varies from 0 to 4.

Q: 2. Set up the triple integral f[Sp I+y+zdV, where D is the tetrahedron with vertices at (0,0,0),…

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Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (1,0,0), (0,3,0), and (0,0,5)

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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: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (4,0,0), (0,3,0), and (0,0,2)

A: we have to find triple integral

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: 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: Evaluate the double integral ∬D2xydA,∬D2xydA, where DD is the triangular region with vertices…

A: Evaluate the double integral ∬D 2xydA where D is the triangular region with vertices (0,0), (1,2),…

Q: • Example 4 Evaluate the double integral /| v²x dA R over the rectangle R = {(x, y) : –3 < x < 2, 0…

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Q: (b) Calculate the volume of the tetrahedron in the first octant bounded by the plane x + 2y + 3z = Q…

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Q: 4.) Assume that the matrix is the arque augimented arove marria of a sustem of linear equntions…

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Q: . Set up the triple integral fSSp r+y+zdV, where D is the tetrahedron with vertices at (0,0,0),…

A: The equation of tetrahedron with intercepts (a,0,0), (0,b,0) and (0,0,c) is given by: Given…

Q: Evaluate the triple integral III xy dV where E is the solid tetrahedon with vertices (0, 0, 0),…

A: The given integral is, ∫∫∫E xydV Here E is the solid tetrahedron with vertices O0,0,0, A10,0,0,…

Q: Evaluate the triple integral ryz dV, where T is the solid “tetrahedron" with vertices (0,0,0), (0,…

A: Identify the limits of integration from the region. The base of the tetrahedron is in the xy-plane.…

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

A: The given problem is to find the centroid of the given shaded area of the region formed by given…

Q: #1. Evaluate (2x – 5y) dA, R where R is the parallelogram with vertices (0,0), (2,3), (–1,4) and…

A: The given region R is a parallelogram with vertices as shown in below graph. We have to use change…

Q: 1. Evaluate the integral ryz dV, where E is the tetrahedron with vertices (0.0,0), (2,0,0), (2,3,…

A: The vertices of tetrahedron are (0, 0, 0), (2, 0, 0), (2, 3, 0) , (2, 0, 4). The equation of the…

Q: 3. Given a matrix X and a vector y of appropriate dimensions, define f(w) = ||y – Xw||? a. If X is N…

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Q: If a system is such that its input X(t) ind its put Y(1) are related by a convolution integral,…

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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: 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: Find ¹JJ²₁ z dV, where E is the solid tetrahedron with vertices (0,0,0), (3,0,0), (0,2,0), and…

A: The solid E is the tetrahedron with vertices 0, 0, 0, 3, 0,0, 0, 2,0 and 0, 0, 1. Draw the solid E:…

Q: Find the value of a if the centroid of the region bounded by the parabola y² = 4px and the line = a…

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Q: Q3. Consider the homogeneous CLTI system i = Ax where 1 01 A = -1 1 1. a) Is A diagonalizable? If…

A: Given problem is :

Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (2,0,0), (0,4,0), and (0,0,1)

A: We have to find the volume integral of the given function.