Solve by Cramer’s rule         3x  + y   + 4z = 11         4x  – 4y + 6z = 11                                              6x  – 6y           =   3

Q: Compute the triple integral and please show work

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Q: Let T be the tetrahedron with vertices (2, 0, 0), (0, 3, 0), (0, 0, 5) and the origin. Write (a, y,…

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Q: Given that the system zy² + zu + v 2r+ 2y-uv 2 zu + yu – ryz = 1 at (u, v) = (1,1)? can be solved…

A: Given system of equations as follows, xy2+zu+v2=3x3z+2y-uv=2xu+yv-xyz=1

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: Find c > 0 c > 0 such that the area of the region enclosed by the parabolas y = x 2 − c 2 y = x 2 -…

A: To find the value of c given area between the curves.

Q: Find ff -6xydA over tl D triangular region D with vertices (0,0) (2,0), (0, 4) 16 O -8 8 O -16 68 O

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Q: Sketch the solid described by the given inequalities. 2 sps 3, 0s p s a/3, 0s0sa 1.5 1.0 0.5 0.0

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Q: [1 1 2 3 4 5 1 1 'ind the nullity, dimensions of column space and the rank of the given matric A

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Q: 6. Evaluate (a + y) da dy dz, where D is the tetrahedron with vertices (0,0,0), (1,0, 0), (0, 1, 0)…

A: Introduction: The triple integral is applicable to find the volume of a solid enclosed by given…

Q: If b = 6 cm, c = 3 cm, h = 6 cm, and a = 2 cm, the centroid of the area about x axis is equal to:…

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Q: 10. Use Green's Theorem to evaluate the integral fe y dx + 2xy³ dy, where C is the square with…

A: Introduction: By applying Green's theorem, one can determine line integral through surface integral.…

Q: 17. Integrate G(x, y, z) = xyz over the triangular surface with vertices (1, 0, 0), (0, 2, 0), and…

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Q: 5. Use Cartesian coordinates to evaluate JIJ ² av where D is the tetrahedron in the first octant…

A: As there are multiple questions with subparts, I am doing the first question only as per the…

Q: Show that, in the triangular region with vertices (0,0), (1,0) and (1,1) the following double…

A: Double integral

Q: Find S. (12z+ z²) dz, where C is the boundary of the rectangle with vertices at the points 1+ 2i, –…

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Q: 6. What is an equation for the largest ball centred at (0,0, 1) that can fit in the paraboloid z…

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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: Considering f(, Y, z) = z + x²y and S as part of the cylinder y² + z² = 25 that is between the plans…

A: It is given that surface S is the part of the cylinder y2+z2=25 lies between the planes x = 0 and x…

Q: Find the coordinates of the centroid (to the nearest 0.01 in.) of the uniform flat-plate machine…

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Q: 3) . Find the centroid of the upper half of a sphere of radius 1, that is, of the set of points in…

A: Given the upper half of the sphere with radius 1, that is x2+y2+z2=1,z≥0. Find the centroid x¯,y¯,z¯…

Q: Let C be the positively oriented square with vertices (0, 0), (3, 0), (3, 3), (0, 3). Use Green's…

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Q: 2. Find the coefficients in the interval [0, 2], where s (x) is a natural cubic spline. 1+x - ax? +…

A: we have s(x)=1+x-ax2+bx3                               x∈0,1c+d(x-1)+e(x-2)2+(x-2)3      x∈1,2 s(x)…

Q: - 9 + 3 + 3y and Find the volume of the solid bounded by the paraboloids z == z = 8 – 3x - 3y

A: To find volume of the solid bounded by the paraboloidsz=-9+3x2+3y2 and z=8-3x2-3y2

Q: 1. Sketch carefully the solid enclosed by the three cylinders x + y* – 1,x² + 2² = 1, and y + z² =…

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Q: The altitude of a tetrahedron is 2.5 cm. 1. Compute the lateral surface area.  a. 15.21 cm² b. 17.21…

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Q: Q6/ Find the volume of the parallclogram-sided determined by: u- -3i +7j +5k, v -3i + 7j-3k, and w-…

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Q: 5. Evaluate y* dV, where E is the solid tetrahedron with vertices at (0,0,0), (2,0,0), (0, 2,0), and…

A: we can evaluate the given integral. ∫∫∫R f(x,y,z) dV =∫∫∫R f(x,y,z) dzdydx

Q: The upper half of the unit sphere x2+y2+z2=1 is z=Square root of 1-x2-y2. Find its centroid

A: Solution Given The intersection gives z2=1-x2+y2we need to find the centroid

Q: The shape of a redwood tree (without any branches) can be modeled by an upside down paraboloid, f(x,…

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Q: Evaluate the triple integral. 4xyz dv, where Tis the solid tetrahedron with vertices (0, 0, 0), (1,…

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Q: 1. 2. The area bounded by y = = -(x - 1)² + 4 , and the lines x =1, y = 2, and y = 4 rotated about…

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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: Which is the equation of a sphere with a center at (1,0,-2) with a volume of 36(pi)(u^3)? a.…

A: We first defined the equation of sphere and centre,volume . Using this formula we have equation (a)…

Q: 1) Consider the solid Q in the first octant, generat surfaces: z = (y – 3)² + 1, 2r + 4z = 16, 1= 1,…

A: Volume of solid: Let z=f(x, y) and z=g(x, y) be the functions of x and y of a solid, and let x=a to…

Q: Find (x ,y, z) by using Jacobi or Gauss of Gauss Jordan method 5z — Зу + х%3 -1 2y – z = 2 z - 4x =…

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Q: 4. Evaluate ([[. (2x+3y)dxdydz where S is the tetrahedron in the first octant bounded by the…

A: The objective is to solve the integral: ∫∫∫S2x+3ydxdydzS: tetrahedron in first octant bounded by the…

Q: number 44 and it says use example 4 so i attached that as well

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Q: show that a=(2x^2+8xy^2z)i+(3x^3y-3xy)j-(4y^2z^2+2x^3z)k is not a solenoidal but b=(xyz^2.A) is…

A: Given:A=2x2+8xy2zi+3x3y-3xyj-4y2z2+2x3zk To check solenoid we will check ∇.A=0 or not…

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: 1) Evaluate the triple integral SS, f(x,y,z)dv : B) f(x,y,z) = 3y² – 2z , Q is the tetrahedron…

A: given f(x,y,z) = 3y2-2z, Q=3x+2y-z=6 The region bounded by the equation Q is a tetrahedron cutting…

Q: Find the equations of the system of curves on the cylinder 2y = x² orthogonal to its intersections…

A: The given family of curves is got as the intersection of F(x,y,z)=2y-x2=0 with a one-parameter…

Q: 27) If the solid of revolution formed by rotating R2 about the y-axis is a cylindrical shell, then…

A: Solid of revolution

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: EXAMPLE 6 Find the volume of the box (parallelepiped) determined by u = i+ 2j – k, v = -2i + 3k, and…

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Q: 5. Find the volume generated by the equation x2 +y² – 4x - 6y –- 12 = 0 if it is rotated about the…

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Q: 5xyz dv, where T is the solid tetrahedron with vertices (0, 0, 0), (1, 0, 0), (1, 1, 0), and (1, 0,…

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Q: 2) The solid lies between planes perpendicular to the x-axis at x = -2 and x = 2. The cross sections…

A: Let's find.

Q: 4 In AVYX, the centroid is Z. Use the diagram to solve the problems. A. If XR = 24, find XZ and ZR.…

A: In given triangle we have: XO=OV, XP=PY & YR=RV Therefore, OY, XR & PV are median of given…

Q: 1. The accompanying figure shows two polygonal paths in space joining the origin to the point (1, 1,…

A: Given: The function with two polygonal paths in space joining the origin to the point (1, 1, 1).…

Q: 2) The double integnal | 3x ekdy, whetzeT is the tniang le of VErtices 6,0),c2,0) ond (eti-2),…

A: The double integral is an integral with respect to two different variables the integral of a…