The diagonals of an isosceles trapezoid ABΓΔ (ΑΒ // ΓΔ) intersect at O. If E, Z, H, Θ are the means of OA, OB, OΓ, OΔ, respectively, prove that ΕΖΗΘ is an isosceles trapezoid.

Q: In AMNP, T is the centroid. If MR=30 find MT. N R T M S

A: We are given that T is the centroid and MR=30. We know that the centroid divides each median in a…

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: Consider AABC with its centroid at point G and median at BH. What is the length of GH if BG = 3x + 4…

A: Given Data: The length of BG is: BG=3x+4 The length of GH is: GH=x+10 The ∆ABC with its centroid at…

Q: Let C be the positively oriented square with vertices 0, 1, 1 + i, i. Evaluate using the definition…

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Q: Evaluate ://| y} dV, where E is the solid tetrahedron with vertices at (0,0, 0), (2,0, 0), (0, 2,0),…

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Q: Given: ZWZX ZYZX; ZW = ZY Prove: ZX is a perpendicular bisector of WY

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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: D

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Q: Let S be the solid tetrahedron bounded by the four planes a = 0, y = , z = 30, and z = 4x + y. !!…

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Q: Prove that the volume of the sphere x² + y² + z² = a² is V =÷na³

A: In this question, we find the volume of sphere by using triple integral

Q: (b) Let the distance between two adjacent planes parallel to the plane (hkf) in the direct lattice…

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Q: Evaluate e dV where E is enclosed by the paraboloid z = 4+ x² + y?, the cylinder E x2 + y? = 1, and…

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Q: Evaluate e dV where E is enclosed by the paraboloid z = 2 + x² + y°, the cylinder z² + y² = 2, and…

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Q: Let M be an elliptic paraboloid z = y² + 2?. (A) "Compute the Gauss map and the shape operator. (B)…

A: Answer for sub question a: Given x=y2+z2 A parametrization is given by: Xu,v=u2+v2,u,v Then,…

Q: Every triangle has a balancing point, called the centroid. O True O False

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Q: Apply Stoke's theorem to calculate S. (x + y – 4)dx + (2x – z)dy + (y + z)dz, where C is the…

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Q: a) Evaluate (-ri-yj+2z k) n dS, where a is the portion of the paraboloid : 3x +3y between the planes…

A: We have to Evaluate the Integral using polar coordinate

Q: In isosceles trapezoid WXYZ with bases ZY and WX, ZY = 8, YX = 10, and WX = 20. Find height h (the…

A: Given  The  WXYZ  is isosceles trapezoid  with bases ZY and WX .  Here ZY =8  , YX =10  and WX =20

Q: Let T be the tetrahedron with vertices (3, 0, 0), (0, 5, 0), (0, 0, 4) and the origin. Write /| f(x,…

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Q: Let C be the positively oriented square with vertices 0, 1, 1 + i, i. Evaluate using the definition…

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Q: Evaluate // e² dV where E is enclosed by the paraboloid z = 2 + x² + y², the cylinder E x² + y? = 3,…

A: Since we are given with the multiple number of questions and answered according to the guideline.

Q: do 10 please

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Q: Let M be an elliptic paraboloid a = y? + z². Compute the Gauss map and the shape operator. Find k…

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Q: Use the flux form of Green's Theorem to evaluate |(6xy + 8y°) dA, where R is the triangle with…

A: Greens' Theorem : Let D be the region bounded by the curve C. Let F(x,y)=P,Q be the vector field…

Q: Let E be the solid parallekepiped with vertices Co,0,o).(LLO).co,l,3),(1,0,). C1,2,3),Cし,4).(2,1,1)…

A: Here, vertices are given in 3D. So, for taking limits of X and Y, we'll look for the projection of…

Q: 4. If M is a centroid of triangle WOR and WM = 16, what is WX? %3D W Y M R

A: centroid:- i). It is the intersection point of all the medians of a triangle. ii). It divides the…

Q: Identify the correct notation to transform rhombus PALE onto P"A"L"E" to show the figures are…

A: Geometry

Q: In trapezoid WXYZ with bases ZY and WX, ZY = 12, Exercises 19, 20 YX 10, WZ 17, and ZD = 8. Find the…

A: Given: ZY=12 YX=10, WZ=17 ZD=8

Q: Use the Green's theorem to calulate So (3x²y – xy? – 3.x²y²) dx + (x³ – 2.x³y+ x²y) dy, where C is…

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Q: Surface Area top front width length area of front = h x w area of top = w x 1 area of bottom = w x 1…

A: Explanation of the answer is as follows

Q: In isosceles trapezoid WXYZ with bases ZY and WX, ZY = 4, YX = 10, and WX = 20. Y. D. Find height h…

A: Consider the given figure, First find value of EX. Lets assume EX=x As it is isosceles trapezoid, so…

Q: Given a ray r(t) = (0; 0; 0) + t(1; 0; 0), t ≥ 0, and a set of spheres of unitradius and centered…

A: Given ray is rt=0,0,0+t1,0,0, where t≥0. The given ray can be written as: rt=0,0,0+t1,0,0x,y,z=t,0,0…

Q: The barycentric coordinates of a point P with respect to the non-collinear points A, B,C is given by…

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Q: If T is the centroid of MNP, TN=16, MQ=23, and RP=18, find each misiing measure

A: Here T is the centroid of ∆MNPTN = 16,  MQ = 23 and RP =18We find missing measure

Q: Let T be the tetrahedron with vertices (4, 0, 0), (0, 3, 0), (0, 0, 5) and the ori I f(x, y, z) dV…

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Q: (b) Evaluate SSI, zdV, where D is the solid tetrahedron bounded by the four planes x = 0, y = 0,z =…

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Q: ABCDEF is a regular hexagon with centre O. OA = a,OB = b and M is the midpoint of BC. X is the point…

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Q: n trapezoid WXYZ with bases ZY and WX, ZY = 14, YX = 10, WZ = 17, and ZD = 8.   what is the base

A: we have ; In trapezoid WXYZ with bases ZY and WX, ZY = 14, YX = 10, WZ = 17, and ZD = 8.

Q: Use Green's Theorem to evaluate x dx + xy dy where C is the triangle with vertices (0,0), (1,4),…

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Q: Evaluate e dV where E is enclosed by the paraboloid z = 4+x² + y°, the cylinder x² + y? = 3, and the…

A: Here we have to evaluate ∫∫∫E ez dV , where E is the enclosed by the paraboloid z=4+x2+y2 , the…

Q: let s is the curved surface of the cylinder x²÷a² + y²÷b²=1 0≤z≤c , then evaluate…

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

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Q: a) Evaluate /| (-ri-yj+2: k) · n dS, where o is the portion of the paraboloid z = 3x2 + 3y? between…

A: Define a function fx,y=z or fx,y=3x2+3y2.  So, the flux integral is:…

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: Use Green's Theorem to evaluate x' dx + xy dy where C is the triangle with vertices (0,0), (1,4),…

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Q: Find the average haight of the Paraboloid z- xry* over the square osx <2, osd<2

A: We need to find the average height of paraboloid

Q: a) Evaluate //(-ri-yj+2: k) n dS, where a is the portion of the paraboloid : = 3r - 3y between the…

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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.

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…