2. If Z is the centroid of ATUV, TZ = 60, XZ = 28, and WZ = 25, find each missing measure. a) ZV = b) ZY = W c) ZU = d) TY = e) XV =

Q: Find the centroid of the solid hemisphere of radius a that is enclosed between the ry-plane and z =…

A: Given solid hemisphere of radius a enclosed by xy-plane and z=a2-x2-y2 The centroid is given by the…

Q: In Exercises 53 and 54, use a theorem of Pappus to find the centroid of the given triangle. Use the…

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Q: If KN=2x+1 and NJ=3x+5, what value of x makes point N the centroid? K, J M

A: (1).   If in the given triangle N is the centroid then the point N divides the line HL, JK and LM in…

Q: Verify Stokes' Theorem if o is the portion of the sphere x + y +z² =1 for which z20 and F(x,…

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Q: Let D be the solid in space lying beneath the ry-plane and between the sphere r2 + y? + z² = 3 and…

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Q: B) Show that V=367 is the volume of a sphere of radius 3 by using spherical coordinates.

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Q: Determine the centroid of plane lamina having channel section as shown in figure below. 30 cm- cm…

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Q: 9. Use spherical coordinates to find the volume of the part of the ballps 4 that lies between the…

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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: In AABC, X is a centroid. If AX = 6 units, calculate XE. E D B A

A: topic - centroid of a triangle

Q: Evaluate ze*²+y²+z? dV, where E is the portion of the ball centered at the origin of radius 5, x2 +…

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Q: In the strip of rectangles shown below, a certain rigid motion applied to the leftmost rectangle…

A: The given pattern has vertical reflection symmetry since it would have two mirror images if we draw…

Q: If point N is the centroid of AHIJ, IM = 18, KN = 4, and HL = 15, find JN. %3D %3D %3D K /N/

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Q: Draw an obtuse triangle and, by construction, find the centroid of the triangle. (HINT: Begin by…

A: To get an obtuse triangle, draw a triangle with one of its interior angle should be greater than…

Q: Use Exercise 22 to find the centroid of the triangle with vertices (0,0), (a, 0) and (a, b) where…

A: To find the centroid we add the x coordinates and the y coordinates respectively and then divide by…

Q: 21. Show that the volume V of a region D in space enclosed by the oriented surface S with outward…

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

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Q: Consider the area of the part of the plane z=ax+by+c that projects onto some region D in the…

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Q: Use Stokes' theorem to evaluate (ry – y) i – In zj+ (r+r²) k) - dr, where C is the intersection…

A: Let F be a vector field and C be the boundary of the surface S. The Stoke's theorem states that…

Q: In RST, U is the Centroid. If SQ=6, find SU and UQ W R

A: Given query is to find SQ and UQ.

Q: ) show thet the pants ACいらり)。 B(2,2,2)) c(o,1,5) and D(1,0,5) are coplanear (in the Same plane). )If…

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Q: Use Stokes' Theorem to compute 1 z? dx + (ry) dy + 2020 dz, where C is the triangle with vertices at…

A: Given I=∮C12x2+xydy+2020dz where C is the triangle with vertices at 1,0,0 , 0,2,0 , 0,0,2 traversed…

Q: Exercise 11. Compute the area of the pseudo-sphere, i.e. the surface of revolution obtained by…

A: Area= ∫2πrds=2π∫r.dr/sin(ϕ)∫2πrds=2π∫r.dr/sin(ϕ) Due to tangent property: r/sin(ϕ)=a,r/sin(ϕ)=a, and…

Q: Use a paragraph, flow chart, or two-column proof to prove that ZX̅̅̅̅ is the perpendicular bisector…

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Q: In AQUW, point T is the centroid, and VT = 5 . Find QT and VQ. W V QT= VQ =

A: We know centroid divide each median in 2:1 ratio.

Q: In ANPQ, U is the centroid. If NS=15 find US. R S U

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Q: 4. Find each volume. (a) A solid is being bounded by paraboloids z = 2x² + y? and z = 27 – x² – 2y?.…

A: We have to find the volume  from the given condition

Q: Find the volume of the solid bounded by the paraboloid z = 2 – 4x? – 4y? and the plane z =

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Q: 8. Evaluate ze+y´+z² dV, where E is the portion of the ball centered at E the origin of radius 5, x?…

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Q: b. Describe the rigid motion(s) that would map AUVT onto ASVR.

A: Triangle SVR is congruent to triangle UVT by SAS congruence rule as per a. part. Four types of rigid…

Q: Draw the solid of revolution obtained by rotating the given plane region about line L. Which figure…

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Q: In APQR, V is the centroid. If QU=54 find QV. S T V R U

A: Centroid is the point of intersection of the medians.we know that centroid divides the each median…

Q: 5/10 Determine the coordinates of the centroid of the shaded area. y * = ky? a b.

A: Given:

Q: 1- Find Aue Volume the Paralle RPed by usi+j-21k and V= -i_-k ,W = 2i44j-2K %3D

A: As we know that the volume of the parallelepiped is: V=u→·v→×w→ Given:…

Q: The volume of the parallelepiped is Volume = |a x b||c|| sin | = |(a × %3D b). c| True False

A: Using direct formula

Q: Consider the area of the part of the plane z = ax + by+C that projects onto some region D in the…

A: If the area of the region D on xy-plane is k. That is, ∫∫DdA=k. If the area of the some region of…

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: Determine the coordinates of the centroid of the shaded area. 25 y 70 I 50 25 60 60 50. 175…

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Q: 3. Please give clear explanations

A: The parametrization of a surface S is given by       G(u, v)=(u, v, uv) where D is u2+v2≤1.

Q: (1) Compute where Cis the couater dockwise oriented boundary of upper half unit disc D.

A: It is given that, ∮Cy2dx+3xydy here C is counter clockwise oriented upper half disc D.   Here,…

Q: Evaluate the surface integral. JI (12 + y2 + 2) ds S is the part of the cylinder x2 + y2 = 9 that…

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Q: Locate the centroid of the plane area shown if a 25 in. 20 in. r = 15 in. 30 in.

A: Area of Rectangle equals to : Arectangle=20+3025                =1250in2 Area of semi circle equals…

Q: A: Determine the mass and center of mass of the solid that bounded by the paraboloid z = 9y? + 9x?…

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Q: What is the center of gravity of the solid formed when the plane region bounded by y = x, y = 2x,…

A: Let us start solving the problem step by step

Q: Let B be the ball with center at the origin and radius 1 SIS 4(z² + y² + z*)dv = B

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Q: (b) Use Stokes' Theorem to evaluate (f, curlF .n dS, where F(x,y, 2) = x²yzi + yz?j + z³e™Yk and S…

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Q: 3. If D is the centroid of APQR, PA = 17, BD = 9. and DQ = 14, find each missing measure. %3D P a)…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Show that the sphere of radius 5, X(u, v) = (u, v, v25 – u? – v²) is regular.

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