Given: ABCDE and FCG, C is the midpoint of BD Z1 = 2 4. Prove: ZF = ZG F/ A1 В C DE G Describe a single rigid motion that maps ABFC onto ADGC .

Q: Let F = Use Stokes' Theorem to evaluate · dī, where C is the curve of intersection of the parabolic…

A: To find the curl , ∇×F=i^j^k^∂∂x∂∂y∂∂zxy5z7y=i^7-5-j^0-0+k^0-x=2i^-xk^ To find the normal vector,…

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

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Q: Let C be the positively oriented circle x? + y? = 1. Use Green's Theorem to evaluate the line…

A: Compare the integral ∫C19ydx+20xdy with ∫CMdx+Ndy to obtain M=19yN=20x Consider…

Q: Find the moving tri hedral of f R CE) = t, 2E> at %3D

A: This is a problem of differential Geometry.

Q: Evaluate f, A.n ds, where A = zi +j- 3y²zk and S is the surface of cylinder x? + y? = 16 included in…

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Q: Evaluate: I| (x2 + y?) ds over the surface S of the sphere x2 + y? + z? = 5. Use Formula (5.22a)…

A: The solution is given below:

Q: Find the area of the surface with the following parametrization: u COS V Τ (u, υ) - u sin v u? 0<u<…

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Q: 13-Evaluate JSS zdV E where E lies between the spheres x2 + y? + z² = 1and %3D x? + y? + z? = 4 in…

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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: Which composition of two rigid motions maps ΔABC to ΔA'B'C?  A.Rx-axis ∘ Ry-axis B.Ry-axis ∘ Rx-axis…

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Q: Evaluate F · dī where C F = , and C is the circle of radius 3 centered at the origin parametrized…

A: To find  ∫CF→.dr→ where c is circle of radius 3 centered  at origin parametrized in counterclockwise…

Q: e dV where E is enclosed by the paraboloid z =1+ a? + y", the cylinder a? + y = 3, E Evaluate and…

A: We will use triple integration here

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: In which part of the (x, y) plane the following equation is elliptic? Uzr + 4ury + (x² + 4y*) uyy =…

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Q: Let f (z) = 33O = Q A = 10and B= 10 + 10iet C be the contour composed of the line segments OAand…

A: The given problem is to evaluate the complex integral of the given function over the given semi…

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: Evaluate ez dV where E is enclosed by the paraboloid z = 4 + x? + y², the cylinder x? + y? = 1, and…

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Q: (a) Let r = where C is the unit circle oriented counterclockwise, and Vr2 + y?. Calculate fF Tds…

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Q: If the curve y = f(x), a ≤ x ≤ b, is rotated about the horizontal line y = c, where f(x) ≤ c, find a…

A: Given, Curve y= f(x) , a≤x≤b Rotated about a horizontal line y=cwheref(x)≤c

Q: Calculate ff. (6 – z) dS if S is the cone portion z = limited by the plane z= 6 = 2/x² + y² Answer:…

A: Given the cone z=2x2+y2 limited by the plane z=6 At z=6, 2x2+y2=6x2+y2=3x2+y2=32 Thus, the…

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: 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: Let E be the part of the unit sphere r² + y²- = 1 where z > vx² + y². Calculate 22 dA.

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Q: Let F = . Use Stokes' Theorem to evaluate curlF · d§ , where S is the part of the paraboloid z…

A: Given: F=-yz,xz,xy To Find: Use Stokes' Theorem to evaluate ∬Scurl F·dS, whereS is the part of the…

Q: Let o be the surface of the sphere given by r? + y? + z² = a². Evaluate the surface integral f,(x² +…

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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: Use Stoke 's Theorem to evaluate [ V. dr, where v= y²i + xyj + xzk, and c is the bounding curve of…

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Q: 4 Assuming that the curve ris thex + y +z = 0 intersection of the plane and the sphere , then the…

A: As per the question we are given a closed curve Γ , defined as the intersection of the plane x+y+z =…

Q: Find The or rthoganal tajeclolies. ! d faly Curver r= 4C cose, where C be being parameer

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Q: Evaluate fff(x +y +:' dV, where a is the solid hemisphere (half of the sphere) enclosed by x +y+ =1…

A: Here in the given question, find the integration of the given function:∭Dx2+y2+z232dVWhere Ω is the…

Q: Please help.

A: Note: The tangent plane to the surface given by f(x, y, z) = 0 at (x0, y0, z0) has the equation,…

Q: The spherical surface S is tangent to the z=0 and x+y+3z−2=0 planes, with (−1,2,0) being one of the…

A: Explained below

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 F = . Use Stokes' Theorem to evaluate curlF · dS,where Sis the part of the paraboloid z = 10 –…

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Q: Exercise 7 T. Given: SU and RT bisect each other a. Prove: ASVR = AUVT b. Describe the rigid…

A: Given: A quadrilateral STUR, where SU and RT bisect each other. a. Since SU and RT bisect each…

Q: b) Use Gauss' theorem to evaluate SS F · ndS where F = (x² – y)i + y°z²j+ (xy – yz³)k and o is the…

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Q: Evaluate e dV where E is enclosed by the paraboloid z = 1+ æ² + y°, the cylinder a? + y? = 4, and…

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Q: Evaluate (xr + y² + =³)? dV, where 2 is the solid hemisphere (half of the Ω sphere) enclosed by x +y…

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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: Evaluate T// y dV, where E is the portion of the sphere x² + y? + z² = 9 in the first octant (where…

A: Let, x=rsinθcosϕy=rsinθsinϕz=rcosθ

Q: The distance from a point S(xo, Yo, Zo) to a plane M: ax + by + cz + d = 0 is given by In PS| d :…

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Q: Let F = . Use Stokes' Theorem to evaluate curlF · dS , where S S is the part of the paraboloid z = 9…

A: Find your answer below

Q: Let S be the sphere x + y² + z? = 9 oriented outwards, and F = (5x, 7z, –3y). Evaluate: F. dS. The…

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Q: 2. Use Stokes' Theorem to evaluate ſ. V × F·n dS where F(x, y, z) = and C is the part of the sphere…

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Q: Let F = · Use Stokes' Theorem to evaluate curi curlF · d§, where S is the part of the paraboloid z…

A: here i had written stokes theorem and done some basic calculation to find the curve of intersection…

Q: Evaluate z dv, where E is enclosed by the paraboloid z = x² + y2 and the plane z = 16.

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Q: Use Gauss's D.T. to evaluate SSA.ds where Ã=x'i+y°§+7f qud S is the , surdace of the sphere x+j+z²=…

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