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

Q: Calculate fo(7x + 6y) i + (4x + 7y) j) dr where C is the circular path with center (a, b) and radius…

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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: Evaluate the surface SS₂ xz ds S is the part of the 2x+2y+z=4 that li- the first octant.

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

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Q: Which of the following is not a parametrization of the parabola y = ² ? O x = vt, y =t O x = t, y…

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Q: Let S be the closed surface composed of the parabaloid z = x2 + y? and the planes z = 2 and z = 4.…

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Q: Consider the solid that is bounded above by x² + y? + z? = 169 and below by z=5. %3D

A: In this question, we have to write the triple integral to find the volume of the solid bounded by…

Q: Below is the solid Q bounded by the surfaces S,: x? +y? +z? = 4, S;: z = V3 and S,: y= x in the…

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Q: Consider the surface S: z = 4 - x2 ,bounded by y = −5(x2 - 1) and y = 0, just as it is shown in the…

A: We have to find the area of the surface S, and we will use surface integral to do that.

Q: A solid G is bounded by the paraboloid z = 4 - x? – y?, the cylinder x² + y? = 4 and the plane z =…

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Q: Use Stokes' Theorem to evaluate F. dr, where F (x, y, z) = zi + yj – xk and C is the boundary of the…

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Q: 6. Use Stoke's Theorem to evaluate fF dr, where F =, and C is the part of the paraboloid z = 4 - x2-…

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Q: Let S, be the part of the paraboloid z = a² + y² that is inside the cylinder a? + y? = 1, S2 the…

A: “Since you have asked multiple questions, we will solve the first question for you i.e. (c). If you…

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 e dV where E is enclosed by the paraboloid z = 5 + x² + y°, the cylinder 2² + y? = 5, and…

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

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Q: WY bisects ZXWZ and ZXYZ. Complete the proof that AWXY E AWZY. Y. W

A: Given that WY bisects ∠XWZ and ∠XYZ. We know that when a line bisects an angle, it means it divide…

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

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Q: Use the Divergence Theorem to evaluate (5x + 10y + z) ds where S is the sphere x2 + y2 + z2 = 1.

A: In the given problem, S is the sphere x2+y2+z2=1Divergence Theorem:∬SF·n dS=∭Ediv F dVNow, the…

Q: Use the Divergence Theorem to evaluate (4x + 9y + z2) ds where S is the sphere x2 + y2 + z? = 1.

A: Thanks for the question :)And your upvote will be really appreciable ;)

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

A: Given : C is a positively oriented circle x2+y2=1 We have to evaluate the line integral…

Q: Let F(z, y, 2) = 12?ri + (ty + tan(z))j + (1z?z+ 4y?)k. Use the Divergence Theorem to evaluate f, F…

A: We must apply the Divergence theorem on a closed solid, but the surface S is not closed (it is just…

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: ded above by surface z = 10 – x2, bou e planes y = 0 and y = 3.

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Q: Let S be the closed surface composed of the parabaloid z = x² + y? and the planes z =2 and z = 4.…

A: Please see the answer below.

Q: Consider the following figure. R. Given: ST bisects RSV MERST - (x + y)e mzTSV = (2x - 3y)° !3!…

A: Given: The line ST bisects the ∠RSV. m∠RST=x+y°. m∠TSV=2x-3y°. m∠RSV=80°. Since, the line ST…

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: Evaluate e dV where E is enclosed by the paraboloid z = 5 + x² + y°, the cylinder 2² + y? 1, and the…

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Q: 10. Using Stoke's theorem, evaluate y dx+ xz dy+x² dz where C is the boundary of the triangle cut…

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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: 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: Let S be the closed surface composed of the parabaloid z = x² + y? and the planes z = 2 and z = 4.…

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Q: Consider the surface: S:z = 4 – a?, in the first octant and bounded by x² +y°, as shown in the…

A: The equation of the surface given is as follows: z=4-x2 The surface is bounded by the curve x2+y2=4.…

Q: Evaluate ffp(4xy + 1) dA, where R is the region in the upper half-plane bounded by the circles a? +…

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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: Use the Divergence Theorem to evaluate (4x + 7y + z²) dS where S is the sphere x2 + y2 + z² = 1.

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Q: Calculate fc((7x + 6y) i + (4x + 7y) j) dr where C is the circular path with center (a, b) and…

A: The path is given as the circular with center (a, b). Now the integral is: I=∫C (7x+6y)i→ +…

Q: Give an example of a parametrisation of the unit circle, C = {(x,y) E R² |x²+y² = 1}, that generates…

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Q: Given: ABCDE and FCG, C is the midpoint of BD Z1 = 2 4. Prove: ZF = ZG F/ A1 В C DE G Describe a…

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Q: V = (x +y) z, evaluate ∮ VdS, where S is the surface of the cylindrical wedge defined             by…

A: Consider the given information. V=(x+y) z And, the given limits are 0<ϕ<π2, 0<z<2.…

Q: Use the Divergence Theorem to evaluate (4x + 3y + z) dS where S is the sphere x2 + y2 + z2 = 1.

A: The divergence theorem establishes the equality between surface integral and volume integral.

Q: Given: ZW ~= ZY , X is the midpoint of WY Prove: ZWX ~= ZYX

A: Given: ZW≅ZYX is midpoint of WY

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 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: Evaluate e dV where E is enclosed by the paraboloid z = 5 + x + y°, the cylinder + y = 1, and the ry…

A: To Determine: evaluate ∫∫∫eZdV  where E is enclosed by the paraboloid z=5+x2+y2,the cylinder…

Q: Evaluate F. dS, where F = 6xy²i + 6x²yj + 2z°k and S is the surface of the unit sphere.

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