# 20. Let ADEF be the medial triangle with respect to AABC, and let O be the circumcenter for AABC. Then which of the following is correct? (A) 0 is also the circumcenter for ADEF. (B) O becomes the orthocenter for ADEF. (C) 0 becomes the incenter for ADEF. (D) O becomes the centroid for ADEF.

Q: 2. Use Green's Theorem (and only Green's Theorem) to evaluate |(2? + y)dx + (x² – y³)dy, where C is…

A:

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: |Use Green's Theorem to evaluate [(3x² +y)dx+4xydy where C is the triangular C region with vertices…

A: The solution is given as

Q: F D' Point D is the Nof AABC because AF, BG, and CE are all centroid incenter Submit Answer…

A: We know that, The circumcenter of a triangle is the point where the perpendicular bisectors of the…

Q: Consider the following. C: line segment from (0, 0) to (2, 4) (a) Find a parametrization of the path…

A: Given- C: line segment from (0, 0) to (2, 4)

Q: D

A:

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: Determine the distance y measured from the x axis to the centroid of the area of the triangle shown…

A:

Q: 3.use Greens theorem S(1+x dx + 2xy dy ,where C is triangle With vertices (0,0),(1,0).(1,3) oriented…

A: "Since, you have asked multiple questions, we'll solve the first question for you. If you want any…

Q: The curve C is the circle of radius 5 contained in the plane z 5 and centered around the z-axis,…

A: Solution:-

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: .2 y = z, -2 < z < 2 %3D (x - 2)² + 4y2 = 4

A: (b)  The given equation is y=z2, -2≤z≤2. Observe that y-coordinate will always be positive and…

Q: Find the centroid of the region in the polar coordinate plane defined by the inequalities 0&lt;=…

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Q: Part 4 of 8 Since we want the portion of the sphere which is above this circle, we return to the…

A:

Q: The plane z =0 separates region 1 (z 0), which is a dielectric material with ɛ, = 4, from region 2…

A: The complete solutions are given below

Q: Two particles travel along the space curves r(t) and u(t). If the particles collide, do their paths…

A: Given that Two particles travel along the space curves r(t) and u(t) collides. That mean there exist…

Q: Which one of the following is the parametric equa- tions of the line that is normal to the surface…

A:

Q: 3. Consider Hhe following two surfaces. 8x-54-82 = -13 a) Show that the surdaces intersect at the…

A: Given surfaces are  z=2 xy2 and 8x2-5y2-8z=-13 (a)  Let fx,y,z=z-2 xy2=0 Let gx,y,z=8x2-5y2-8z+13=0…

Q: 4. Locate the centroid (x, y)of the following composite areas: -3 ft 3 ft I 1.5 ft 1 ft

A: Consider the given composite area and divide then into four areas as shown in diagram below,

Q: 2r find the moment with respect to the wavic of the area hounded by the parabola v - Av-172 and v

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Q: ch is the centroid of the section reckoned lower left hand corner. 100 100 600 100 -500- Dim

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Q: . Find a parametrization for the circle (x – 2)² + y² = 1 starting at (1, 0) and moving clockwise…

A: Consider the equation of circle

Q: (6) Suppose the closed curve C in R? starts at the point (-1, 1), goes along the parabola y = r? to…

A:

Q: 2. Obtain the eccentricity e and centroid a, and y. of the following image. f(x.y)=1 (object: dark)…

A: From the figure, we have to write down all the dark box function, for which f(x,y)=1 x,y=3,2, 4,2,…

Q: The classification of az дх2 дхду ду dz, dz O A. Elliptic B. None of these О С. Нурerbolic D.…

A: Answer and explanation is given below

Q: xy = 4

A: Solution

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

A: Given:

Q: 7. Given the space curve r(t) = (4 sin t,4 cos t, 10t), Find T, N, B, and T(torsion)

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Q: Calculate (1+ cos(y²))dA,where D is the triangular region with vertices(0, 0). (–2 - Vĩ,2· VT) e (0,…

A: Given problem:- The given integral is ∫∫D1+cosy2dA, where D is the triangular region with vertices…

Q: Find the points of horizontal tangency to the polar curve. r = 3 csc 0 + 5 0 < 0 < 2n (r, 0)…

A: Solution:- Given,  r=3 csc θ+5    0≤θ≤2π To find Horizontal tendency, find horizontal tangent lines…

Q: Determine the centroid of the following Fig from X and Y axes. Y, 30 centT1 2 CentQ1 -4 -3 -2 -1 1 2…

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Q: Sketch the bifurcation diagram for y = (A– 4t)y (where A is a parameter, as usual). 2

A: To find- Sketch the bifurcation diagram for y' = λ - 4t2y (where λ is a parameter, as usual)

Q: Which of the following graphical representations shows the intersection curve, in the first octant,…

A: We have to choose which one shows the intersection curve in first octant between a cylinder of…

Q: 9) Sketch x = indieate the onientatiba of the 2t°, y = 3t, -4sts4 aud with %3D Curve an arow,

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Q: 3. WHEN THE LOAD IS UNl FORMLY DISTrRIBUTED ADRIZONTALLY A SNSPENSION BRIDGE CABLE HANGS IN A…

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Q: To illustrate that the length of a smooth space curve does not depend on the parameterization used…

A: Since you have posted multiple questions but according to guidelines we will solve the first…

Q: - I he symmetrie equidton of alne quation of alme Find the paramedic equation

A: Since you have asked multiple question, we will solve the first question for you. If you  want any…

Q: Consider the following. C: line segment from (0, 0) to (4, 8) (a) Find a parametrization of the path…

A:

Q: 56 Consider points P and Q in the x-y plane, with P = (1,0) and Q = (0,1). The line integral %3D Q…

A: Line integrals

Q: Find the centroid of the arc of the circle r = 2sin0 + 4cos0 from 0 = 0 to 0 = T1/ %3D O (2.637,…

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Q: a. Find a parametrization for the hyperboloid of one sheet x2 + y2 - z2 = 1 in terms of the angle u…

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Q: 33. Figure 14.13 shows the saddle-shaped surface z = S(x, y). (a) What is the sign of f,(0, 5)? (b)…

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Q: 12. Let H be the hyperboloid where x² – y² + z² = 6. Find an equation for the tangent plane to H at…

A: As you asked only solution for Q12 so, I answered here only Q12

Q: To illustrate that the length of a smooth space curve does not depend on the parameterization used…

A: To find - To illustrate that the length of a smooth space curve does not depend on the…

Q: 12. Find the distance from the point P(0,0,0) to the plane given by x + y +z= 6.

A:

Q: Find the polar eauation for Hhe curve Cartesianm eavation. represented by the given 2.

A:

Q: #1. Find a parametric representation of the part of the cylinder x² + z? = 9 that lies above the…

A: parametric equations for a cylinder of radius 3 x^2+y^2+z^2=r^2 Where r=3

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.