Why do special kinds of differentiable manifolds, such as Pseudo- Riemannian manifolds of signature (3, 1), form the basis for General Relativity, rather than other mathematical methodologies?
Q: Can one draw two non-intersecting closed curves that each do not bound disks on RP ^2? How about on…
A: The real projective plane (RP^2 ) is classically defined as the space of lines through the origin in…
Q: Parametrize a path for the curve that is a circle in the x-y plane that has radius 2 (a) with center…
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Q: Does the Divergence Theorem apply to surfaces that are not closed?
A: By Stokes' theorem:
Q: find a parametrization of the curve. The line passing through (1, 0, 4) and (4, 1, 2)
A: Given: A line is passing through the points 1, 0, 4 and 4, 1, 2.
Q: Use Lagrange multipliers to find the highest point on the curve of intersection of the surfaces.…
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Q: Can point normal form of a plane have no y? Leaving only constant (x - constant) + constant (z -…
A: Introduction: A aircraft is a flat, two-dimensional floor that extends to infinity in mathematics.…
Q: メメュメ *+2* + 0.5(*) +2X, +2 Use Center Manifold Theorem to determine the stability at the origin…
A: Given: x1∘=x2-x1x2∘=x12+2x1+1x12+2x1+2-0.5x2+1 Now, f1x1=∂f1∂x1=-1 f1x2=∂f1∂x2=1…
Q: bounded by the curve f(x)= Vx-1, y-axis, line y =1 and line y =
A: We will find the area bounded by the curves.
Q: AREA UNDER THE PLANE 6x +4y +z = 12 above the disk W/ BOUNDARY CIRCLE
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Q: IntegrateF(x, y, z) = z, over the portion of the plane x + y + z = 4 that lies above the square…
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Q: 55. A point moves along the intersection of the elliptic parab- oloid z = x+ 3y and the plane y = 1.…
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Q: Is the below statement True or False? The parametrization for a given curve is unique.
A: No. Parametrization of a curve is not unique. For example y = x2 can be written as (t,t2) or…
Q: A solid cube, 2 units on a side, is bounded by the planes x = +-1, z = +-1, y = 3, and y = 5. Find…
A: Given:
Q: Jategrate h (x.y) = (x+y)i+(-x)j over the closed curve that begins at (-1, 0), goes along the x-axis…
A: we will use green theorem here to solve this question
Q: Find a parametrization of the curve. The vertical line passing through the point (3, 2, 0)
A: Consider the given point 3 , 2 , 0
Q: Find a parametrization of the circle of radius 5 in the xy-plane, centered at (−4,−4), oriented…
A: If the radius of the circle is r and the centre is (h,k), oriented counterclockwise. Then the…
Q: Find a parametrization for the sphere of radius 2.
A: Consider the equation of the sphere x2+y2+z2=22. Here the sphere is centered at origin.
Q: Find the points on the hyperbolic cylinder x2 - z2 -1 = 0 that are closest to the origin. please…
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Q: Express the operators ( gradient , divergence curl and laplacian ) in spherical coordinates.
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Q: cally integra then in any ng curves is
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Q: 3. Calculate the centroid of the given illustration below. y-axis 7.5ft- 4ft 2ft 5ft- х-ахis 2ft
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Q: 1. A such that the difference in distances between (x, y) and two fixed points (called is the set of…
A: A___ is the set of points (x, y) in a plane such that the difference in distances between (x, y) and…
Q: What is a parametrization of a curve in the xy-plane?
A: we have to tell what is parametrization of a curve in the xy-plane?
Q: Find the Largest open rectangle in the plane in which the hypotheses of Existence and uniqueness…
A: Answer
Q: Obtain the dirfferential equation of the family of curves: 1. All circles passing through the…
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Q: 5 – 4z Show that the reactiob w= transformation the circle z =1 4z -2 in to a circle of a radius…
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Q: 5. Are there any points on the graph of x2 - y? – 22 = 1 where the tangent plane is parallel to the…
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Q: -axis. 5. Evaluate dV, where E is the solid tetrahedron with vertices at (0,0, 0), (2, 0, 0),…
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Q: 1 4. Let f(=) =- s · Show that J (z)dz = 0 , where C is a simple closed contour not passing…
A: Moreras theorem
Q: 9-x²-y² is the upper √y half of the disc centered at origin with radius r = 3 The domain of f(x, y):…
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Q: Find the points on the hyperbolic cylinder x2 - z2 -1 =0 that are closest to the origin. please…
A: The parametric equation of hyperbolic cylinderx2-z2-1=0 is , x=cos hθ y=y…
Q: Attached. I have to determine if the isolated singularity is removable, a pole, or essential.
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Q: 4. Parameterize the curve of intersection of the surfaces z = x² + y² and y² + (z – 1)² = 1.
A: parameterisation
Q: 2.Proof that any tangent plane for the surface F(- point = 0 passses through a fixed
A: Given below clear explanation
Q: A rectangle ℛ with sides a and b is divided into two parts ℛ1 and ℛ2 by an arc of a parabola that…
A: A rectangle ℛ with sides a and b is divided into two parts ℛ1 and ℛ2 by an arc of a parabola that…
Q: Find the centroid (¯x,¯y) of the triangle with vertices at (0,0)(1,0) and (0,5) x¯= y¯=
A: Answer is given in next step.
Q: Find the orthogonal trajectories of the conicoid (x + y)z = 1 of the conics in which it is cut by…
A: Given:The equation of conicoid is (x+y)z=1The system of the plane is x-y+z=K, where k is…
Q: Draw the parameterized surface. (Decide on a reasonable domain for u and v.)
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Q: Use Cauchy-Riemann equations to find all points z such that fis differentiable: (a) f(z)= (b)…
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Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x2 + y2 + z2 = 1 is T =…
A: We have given; The temperature T at any point (x, y, z) in space isT = 400xyz2and the unit spherex2…
Q: Region Ris enclosed by the curve y = 2 Vx – 3, the line y = 4, and the line a = 3. y = 2/z – 3 y = 4…
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Q: What is the general process to fit random 3D points to a surface?
A: Hint: Here 3D points are given we need to plot them on a surface. Write the general process to plot…
Q: Every plane curve has a unique parameterization. O False. OTrue.
A:
Q: 5. Are there any points on the graph of x2 – y² – 22 = 1 where the tangent plane is parallel to the…
A:
Q: Find a parametrisation of the curve of intersection of the surfaces: x^2 + 2y^2 + z^2 = 5 and x^2 +…
A: This is parameterisation of curve problem
Q: What is a parametrization of a curve in the xy-plane? Does a function y = ƒ(x) always have a…
A: Parametrization of a curve in the xy-plane:Parametrization of a curve consists of both equation and…
Q: Determine all singular points of the projective plane curve C whose affine equation is given by (y…
A: Consider the function fx, y=y-x22-y4. Observe that, ∂f∂x=0∂∂xy-x22-y4=02y-x2 -2x=0x=0 or y=x2
Q: Stress quadric surface of Cauchy g1ven by 6,2 18pr ulge O
A: No, the given is not the stress quadric surface of Cauchy.
Q: Stress quadric surface of Cauchy given by 6ij<132= ±6,r2 ulgn O
A: Thanks for the question :)And your upvote will be really appreciable ;)
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- Discuss the hyperbolic geometry of spacetime in comparison to circular geometry of 3-vector space.Find the appropriate parametrization for the given piecewise smooth-curvein R^2, with the implied orientation. The curve C, which goes along the circle of radius 3, from the point(3,0) above the x-axis to the point (-3,0), and then in a straight line along the x-axis back to (3,0).Sketch the graph of x=z^2 in the xy plane (2d context) and xyz space (3d context)
- This is a static of rigid bodies (mechanics) problemSketch the cylinder given by x = 4- Z*2(z square)in three-dimensional space.Compute the intersections of the curve xy = 1 and the lines x +y = 5/2, x+y = 2, x+y = 0, x=0 , x=1 in the affine space and then in the projective space by using homogeneous coordinates. Complex solutions are valid. Please show your steps for both affine space and in project space. Box your final answer.
- This is a static of rigid bodies problemThe upper half of the unit sphere x2+y2+z2=1 is z=Square root of 1-x2-y2. Find its centroid?Find the Largest open rectangle in the plane in which the hypotheses of Existence and uniqueness Theorem are satisfied fory'=−2t/(1 + y^3), y(1) = 1 Describe then sketch the regions.