Let T be the tetrahedron with vertices at the origin and (4,0,0), (0,5,0) and (0,0,2). A fluid flows with

Q: Let T be a triangle with the vertices (0,0), (1,0) and (1,2). Also, let V be the volume of the solid…

A:

Q: Find the flow of F=xzi-yk through the upper part of plane z-1 in the x +y² +z = 4sphere. %3D

A: The general form of a vector-valued function in three dimensions is given by F=F1i+F2j+F3k, where…

Q: Evaluate the triple integral |// xy dV where E is the solid tetrahedon with vertices (0,0,0), (7, 0,…

A: Consider the following: Equation of plane passing through 7,0,0,0,5,0,0,0,10x7+y5+z10=1x ​ranges…

Q: A fluid has density 1000 kg/m³ and flows with velocity = ci +yj + zk, where x, y, and z are measured…

A: We have to find the rate flow outward through the part of paraboloid . We can to use the methods of…

Q: Determine the x-component (m) of the centroid of the given figure if the cut portion is a semicircle…

A: Given, a=39 m, b=16 m and c=2 m To find the x-component of the centroid of the given figure.

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: The masses are located at the points . Find themoments Mx and  My  and the center of mass of the…

A:

Q: part 3: choose a proof method  1. use a paragraph, flow chart, or two column proof to prove that zx…

A: Given:∠wzx=∠yzx,zw=zyprove:zx is perpendiuclar bisector of wy

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

A:

Q: What solid is formed when this net is folded? B D

A: there is no introduction for the above question.

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: Evaluate the triple integral ∭ExydV where E is the solid tetrahedon with vertices…

A:

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: Solve Sff, 3x² + 3y²dV by using cylindrical coordinates, where G is a solid in the first octant that…

A:

Q: A: Determine the mass and center of mass of the solid that bounded by the paraboloid = 9y? + 9x2 and…

A:

Q: Let T be the tetrahedron with vertices (2, 0, 0), (0, 2, 0), (0, 0, 3) and the origin. Write I.f(r,…

A:

Q: If S is the solid bounded by the paraboloid z = 3x2 + 3y and the plane z = 4 (with constant…

A:

Q: Find a parametrization of the hyper-boloid of two sheets (z2/c2)-(x2/a2)-(y2/b2)=1

A:

Q: What are the solids that are formed in the given net?

A:

Q: A fluid has density 800 kg/m³ and flows with velocity i = ri + yj+ zk, where x, y, and z are…

A:

Q: 2 Let S be the positively oriented surface parametrized by R(u, v) = (u, v, u² – v²) where (u, v)…

A:

Q: m, = 4, m2 = 5, m, = 1; P;(2, –3), P2(-3, 1), P3(3, 5)

A:

Q: Evaluate the triple integral. 6xyz dV, where T is the solid tetrahedron with vertices (0, 0,0), (1,…

A:

Q: AP where R is the portion of the ball of radius 1 in 4-dimensions with all coordinates r, y, z, w 2…

A: I = ∫∫∫R∫ dvwhere R = portion of unit ball with x, y,z,w≥0I = ∫01∫01∫01∫01 dx dy dz dw= ∫01∫01yo1 dz…

Q: Find the centroid of the surface cut from the cylinder y2 + z2 = 9, z>= 0, by the planes x = 0…

A:

Q: The solid in the first octant bounded by the coordinate planes, y+ z = 4, and x = y.

A: The objective is to find the volume for y+z=4,x=y The volume of the integral formula is,…

Q: 2. Calculate the circulation of the flow v=-8xy i+ 4 yj around the triangle with vertices (0, 0),…

A: Given that: v=-8xyi+4y2j The triangle is with the vertices (0,0), (3,0), (3,2) To calculate the…

Q: The simple solid Q, drawn in the first octant and generated by the surfaces y – 1 = (x – 2)² 3x + 2z…

A:

Q: A region R consists of a square bounded by the lines x = −7, x = 7, y = 0, and y = −14and a half…

A: Draw the region R as follows.

Q: Let T be the tetrahedron with vertices (4, 0, 0), (0, 5, 0), (0, 0, 5) and the origin. Write f(x, y,…

A:

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: Let T be the tetrahedron with vertices at the origin and (4,0,0), (0,4,0) and (0,0,1). A fluid flows…

A: Given, function is, The rate of flow of the tetrahedron can be calculated by the flux. So, the…

Q: Determine the centroid, C(i, ỹ,z), of the solid formed in the first octant bounded by z+y - 16 = 0…

A: The given curves are, z + y - 16 = 0 and 2x2 - 2(16 - y) = 0 Since the bounded region lies in first…

Q: Exercise 7. In the (yz) plane consider the set A of vertices (3,0), (4, 2), (5, 0) and (4, –2). The…

A: The given question can be solved as shown in step2.

Q: Find the centroid of the polyhedron with four triangular faces in the first octant that is bounded…

A: The region is bounded by the three coordinate planes and the plane x+y+z=1. Thus, the region can be…

Q: Find the centroid of the solid bounded by the parabolic cylinder 1- y? and the three planes given…

A: To find the centroid of the solid bounded by the parabolic cylinder: The region is defined as…

Q: Find the moments and center of mass of the system of objects thathave masses 3, 4, and 8 at the…

A: We use the following equations to find the moments of the system of the given objects: Here mi are…

Q: Find the centroid of the homogeneous lamina enclosed by the graphs of the given equations. y = x2,…

A:

Q: Let T be the tetrahedron with vertices (3, 0, 0), (0, 2,0), (0, 0, 5) and the origin. Writel II|…

A: Follow the steps to find the upper limit of x and z to solve the problem.

Q: Q1- Determine the coordinates of the centroid of the area.: (1, 1) y= x,

A: The given problem is to find the centroid of the given shaded area of the region formed by given…

Q: A cube is defined by 1 < x, y, z < 1.2. If D = 2x?ya, + 3x?y²a, -6z²a.C/m? (a) Apply Gauss's law to…

A: Consider the provided question, A cube is defined by 1&lt;x, y, z&lt;1.2 Given,…

Q: Let V be a solid enclosed by x2 + y? + z² = 4 and z = 0, which can be illustrated by (0,0,4) (0,4,0)…

A: The given curve is: x2+y2+z2=4          and         z=0

Q: Find the center of mass for a system 3 masses placed in the xy - plane with the following masses and…

A:

Q: A thin triangular plate of uniform density and thickness has vertices at V1 = (2,1), v2 = (8,1), v3…

A: Given : Triangle points : (2,1) , (8,1) , (4,7)

Q: Find My for a triangle whose vertices are located at (0,0), (1,0), (1,1) if the density of the…

A:

Q: A fluid has density 1200 kg/m³ and flows with velocity v = xi + yj + zk, where x, y, and z are…

A:

Q: What solid is formed when this net is folded? A C D

A:

Q: Calculate the circulation of the flow v=-8xy i+4y j around the triangle with vertices (0, 0), (3,…

A: According to our policy, we are supposed to answer the first question (question2). By using the…

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.