Find the centroid of the solid between the sphere ρ = cos φ and the hemisphere ρ = 2, z ≥ 0. Use Mathematica to do all the computations (you need integrals for the first moments and the mass (do not forget to use the symmetry), and graph the surfaces bounding the region using SphericalPlot3D, together with the centroid (make it big enough to be seen - you can graph it as a small ball using Graphics3D). Use “Opacity” option to make the surfaces transparent enough so that the centroid can be seen. Recall: for constant density functions, the center of mass is the centroid of the object. Set the density function δ equal to 1

Q: Determine the centroid of a cross section with an isosceles right triangle of base 9 cm, a…

A: Determine the centroid of a cross section with an isosceles right triangle of base 9 cm, a…

Q: Find the points on the ellipse                  x^2/a^2+y^2/b^2=1 such that the tangent at each…

A: Let P be (acosθ, bsinθ), then the equation of tnagent at P is         xacosθ+ybsinθ=1Slope of…

Q: 10. The part of the paraboloid x = y² + z² that lies inside the cylinder y² + z² = 9

A:

Q: Question 4: Let f(x) = x' + x - 3. Find a value n such that f has a solution in [n, n + 1] and…

A:

Q: Question 5. Use Green's theorem to compute the area trapped between the ellipse x2 + 4y? = 4 and the…

A: Given that the area is bounded between the ellipse x2+4y2=4 and the parabola x=22y2. The Green's…

Q: The displacement of an object is given by the parametic equations:  x=0.2t^2+2t and y= -0.4t^3…

A: The displacement of object is given as, x = 0.2 t2+2t   andy = -0.4 t3   we need to find the…

Q: 4) Use integration to find the area of the ellipse 4x² + y² = 9.

A:

Q: A rectangle of maximum perimeter is to be inscribed in the ellipse x^2/22^2 + y^2/10^2 = 1. The…

A:

Q: Find an arc-length parametrization of the line passing through (1, 0, 1) and (1, 2, 3). Upload an…

A:

Q: parametrically define the elliptic hyperboloid of 2 sheets given by 4x^2-y^2-z^2 = 1

A: The parametric representation of the elliptic hyperboloid of 2 sheets given by 4x2−y2−z2=1…

Q: Graph  the elliptical cylinder in 3 dimensions

A:

Q: - The surface 5x^2 + 2z^2 = 3y is heading towards which axis? - Identify the surface generated by…

A: 5x^2 + 2z^2 = 3y x= 3n1 ,  y = -3(5n12 + 2n22) , z = 3n2

Q: the sum of the distances from (x,y) to (-1,0) and from (x,y) to (1,0) is 4. show x and y is related…

A: Distance from (x,y) to (-1,0) is:  Distance from (x,y) to (1,0) is:

Q: use the mthod of trig substitution to prove the area of the ellipse " {(x^2)/(a^2)}+{(y^2)/(b^2)} =…

A:

Q: Suppose top part of the ellipse (x^2/a^2) + (y^2/b^2) = 1 is rotated about the x-axis. Find the…

A: Given, Top part of the ellipse given by equation x2a2+y2b2=1 Rotated about x-axis.

Q: complex integral

A:

Q: Q6/ Find the volume of the parallclogram-sided determined by: u- -3i +7j +5k, v -3i + 7j-3k, and w-…

A:

Q: Find the centroid of a lamina enclosed between the circles of radius 1 and 2 centred at the origin,…

A: Consider the diagram of the lamina as per given information, The centriod of the lamina is defined…

Q: to find the surface area cut from the sphere x^2+y^2+z^2=16 by the cylinder x^2+y^2-4y=0

A: To find the surface area cut from the sphere x2+y2+z2=16 by the cylinder x2+y2-4y=0.

Q: Which is the equation of a sphere with a center at (1,0,-2) with a volume of 36(pi)(u^3)? a.…

A: We first defined the equation of sphere and centre,volume . Using this formula we have equation (a)…

Q: Sez dz along the line segment from 0 to 1+ in/2.

A:

Q: Use the polar coordinates to find the surface area of the part of the conical surface z^2 = x^2 +…

A: Given conical surface is z2=x2+y2 that lies above the semi-circle y=2-x2

Q: Determine by direct integration the centroid of the area shown in the figures. Where a= 22 cm and b=…

A: The centroid of the bounded region: The centroid x¯-y¯ of a region bounded by the graphs of the…

Q: 5) Using transformation and integration, find the area of the region that is enclosed by the ellipse…

A:

Q: How many cells are there in the arrangement of hyperplanes in R^d with equations xi + xj = 0 and x…

A:

Q: Find the trace of the surface 4x^2 − y^2 +6z^2 = 2 in the yz-plane and identify the conic section.

A: Given 4x2-y2+6z2=2

Q: Consider the intersection of the ellipsoid x^2 + 2y^2 + 4z^2 = 22 with the plane x = 2.…

A:

Q: Find a parameterization for a circle of radius 4 with center (-4,4,-6) in a plane parallel to the yz…

A:

Q: Sketch the region in the first octant bounded by z = sqrt((x^2 + y^2)/3) and z = 1. Use spherical…

A: