Use spherical coordinates. Evaluate ∭e ^ (x ^ 2 + y ^ 2 + z ^ 2) dV, where E is inside the sphere x ^ 2 + y ^ 2 + z ^ 2 = 25 in the first octant

Q: 5. Locate the coordinates of the centroid of the first quadrant area bounded by the parabolas y = 4…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Use double integral in polar coordinates to find the area of the portion of the sphere

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A: Given equation of line segment is  y = x/2, 0 ≤ x ≤ 4,

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Q: Find the favily of orthogonal trageclores %3D

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Q: 2. Show that an equilateral triangle can be inscribed in the epitrochoid and that its centroid is on…

A: An equilateral triangle can be inscribed in the epitrochoid and that its centroid is onthe circle of…

Q: Find  the Volumeof the largest rectangular box lying above the xy-plane, with y less that or equal…

A: considerlength of rectangular box =x width of rectangular box  =yheight of rectangular box =z

Q: Consider the double integralf dydx. By converting to polar coordinates the limits of integration of…

A: Given double integral is  ∫-33∫09-x2 dy dx so the region of integration is bounded by  x=-3 , x=3 ,…

Q: over the region E inside x +y +z = 4 in the first octant. Convert the point (2, 2, -2v2) rectangular…

A: We have been given the cartesian coordinates (2, 2, ). We have to convert these cartesian…

Q: what is the formula to find centroid of triangular prism

A: Centroid of triangular prism is determined as shown below.

Q: use spherical coordinates to find the volume of the solid. Solid inside x2 + y2 + z2 = 9, outside z…

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Q: Convert dzdydx /9-x-y Into an integral of cylindrical coordinates

A: Given∫03∫09-x2∫3--x2-y2x2+y2 dz dy dxTo convert it into polar coordinateswe know thatx=rcosθ,y=rsinθ…

Q: Use spherical coordinates to compute the surface area of a sphereof radius R.

A: given,         a sphere of radius R

Q: Use spherical coordinates to show that the volume of a sphere of radius R is V = *nR³.

A: Given the radius of sphere is =R  Then equation  of sphere is                      X2 + Y2 + Z2 = R2…

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Q: Use integration in polar coordinates in order to compute the double ya³ dA, where D is the lower…

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Q: (०हागो 10,3,0)and (0,0,6). Tongular lamina with for of stokes deo theorem.

A: Given

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Q: Use spherical coordinates to find the volume of the solid. Solid inside x2 + y2 + z2 = 81, outside z…

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Q: Show that the volume of a spherical block can be approximated by ∆V ≈ ρ2 sin ϕ ∆ρ ∆ϕ ∆θ.

A: Suppose x,y,z is a point at fixed distance from the origin in the 3D-space.

Q: Find Surface area after revolving about х-ахis y = Vx, 1 < y < 2

A: Use the formula of surface area of revolution along x-axis.

Q: Consider the double integralf dydx. By converting to polar coordinates, the limits of integration of…

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Q: Calculate the volume of the solid which lies above the cone 3z2 = x2 + y² and below the sphere (x –…

A: Given solid lies above the cone 3z2=x2+y2 and below the sphere x-22+y2+z2=4

Q: Find the area of the surface generated by revolving the curve about the indicated axis. SET UP ONLY…

A: The area of the surface generated by revolving the curve around the y axis can be given as:…

Q: Evaluate the spherical coordinate integral.

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Q: Find using spherical coordinates integration zz2 + x2 + y²dzdydx V4-x

A: The conversion formulas for spherical coordinates are…

Q: Find the center of mass of solid revolution if an area in Ist Quadrant (Kuadran Pertama) bounded by…

A: Given functions are Intersection points Area of region is Centre of mass revolution

Q: 2. By changing to cylindrical coordinate, evaluate So 1-x²1542x² dzdydx

A: Introduction: Sometimes, a triple integral given in the rectangular coordinate system is very…

Q: An ellipsoid is given by the equation 4x + 4y2+z2 = 16; Sketch the three-dimensional (3D) graph of…

A: Let's find.

Q: Use cylindrical coordinates to calculate the volume between the surfaces in the first octant if z =…

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Q: Determine the area of the right half of the cardioid formed by r = 8 +7 sin 0 16 14 12 10 8 6 4 -2…

A: The formula to find the area is, A=∫ab12r2dθ Since it is been asked to find the area of half of the…

Q: 6) Find the volume of the solid enclosed by the paraboloid z = 2--y and the plane z = 2.

A: According to question given that z=2-x2-y2z=-2

Q: Find the volume of the solid in the first octant by bounded by the plane 3x +42 = 12, y = 2 and the…

A: Volume bounded by thefirst octent

Q: Determine the area of the right half of the cardioid formed by r = 7 +6 sine 14 12 10 8 6 4 -2 -4…

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Q: Use spherical coordinates to find the volume of a sphere of radius 2 from which a central cy tinder…

A: Let us assume that , x2+y2+z2=22x2+y2=1 The graph will be :

Q: In cartesian coordinate system, differential volume element is dxdydz. Infer the differential volume…

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Q: .Estimate vu in cylindrical form, in the orthogonal curvilinear coordinates

A: Given: We consider elliptic in cylindrical form .

Q: Find a parametrization of the circle of radius 7 with center (5, 3, 9) in a plane parallel to the…

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Q: A right cylinder of radius r is inscribed in a hollow sphere of fixed radius a. The

A: Given, a right cylinder of radius 'r', is inscribed in a hollow sphere of fixed radius 'a'. The…

Q: Determine the area of the surface of revolution of x=sqrt{y} from (1,1) to (2,4), rotated about the…

A: The equation is x=y.   Determine the derivative dxdy=12y   The formula for the area of surface…

Q: Use spherical coordinates to find the volume of the solid. Solid inside x + y- + z² = 81, outside z…

A: To find the volume of the solid inside the sphere x2+y2+z2=81 and outside the cone z=x2+y2, and…

Q: Calculate the centroid coordinates of quarter circle (x² + y² = a*) in the quadrant, use Cartesian…

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Q: Find the centroid by revolving the given plane area about the indicated axis y^2=5-x, x=0 ; about…

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Q: 6) Find the volume of the solid in the first octant bounded by the plane 3x +4z=12, y=2 and the 3…

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Q: 36-х? —у? y'dzdydx by re-writing the integral in spherical coordinates. Evaluate 3x²+3y²

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Q: 16 - х2 р16- х-у? -*-* v+v² dz dy dx

A: First we convert the z boundaries  z=16-x2-y2we know that x2+y2=r2z=16-x2+y2z=16-r2the interval for…

Q: Use spherical coordinates and integrate to find the area of the region 0≤φ≤βon the spherical shell…

A: the spherical shell of radius. to find the area when β= 2π e follow the procedure as

Q: The center of mass of a lamina of total mass 5 has coordinates (2, 1). What are the lamina’s x- and…

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Q: Find the Surface area of the portión of the cylinder ya + z² =9 above the rectangle in the xy plane.…

A: Cylinder y2 + z2  = 9,z = 9-y2,0 ≤ x ≤ 2,and-3 ≤ y ≤ 3