Use polar coordinates to find the volume of the given solid. Enclosed by the hyperboloid −x2 − y2 + z2 = 22 and the plane z = 5

Q: z =x' +y° +1 Y L x' +y? -z? = 1 LY

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Q: What is the surface area of the three dimensional solid formed by rotating the following parametric…

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Q: What is the x centroid position for the shape below? Center:D, 2m 10m 3.4m 3.9m 4.4m 4.9m

A: Formula for centroid, C C=∑Ax∑A

Q: Consider the cylinder in R. a. Identify the coordinate axis to which the cylinder is parallel. b.…

A: B. ) The cylinder is parallel to Y -AXIS

Q: Use spherical coordinates. (2 - x2 - y2) dv, where H is the solid hemisphere x? + y² + z² < 36, z 2…

A: We have to evaluate ∭H2−x2−y2dV, where H is the solid hemisphere x2+y2+z2≤36, z≥0 Changing into…

Q: + y? )dx + (x² – y²)dy , where C is the triangle with vertices (0, 0), (2, 1), and (0, 1), sitive…

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Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. x2/3 + y2/3 =…

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Q: Find the following: The traces of the surface x2 + y? + 22 = 6 in the planes parallel to the…

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Q: Use Cartesian coordinates to evaluate y² dV D where D is the tetrahedron in the first octant bounded…

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Q: The figure below shows the solid that lies under the paraboloid z = 2x? + 2y? and above the…

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Q: Sketch the region in the plane consisting of points whose polar coordinates satisfy the given…

A: Polar coordinate system

Q: Use cylindrical coordinates. Evaluate (x + y + z) dV, where E is the solid in the first octant that…

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Q: Use spherical coordinates. |II (2 – x² – y²) dV, where H is the solid hemisphere x? + y2+ z² s 9, z…

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Q: Find an equation in cylindrical coordinates for the surface represented by the rectangular equation.…

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

A: We have to draw the solid Q in first octant and is generated by the surfaces  y- 1=( x- 2)2 3x+2z=11…

Q: The traces of the surface x2 – y? + z2 = 8 in the planes parallel to the coordinate planes and…

A: Here we have to find the surface in the given traces.

Q: Use spherical coordinates. (a) Find the volume of the solid that lies above the cone p = 1/3 and…

A: Part(a): Given sphere is, ρ=4cosφ Let us assume that , x=ρsinφcosθy=ρsinφsinθz=ρcosφ Where…

Q: Sletch the region in the plane consisting of points whose polar coordinates Satsfy the given…

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

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Q: 1. Consider the parallelepiped with adjacent edges u = 6i + 4j + 2k; v= 2i+ 2j + 4k; w = 2i + 6k +…

A: Let's find.

Q: Use spherical coordinates. Evaluate (6 – x2 - y?) dv, where H is the solid hemisphere x2 + y² + z² <…

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Q: Shetch the region in the plane consisting of points whose polar coordinates satsfy the given…

A: Shaded area is the required area

Q: Find the surface area of the surface S. Sis the paraboloid x 2 + y2-z = 0 below the plane z = 2. O…

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Q: Sketch the solid in the first octant that is enclosed by the planes x = 0, z = 0, x = 5,  z − y = 0,…

A: We have to sketch the solid in the first octant that is enclosed by the planes x = 0 , z = 0 , x = 5…

Q: 2. With the help of polar coordinates and the following formula, find the surface area of the…

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Q: use polar coordinates to find the voluyme of the solid enclosed by the hyperboloid: -x2-y2+z2=1 and…

A: Given : Hyperboloid : -x2-y2+z2=1 Plane : z = 2 Rearranging equation of hyperboloid…

Q: Use polar coordinates to find the volume of the given solid: i. Under the paraboloid ? = ?^2 + ?^2…

A: Given that       Under the paraboloid z = x2+y2 and above the disk x2+y2 ≤ 25. Here by using polar…

Q: ripie the volume of the solid B that lies above the cone z = √3x² + 3y2 and below the sphere x² + y²…

A: Given- Cone: z=3x2+3y2 Sphere: x2+y2+z2=z To find the volume of the solid B that lies above the…

Q: a) Use polar coordinates to calculate SSR(3x+2y)dA where R is the region in the second quadrant…

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Q: Determine the y-coordinate of the centroid of the shaded area shown. 12" Parabolic 5" Answer: y = i…

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Q: Use polar coordinates to find the volume of the solid below the paraboloid z = 27 - 3x^3 - 3y^2 and…

A: We have to apply formula for the volume to solve the problem

Q: Find an equation in spherical coordinates for the surface represented by the rectangular equation.…

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Q: The given curve is rotated about the y-axis. Find the surface area of the resulting surface. 22/3 +…

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Q: Using spherical coordinates, the volume of the solid inside the sphere x²+y² +z² = 9 and above the…

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Q: Use spherical coordinates. I/ y2z2 dv, where E lies above the cone o = n/3 and below the sphere p =…

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Q: Find the center C and the radius r of the sphere S: x2 + y2 + z2 + 4x + 8y – 8z =-11

A: A geometrical object which is in the shape of ball is called sphere. Outer surface of sphere is…

Q: Find the distance on the xy plane between the two points, given below as polar coordinates (7,…

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Q: The simple solid Q, drawn in the first octant and generated by the surfaces I = (y – 3)2 +1 42 + 3r…

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Q: calculate the volume of the solid of ( image 04) which is delimited by z = 9-x²-y²     tip use as…

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Q: Use spherical coordinates. Evaluate z dv, where E lies between the spheres x2 + y2 + z2 = 9 and x2 +…

A: Given equations of spheres: x2+y2+z2=9 x2+y2+z2=36 For spherical coordinates: x=ρ cosθ sinϕy=p sinθ…

Q: The figure shows the surface created when the cylinder y? + z² =1 intersects the cylinder x? + z2 =…

A: Consider the provided question,

Q: 1)using polar coordinates, calculate (x + y)dA R where R is the region to the left of the axis…

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Q: Determine the y-coordinate of the centroid of the shaded area shown. 11" Parabolic - 3" 6" Answer: ỹ…

A: We need to find y co-ordinate of centroid.

Q: Use spherical coordinates. Evaluate //| y²z2 dv, where E lies above the cone o = 1/3 and below the…

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Q: Use cylindrical coordinates. II * + y + z) dv, where E is the solid in the first octant that lies…

A: The objective here is to evaluate the below integral using cylindrical coordinates: ∫∫∫Ex+y+zdVWhere…

Q: Using polar coordinates, evaluate J*** dydr, R where R is the semicircular region bounded by the…

A: For a function f(x, y) In Polar coordinates x = r cos θ, y=r sin θ Find f(r, θ) Formula Used: ∫∫R…

Q: Use polar coordinates to calculate the area of the region inside the disc r+ y 9 and outside the…

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Q: Use polar coordinates to find the volume  Enclosed by the hyperboloid  −x2 − y2 + z2 = 46  and the…

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