3 Describe in words the region in R° represented by the equation x2 + y² – 10y + z? + 2z = 0 A A space between two planes. B A cyllinder CA ball A plane. The exterior of a ball a sphere A noint

Q: Find the point on the plane 5x + 4y + z = 11 that is nearest the origin. What are the values of x,…

A: First we find the distance(d) between a point (x,y,z) on the plane and the origin .Then form a…

Q: Use Cartesian coordinates to evaluate JIJ y² dv 2 D where D is the tetrahedron in the first octant…

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Q: 3) (use DiSk Methad) Fnd the volur Solid genecated by revoluing the bay. the Sraphs Of the equatons…

A: solution:-the region bounded byxy=3, y=1, y=4, and x=5 revolving about the line x=5using the Disk…

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

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Q: Find the area of part of sphere x² + y? + z² = 100 that lies inside x2 + y? = 10x %3D %3D

A: This is a problem of surface integral.

Q: Find the regions of the (x, y)-plane where the equation (1+ x) + 2xy; Əxðy + 2y? 2 + x xy? + (1 –…

A: Given equation is, 1+x∂2u∂x2+2xy∂2u∂x∂y+2y2∂2u∂y2+x2∂u∂x-xy2∂u∂y+(1-y)u=0 The equation…

Q: SSg z(x² + y²)do where S is the portion of the sphere x2 + y2 + z2 = 9 in the first octant that is…

A: Surface integral of a function f(x,y,z) Along the surface S given by z= g(x,y)…

Q: Find the area of the cap cut from the paraboloid y + z? = 3x by the plane x = 1.

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Q: Find the points on the surface y? = 36 + xz that are closest to the origin. smaller y-value (х, у,…

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Q: • Find the area of the portion of the Sphere x² + y² + 2²² = 9 between the planes Z=1 and 2 = 0.…

A: The given equation of  plane is x2+y2+z2=9. The polar coordinates are x=rcosθ & y=rsinθ. The…

Q: Evaluate [[[(x2 + y² +z?)2 dV, where 2 is the solid hemisphere (half of the sphere) enclosed by x +…

A: Apply the spherical coordinate to find the volume integral, x=ρsinφcosθ ; y=ρsinφsinθ ; z=ρcosφ And,…

Q: The plane x=3 cuts the sphere x2 + y2 + z2 =25 What shape does their intersection make? Find a…

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Q: Find the volumes of the regions

A: The Volume of  the wedge, where D is the solid and R is the region, is calculated as,…

Q: Describe in words the region in R' represented by the equation x² + y² – 10y + z² + 2z = 0 O A…

A: we have to check the region of the given equation in R^3 is

Q: 18. Find the surface area of the sphere with radlus 5 by dou- bling the surface area of (x, y)…

A: Given: f(x,y)=25-x2-y2 is the surface bounded by the circle x2+y2=25 where radius, r=5

Q: Evaluate fff(r +y²+y dV, "AP where 2 is the solid hemisphere (half of the sphere) enclosed by x +y…

A: Converting into spherical  coordinates

Q: Find the surface area of the portion of the sphere x2 + y2 + z2 = 25 inside the cylinder x2 + y2 =…

A: Recall:  The formula of surface area is S=∫∫S1+∂z∂x2+∂z∂y2 dA

Q: (a) Evaluate I = SSSp cos(r2 + y?) dA, where E is the region that lies inside the cylinder x2 +y² =…

A: (a). Consider the triple integral To evaluate the integral, use the cylindrical coordinates. So,…

Q: III Find the area of the portion of the cylindrical surface y = 4- a2 in the first octant that is…

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Q: Write down inequalities to represent (a) the region inside the sphere 2² + y² + 2² = 62 and outside…

A: The given problem is to find the inequalities that represent the given solids of region bounded by…

Q: = 8. = 8. 18) Area of a rectangle with base = x and height = y Area of a rhombus with one diagonal…

A: Area of rectangle with base x and height y is given by  Area =base ×height =xy

Q: 5 + 2? + y, the cylinder Evaluate e dV where E is enclosed by the paraboloid z = E 2 + y? = 1, and…

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Q: 4 [It is given that a sphere of radius r has volume 3 cm r cm Handle Cover Disc cm Body h cm 1 cm r…

A: To find the value if r and h i use the calculator.

Q: hy sphere x + y +z = 25 between planes z=2 and z= 4.

A: We need to find surface area using double intergral.

Q: A hemisphere of x? + y? + z2 = a? is shown. A cylinder is placed such the axis of both hemisphere…

A: Surface area is given by ∬D∂z∂x2+∂z∂y2+1dA for a functionz=f(x,y) where D is the projection of the…

Q: || x² + y° – z dS where S is the part of the cone 22 = x² + y? that lies between the planes Evaluate…

A: According to question, Given, S is the part of cone Z2 = x2 +y2, it lies between planes z = 2, and z…

Q: Describe in words the region in R' represented by the equation y² + z² = 9. A ball A cyllinder A…

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Q: Describe in words the region in R' represented by the equation x² + y² + 2y + z² < 3 A plane. A…

A: The given equation is x2+y2+2y+z2≤3. We have to describe the given equation in words.

Q: The volume of the solid whose base is region in the xy-plane that is bounded by the parabola y = 12…

A: Concept: To find the limit of x put equate the values of y  The volume of the solid in the x-y plane…

Q: The base of a solid is bounded by y= x² and y= 4. All parallel cross – sections are squares…

A: Please rate

Q: 100% 10. Consider the portion of the plane a+2y+3z 12 that sits above the circle (z-2) + (y- 2) = 4.…

A: The solution are next step

Q: Find the area of the ellipse cut from the plane z= 8x by the cylinder x +y = 4. Surface area = (Type…

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Q: Evaluate [[(x +y +=')² dV, where Q is the solid hemisphere (E sphere) enclosed by x +y² +z² =1 and…

A: ∫∫Ω∫x2+y2+z232 dv,   f:x2+y2+z2=1 use spherical conditions x=ρ sinϕ cosθ, y=ρ sinϕ sinθ, z=ρ cosϕ…

Q: he volumes of the solids generated by revolving the regions bounded by the graphs of the equations…

A: We have to find the volume about the given lines.

Q: 4. Find the area of portion of the sphere x²+y²+z = 9 between the planes z = 1 and 2 = 0. Draw the…

A: Surface area of a surface z=f(x,y)  A=∫∫D1+fx2+fy2dA Here D is a point on xy plane

Q: Find the area of the cap of the sphere x2 + y² + z? = 2 cut by the cone z = Vx2 + y² |3D

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Q: The solid S above the surfaces 22 = + y? and below r +y +(2 - 5)2 = 25. 2 + y² + (2 - 5) = 25

A: Solution is below.

Q: lo. find a point in the plane x+2y+3z=13 nearest to the point (1,1) usung the methed of Lagrange's…

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Q: Evaluate [[[(x² + y² +=?)2 dV, where 2 is the solid hemisphere (half of the Ω sphere) enclosed by x…

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Q: Describe in words the region in R° represented by the equation x? + y² + z² > 4 A A point R A…

A: The given equation is x2+y2+z2≥4. We have to describe the given equation in words.

Q: Among all rectangular solids defined by the inequalities 0≤x≤ a, 0sysb, 0szs1, find the one for…

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Q: 5) 2z dV, E is the solid enclosed by the cone % = Vr2 + y? and the E plane z 5

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Q: 4 2 + Find the area of the portion of the Sphere x² + y² +2²= 9 between the planes Z=1 and 2 = 0.…

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Q: Find the area of the surface cut from the paraboloid x? + y +z=0 by the plane z= - 20. The surface…

A: The given equation of paraboloid is: x2+y2+z=0

Q: Find the distance between the spheres x2 + y? + 22 = 4 and x2 + y + z = 4x + 4y+4z- 11. %3D Answer +…

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Q: 2. Find the area of the ellipse S on the plane 2x + y + z = 2 cut out by the cylinder x2 + y? = 2x;…

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Q: The radius of the sphere x2+y2+z2+2x-2z-14=0 is r= (Round your answer correct to three decimal…

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Q: 1+ 1 A D 4. Based on the trapezoid shown in the standard (x, y) coordinate plane above, what is the…

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Q: 1) A) Find the area of the portion of the sphere x? + y + =9 lying inside the cylinder x2 + y? = 3y.

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Q: 3. If a circle with center (h, k) and radius R is made as a base of a solid formed by infinitely…

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