Consider the region D with y 20 and : 2 0 bounded by the cones 22 = ² + y? and the hemisphere z = 9-r - y. Use spherical polar coordinates to find the volume of D.

Q: Use polar coordinates to find the volume of the given solid. V = Inside both the cylinder x² + y² =…

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Q: 2 Find the volume of the region between the ellipsoid (=) = 1 and the plane 4 8. - | א + నా | co

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Q: Use polar coordinates to find the volume of the region inside e cylinder ² + y² = 1 and the…

A: Here we use the sphere coordinate to find the volume of solid.

Q: Use spherical coordinates to evaluate the triple integral dV, where E is the region bounded by the…

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Q: Compute the volume of the solid bounded by the hemisphere z = √√4c² - r² - y² and the horizontal…

A: Let's find volume of solid.

Q: the volume of the solid B that lies above the cone z = √3x² + 3y2 and below the sphere x² + y² + z²…

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Q: Use a spherical coordinate integral to find the volume of the given solid. the solid bounded below…

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Q: Compute the volume of the solid bounded by the hemisphere z = the horizontal plane z = c by using…

A: To compute the volume of the spherical cap, use the following formulae and convert the Cartesian…

Q: Sketch the region defined by the following two conditions (in spherical coordinates): 0<p<2, 0<¢s…

A: The region is: Given that 0≤ρ≤2, 0≤φ≤π4 The given region is a part of a sphere of radius 2.

Q: Use spherical coordinates to find the volume of the solid that lies above the cone 0 = 7/3 and below…

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Q: b) Using Spherical Coordinates, find the volume of the solid G bounded above by the sphere x2 + y? +…

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Q: 1. Compute the volume of the solid bounded by the hemisphere z = √√4c²-x² - y² and the horizontal…

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Q: Use polar co ordinates to find the volume of the given solid  above the cone z=sqrt{x^2+y^2} and…

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Q: Write the volume of the solid above the surface z = (x² + y²)'/4 and inside the sphere x? + y² + z2…

A: in spherical coordinates x=ρsinϕcosθ,y=ρsinϕsinθ,z=ρcosϕ x2+y2+z2=ρ2 x2+y2+z2=2=(√2)2…

Q: Use polar coordinates to find the volume of the given solid. Bounded by the paraboloid z = 5 + 2x2 +…

A: We have to find volume of paraboloid in the first octant-

Q: Evaluate , x*+2y* D 2x++8y++2z+ dV, where D is the region enclosed by the spherical surface x2 + y?…

A: Given: To evaluate ∫∫∫D x4 + 2y42x4  + 8y4 + 2z4 dV  Where D is the region enclosed by the spherical…

Q: Find the volume of the region bounded below by the cone ( z=V(x2 + y?) ,and above the plane ( z=1),…

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Q: 7. Use spherical coordinates to find the volume of the solid that lies within the sphere 2 + y* +2 -…

A: As per norms we have to answer one question. So we answer the question 7. Given: x2+y2+z2=4…

Q: 22 dV, R is the region enclosed by x² + y? + z2 1 and a2 + y² + z² = 2z. Rewrite, but do not…

A: Given:  The integral ∭Rz2 dV , R is the region enclosed by x2+y2+z2=1 and x2+y2+z2=2z. To rewrite:…

Q: Let S be the region bounded by Pi = 2, P2 = 3,81 = z,82 =.91 =5, and 2 = a in spherical coordinates.…

A: Consider the provided question, Let S be the bounded by ρ1=2, ρ2=3, θ1=π, θ2=3π2, ϕ1=π2 and ϕ2=π in…

Q: Use polar coordinates to find the volume of the given solid. Under the cone. := V² + y² And above…

A: Consider the provided information, z=x2+y2 and above the disk x2+y2≤9. Use the polar coordinate to…

Q: Use spherical coordinates to find the volume of the solid bounded above by the sphere p = 2 /2 and…

A: First we have to set up a triple integral for the volume of the solid region bounded above by the…

Q: Use​ Pappus's theorem for surface area and the fact that the surface area of a sphere of radius a is…

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Q: Use polar coordinates to find the volume of the solid region bounded above by the hemisphere z = /…

A: Given  The solid region bounded above by the Hemisphere z=25-x2-y2 and below by the circular region…

Q: 2. Use spherical coordinates to find the volume of the solid that lies above the cone z = v3Vr?² +…

A: Volume

Q: 8. Find the volume of the region bounded by the plane z = 16 and the paraboloid z = (Use cylindrical…

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Q: ) Set up, but DO NOT EVALUATE, the integral of f(r, Y, z) = over the region E, where E is inside the…

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Q: 2. Use spherical coordinates to find the volume of solid within the sphere x² + y² +z? = 16 and…

A: we have to given equation of sphere is x2+y2+z2=16 and equation of cone is 3z2=x2+y2 we have to find…

Q: 9. Use spherical coordinates to find the volume of the part of the ball p <4 that lies between the…

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Q: Use polar coordinates to find the volume of the given solid. 21. Below the plane 2x + y + z= 4 and…

A: Given, The region D lies Below the plane 2x + y + z= 4 and above the disk x2 +y2 ≤1

Q: Compute the volume of the solid bounded by the hemisphere z = √√4c² - x² - y² and the horizontal…

A: hemisphere z=4c2-x2-y2 and plane z=cTo Find: Compute the volume of the solid using spherical…

Q: Compute the volume of the solid bounded by the hemisphere z = √4c²-r² - y² and the horizontal plane…

A: The given problem is to find the volume of the solid bounded by given hemisphere and plane by using…

Q: 2. Find the volume of the solid formed by the region inside the sphere x? + y? + z? = 16 and outside…

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Q: Find the volume of the solid E whose boundaries are given in rectangular coordinates. E is bounded…

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Q: b) Using Spherical Coordinates, find the volume of the solid G bounded above b x² + y? + z? = 25 and…

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Q: Compute the volume of the solid bounded by the hemisphere z = = √4c² - x² - y² and the horizontal…

A: The given problem is to evaluate the volume of the solid bounded by given hemisphere z=√(4c2-x2-y2)…

Q: Find the volume of the solid bounded by the paraboloid z = 14 - 5x - 5y and the plane z=9 V= (Type…

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Q: 2. Find the volume of the region bounded by the cylinder r? + y? Hint: you will need to use polar…

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Q: Use polar coordinates to find the volume of the given solid. Above the cone z = Vx2 + y2 and below…

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Q: ordinates to find the volume

A: Given surface: z=e-x2-y2-e-9 and XY plane To find: Using polar coordinates, find the volume of the…

Q: 2. Use spherical coordinates to find the volume of the solid that lies above the 1 cone z = + y? and…

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Q: Let S be the solid inside the sphere p _ 6cos@ and below the cone Ø = π/4 Find the volume of the…

A: S be the solid inside the sphere ρ=6cosϕ and below the cone ϕ=π4

Q: 8. Find the volume of the region bounded by the plane z = 16 and the paraboloid z = x² + y?. (Use…

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Q: Use a Spherical Coordinate integral to find the volume of the solid bounded above by the sphere p =…

A: Given, Region is bounded above by the sphere and below by the cone .

Q: Use spherical coordinates to find the volume of the region bounded by the sphere p= 20 cos q and the…

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Q: What is the volume of the following region, described in spherical coordinates? 1<p< 9, 2' 4

A: Given- 1≤ρ≤9, 0≤θ≤90° , π6≤ϕ≤π4. To Find- The volume of the above region which is described in…

Q: Find the volume of the first octant of the sphere x^2 +y^2 +z^2 = a^2 using dz dr d(theta)

A: Consider the sphere x2+y2+z2=a2. Therefore the given equation can be written as:…

Q: Use spherical coordinates to calculate the volume of the region outside the sphere p = 2 cos Ø and…

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Q: Compute the volume of the solid bounded by the hemisphere z = √4c²-x² - y² and the horizontal plane…

A: Here we will use spherical co ordinate to find volume of solid bounded between sphere and plane .…

Q: Find the mass of the lamina described by the inequalities, given that its density is p(x, y) = xy.…

A: Given that, Density of the lamina is ρx, y=xy 0≤x≤4,0≤y≤16-x2

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.