Use spherical coordinates. Evaluate ∫∫∫E y2z2 dv, where E lies above the cone φ = π/3 andbelow the sphere ρ = 1.

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Q: on? 26. Use spherical coordinates to evaluate: on height Vx? + y² + z² dz 1+[x² + y² + z²1} Jo psing…

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Q: V4-y? '8-x²-y² By converting to spherical coordinates, evaluate 2? dz dx dy.

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Q: Problem. Use the spherical coordinatas, I= psin o cos 0, y= psin osin 0, z= pcos o; p = r +y° +z, dV…

A: Let us first analyse E to get the limit values of integration. We are given that E is the solid…

Q: Q3//A:- Verify that dV = p² sin p dp d0 do when using spherical coordinates.

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

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: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = Vx, 1sy& 4

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Q: Find a spherical coordinate equation for the sphere x². + y? + (z – 1)2 = 1 Select one: а. p = cos Ø…

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Q: Use spherical coordinates. |II (1 - x² - y²) dv, where H is the solid hemisphere x2 + y2 + z? s 25,…

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Q: Convert the following to rectangular coordinates and spherical coordinates. Do not evaluate the…

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A: Given:y=x3  ,     3≤y≤4Surface area :S=∫ba2πx 1+dxdy2   dy

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A: TO FIND THE PARAMETERIZATION USING COS(t) and SIN(t) GIVEN - Plane  y=3 and  given sphere intersect…

Q: 6. By converting to spherical coordinates, evaluate 22 dz dx dy. 0.

A: triple integral

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Q: The equation of a sphere of radius 5 , centered at the origin in spherical coordinates is: O r2 + z?…

A: We know, the equation of a sphere of radius r, centered at the origin in rectangular coordinates is…

Q: Find a spherical coordinate equation for the cone Z =Vx² + y2? Select one: а. 4 b. TT 4 С. 4 d. Non…

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Q: Find an equation of the form p = f (0, $) in spherical coordinates for the surfac z = 8

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Q: In changing variables to spherical coordinates, the dV in J f(x, y, z) dV becomes p² cos o dp do do.

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Q: Q.1 Use cylindrical coordinates to evaluate (x+y )dzdxdy

A: ∫-11∫01-y2∫0xx2+y2dzdxdy =∫-11∫01-y2∫0xdzx2+y2dxdy=∫-11∫01-y2z0xx2+y2dxdy=∫-11∫01-y2xx2+y2dxdy…

Q: find an equation of the form ρ = f (θ , φ) in spherical coordinates for the following surfaces  x2…

A: Solution:- x2-y2=4 x=ρ sinφ cosθ y=ρ sinφ sinθ   ρ sinφ cosθ2-ρ sinφ sinθ2=4 ρ2 sin2φ cos2θ-ρ2 sin2φ…

Q: Identify the given radius if the center lies at the origin. a. x2 + y2 = 15, 129 b. x2 + y2 = 121 с.…

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Q: Find the points on the surface y? = 81+ xz that are closest to the origin.

A: Distance formula is                   d2=x2+y2+z2                  d2=f=x2+81+xz+z2 Since,…

Q: Evaluate y*dV, where E is the solid hemisphere x? + y? + z² 0. E (Hint: spherical coordinates)

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Q: dV , where V is the unit sphere.

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Q: Find the EXCESS (E) and AREA of a spherical triangle whose radius is 12 m and angles are A=30°;…

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Q: The value of Jacobian in cylindrical coordinate system is given by a. r b. r? sin e c. p2 d. rsin?e

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Q: The spherical coordinate equation of (x – 4)² + y² + z? = 16 is p= 8sinØcose

A: The spherical coordinates are given by  x=ρcosθsinφy=ρsinθsinφz=ρcosφ The given equation is…

Q: Find a spherical coordinate equation for the sphere x² + y? + (z – 1)? =1 Select one: а. p = 3cos Ø…

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Q: The cylindrical equation z = r2 represents which of the following? O a paraboloid O a semisphere O a…

A: The cylindrical equation z=r2

Q: (d) r2 + x? = 9 in cylindrical coordinates (e) pcos(o) = 1 in spherical coordinates %3D

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Q: Q 2/ Sketch and shows the relationship between the Cartesian and Spherical coordinate Pt Te B

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Q: Convert the following Cartesian points to cylindrical and spherical coordinates: (a) P(2, 5, 1) (b)…

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Q: з 3 Let P be a point in R³ with rectangular coordinates (,,-V3) (b) Give the spherical coordinates…

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Q: 48. Use spherical coordinates to evaluate y'Vx +y +z dz dx dy

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Q: Which of the following is a correct conversion formula when changing from spherical to cylindrical…

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Q: Find a spherical coordinate equation for the sphere x² + y? + (z – 1)² = 1

A: All real numbers can be represented on a line called the number line. The number zero corresponds to…

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A: Given the cylindrical co-ordinates (r,θ,z)=(2,−5π4,−2)

Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. = Vx, 1sys 5

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Q: Use spherical coordinates. Evaluate yez2 dV, where E lies above the cone = /3 and below the sphere p…

A: detailed solution is given below

Q: Find the center and the radius r of the sphe S: a +y ++ te + 8y – 8z = -11 82 -11 %3D

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Q: Use spherical coordinates. I/| y? dv, where E is the solid hemisphere x2 + y2 + z? s 4, y > 0.…

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Q: Find a spherical coordinate equation for the sphere x²+y? +(z- 1)? = 1 Select one: a. P= cos Ø O b.…

A: All real numbers can be represented on a line called the number line. The number zero corresponds to…

Q: Q3/|A:- Verify that dV = p² sin o dp do dp when using spherical coordinates. %3D

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