Use spherical coordinates. SI. Evaluate Vx2 + y2 + z2 dV, where E lies above the cone z = Vx2 + y2 and between the spheres x2 + y2 + z² = 1 and x² + y2 + z² = 36.

Q: Use spherical coordinates to evaluate /R Vx2 + y² + z² dV , where B is the ball x² + y? + z? < 10 В

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Q: Evaluate ||E y²z² dV, where E lies above the cone o and below the sphere p = 1. = T/3

A: Given, ∫∫∫Ey2z2dV   ....(i)Let x=ρsinϕcosθ y=ρsinϕsinθ and z=ρcosϕAnd we know…

Q: Use spherical coordinates to evaluate // | eva*+*** dV, where E is enclosed for E by the sphere x² +…

A: Please see the below picture for detailed solution.

Q: Use spherical coordinates. Evaluate ∭e ^ (x ^ 2 + y ^ 2 + z ^ 2) dV, where E is inside the sphere x…

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Q: Use spherical coordinates to evaluate f[[, 3e(a+y´+z²)°/² dV, where E is the region inside the…

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Q: Evaluate: I| (x2 + y?) ds over the surface S of the sphere x2 + y? + z? = 5. Use Formula (5.22a)…

A: The solution is given below:

Q: Evaluate fff 1- x2 - y2-z2 dx dy dz where V is the volume of the sphere x? + y? + z2 = a? by…

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Q: Consider the following cylinder in R° and complete parts a. and b. below. y - 3 In z = 0 a. Identify…

A: The given function is, y-3lnz=0y=3lnz

Q: Find a spherical coordinate equation for the cone z= Vx2 +y?? Select one: a. 4 b. Non of them С. r…

A: Use the spherical coordinates for this cone as in next step.

Q: Use cos(t) and sin(t), with positive coefficients, to parametrize the intersection of the surfaces…

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Q: Which of the following surfaces cannot be described by setting a spherical variable equal to a…

A: Given,ρ=k , ϕ= k , θ=k To check which one of the given surfaces cannot be described in the above…

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

A: triple integral

Q: In isosceles trapezoid WXYZ with bases ZY and WX, ZY = 8, YX = 10, and WX = 20. Find height h (the…

A: Given  The  WXYZ  is isosceles trapezoid  with bases ZY and WX .  Here ZY =8  , YX =10  and WX =20

Q: By changing to polar coordinates, evaluate the integral ∬D (x2+y2) 3/2 dxdy where D is the disk…

A: Given integrand is ∬Dx2+y232dxdy where, D is the disk x2+y2≤49 We have to evaluate ∬Dx2+y232dxdy…

Q: Use spherical coordinates. Evaluate I|| y²z? dV, where E lies above the cone o = n/3 and below the…

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

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

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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: 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: Identify and sketch the following set in cylindrical coordinates. {(r,0,z): 3r szs 3}

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

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Q: Use spherical coordinates. SIL Evaluate |I| (x² + y2 + z²)² dV, where B is the ball with center the…

A: We need to evaluate the following triple integration ∫∫∫Bx2+y2+z22dV Where, B is the ball with…

Q: Use cylindrical or spherical coordinates, whichever seems more appropriate, to evaluate lies above…

A: Solution: ∬∫E z dV z = x2 +y2  ,     z =4

Q: Find the center C and the radius a for the spheres (x + 2)2 + y2 + (z - 2)2 = 8

A: We have to find the center C and radius for the given sphere equation: x-22+y2+z-22=8 We know that…

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

A: Let us consider rectangular coordinates x,y,z and spherical coordinates ρ,θ,φ. Equations which…

Q: In the 3D coordinate system, for the quadric with euqation ax2 + y2 + 4z2+x + 6y − 4z = −a − 10…

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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: Evaluate tot? xe*< + y2 + 22 dv, where E is the portion of the unit ball x2 + y² + z2 s 1 that lies…

A: Triple integral

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 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 a parametrization, using cos (t) and sin(t), of the following curve: The intersection of the…

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Q: Use spherical coordinates. Evaluate ||| (x² + y²) dv, where E lies between the spheres x2 + y? + z²…

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Q: 3. Use spherical coordinates to valuate ff, y? dV where E is enclosed by the hemisphere x? + y? + z?…

A: Given that  ∫∫∫Ey2dV and  enclosed by the hemisphere, x2+y2+z2≤9,y≥0 Here to evaluate the integral,…

Q: By changing to spherical coordinate, evaluate (a) z' Vx² + y² +z² dz dy dx (b) " ST* E x² + y° +z?…

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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: Use spherical coordinates to evaluate the triple integral [[[ 2² + 3² + 2²dV, where E is the ball:…

A: We will first change it into spherical coordinate and then solve it.

Q: Use spherical coordinates. SIL Evaluate xyz dV, where E lies between the spheres p = 2 and p = 6 and…

A: Consider the given statement. Let  x=ρsinϕcosθy=ρsinϕsinθz=ρcosϕ Then dV=ρ2sinϕdρdθdϕ The limits…

Q: (b) To change from spherical coordinates to Cartesian coordinates we use the equations x =r cos 0, y…

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Q: (a) Find the point of intersection between the curv urve r(t) = (cos(at), sin(at), t²) and the…

A: We’ll answer the first part of this question since due to complexity. Please submit the question…

Q: For the following cylindrical coordinate (r, 0, z) of a point, find its associated spherical…

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

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

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Q: 3. Evaluate /// x² + y? dV where E is the part of a2 + y? + 2? = 4 with y 2 0, using spherical E…

A: (3) Given integral is ∭Ex2+y2dV, where E is the part of x2+y2+z2=4 with y≥0, using spherical…

Q: Consider the following cylinder in R. x? + z? = 1 a. Identify the coordinate axis to which the…

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Q: Evaluate e dV where E is enclosed by the paraboloid z = 1+ æ² + y°, the cylinder a? + y? = 4, and…

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Q: Use spherical coordinates. // xex2 + y2 + z? dv, where E is the portion of the unit ball x2 + y2 +…

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Q: Find the center and radius of the following spheres x² + y² + z² – 2x – 4y + 8z + 17 = 0 %3D

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Q: Use Cartesian coordinates to evaluate JJJ² dV D where D is the tetrahedron in the first octant…

A: Given ∭y2 dVD

Q: Let B be the ball with center at the origin and radius 1 SS $3(x² +y? + z²)dV = 16 12m 24m :5

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Q: Use spherical coordinates. Evaluate TI (x2 + y2 + z²)² dv, where B is the ball with center the…

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Q: Evaluate z dz, where the contour C goes from z = 0 to z = 1 to z = 1+i.

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