By transforming into spherical polar coordinates, evaluate JJ) 1-x². ff - (- dxdydz , taken throughout the V1-x²-y2-z2 volume contained in the positive octant of the sphere x2 + y2 + z2 = 1.

Q: Describe how the surface with spherical equation p²(1 + A cos² ¢) = 1 depends on the constant A.

A: Given : ρ2(1+Acos2ϕ)=1To describe: How the surface with spherical equation  ρ2(1+Acos2ϕ)=1depends on…

Q: Convert the point (x, y, z) = (2, — 2, 1) to spherical coordinates. Give answers as positive values,…

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Q: Use spherical coordinates to evaluate 2π FT S 2-r r+z 0 (r² +2²) ³/ rdz dr de.

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Q: V18-x2-y Convert (x² + y + z?)dzdxdy into spherical coordinates. 2n/3 3V2 4 p* cos pdpdpdO /2 -n/2

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Q: 1) Use spherical coordinates to evaluate 4-x² -y² 4-x2-y2 4-y² LaSNa- y²/x² + y² + z² dzdxdy

A: The given problem is to evaluate the given triple integral using spherical coordinates, We have to…

Q: 3. a) Find polar coordinates (r, 0) of the point (1, -/3), where r> 0 and 0 <0 < 2 p2 = x² + y?, tan…

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Q: 16-y Convert (z² + y² + z²)dzdrdy into spherical coordinates.

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

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Q: Convert the following lines to parametric equation. a) l₁: = (1,0,1) + t(1,0,−2), t = R Z-3 b) 1₂: x…

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Q: II. Evaluate in rectangular form (a + jb) and in polar form (rz0) given: Z1 = -5 + j12,Z2 = 3 + j4,…

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Q: Verify that dV = p sin o dp de dy when using spherical coordinates. %3D

A: We have to represent a differential element.

Q: #5. Find the rectangular coordinates of the point (3,57/4, 7/6) given in spherical coordi- nates.

A: We have given a spherical coordinates:…

Q: 1.Find the area of the triangle in the xy-plane with vertices A(n,n2, n3),B(m,m2,m,),C(r..). 2.…

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Q: Describe the quarter globe in space polar coordinates. K := {(x, Y, z) E R³ : x² + y² + z² < 169, x…

A: We are given the quarter globe by K = x, y, z∈ℝ3 : x2+y2+z2≤169, x≤0, z≤0. Let x=r sin θ cos φ, y=r…

Q: (a) (b) (c) r(u, v) = (u cos v, u sin v, v); u € [0, 2], v € [0, π]. (*) Find r, and r. (**)…

A: Surface integral of a function f(x,y,z) on a parametric surface r(u,v) in the region D  ∫∫Dfx(u,v) ,…

Q: Please solve asap: 9. Give a parametric description of the form r(u,v) for the equation 6x - 3y +…

A: To obtain a parametric description of the equation 6x−3y+2z=18, write it in terms of two variables,…

Q: Transform to spherical coordinates: F 102-8ỹ+6ż at point P (10, 8, 6)

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Q: Cartesian equation of the curve given by the equation in polar coordinates ? O A) y= v3x O B) x =…

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Q: Find a set of parametric equations for the curve of intersection of the paraboloid r² + 4y² -z = 0…

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Q: Find the surface area of the portion of the paraboloid z= (Hint: It's easiest if you use polar…

A: The paraboloid is given as÷

Q: Find the centroid of the quarter of the unit circle lying in the third quadrant. ICM усм

A: The equation of the circle is x2+y2=1 The radius of the unit circle is 1 unit.