Verify in cylindrical coordinates that а) b) V. (üv)= (V -ū)ỹ +ū ·Vỹ

Q: Find an equation of the tangent plane to the given parametric surface at the specified point. x = u…

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Q: Let D be the solid in space lying beneath the ry-plane and between the sphere r2 + y? + z² = 3 and…

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Q: The area of the plane z = 2x + 1 above the disk of radius 1 centered at the origin is (а) 4л. (b)…

A: As we know, z=fx,y defines a surface in xyz-space.  Formula for the surface area of the surface…

Q: Find the surface area of the helicoid (spiral ramp) with vector equation T(u, v) = (u cos v, u sin…

A: We need to find the area of the surface:r→u,v=ucos v, u sin v, v ; 0≤u≤1, 0≤v≤3π

Q: Describe the set in cylindrical coordinates. y^2 + z^2 ≤ 9, x ≥ y

A: Let x=rcosθ, y=rsinθ  and z=z. And the given equation is x ≥ y ⇒ cosθ ≥ sinθ

Q: Find the surface area of the helicoid (spiral ramp) with vector equation F(u, v) = (u cos v, u sin…

A: The area of given helicoid is given by using double integral as follows

Q: Which of the following is the cylindrical coordinates of (-1,-V3,2)? Oa (4, 품, 2) O b. (2, 5,2) O…

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Q: The vector equation r(u,v)=ucosvi+usinvj+vk, 0≤v≤4π, 0≤u≤1, describes a helicoid (spiral ramp). What…

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Q: Exercise 9.6. Find the average distance of the space between a sphere of radius 2 and a sphere of…

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Q: Evaluate ∫W z dV, where W is the first-octant portion of the solid sphere of radius 2 centered at…

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Q: Convert the following point from cylindrical to rectangular coordinates: 10, (x, y, z) = Usage: To…

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Q: Convert the following point from cylindrical to rectangular coordinates: (6. 52). (x, y, z) = Usage:…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: | a2 dA, where D is the part of the unit disk where r+y 2 0.

A: To find :         ∬Dx2 dA where D is the part of the unit disk where x+y≥0

Q: Show that the cylindrical equation ,2(1 – 2 sin² 0) + z² = 1 is a hyperboloid of one sheet.

A: Given a cylindrical equation r21-2sin2θ+z2=1 To show that this equation is a hyperboloid of one…

Q: Find the center of mass, the moment of inertia about the coordinate axes, and the polar moment of…

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Q: Find a parametrization and the equation associated with the cylindrical surface whose directrix and…

A: answer is in step 2

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

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Q: A hole is drilled through the center of a sphere x +y +z? = R,', leaving a ring-shape solid. If the…

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Q: Exercise 2 Use spherical coordinates to evaluate [[[(9-x - y³) dV , where E is the solid hemisphere…

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Q: Find a parametrization for the line segment joining points (0, 2) and (4, 0) using the angle 0 in…

A: Modify the given figure as shown in Figure 1.

Q: A hole is drilled through the center of a sphere x?+y² + z² = R,?, leaving a ring-shape solid. If…

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Q: Describe the set in cylindrical coordinates. x^2 + y^2 + z^2 ≤ 1

A: To convert into cylindrical co-ordinates let x = r cosθ, y = r sinθ, z=z   For x^2 + y^2 + z^2 ≤ 1…

Q: Let B = xa,. Express B in %3D (a) cylindrical coordinates, (b) spherical coordinates.

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Q: Convert the point (x, y, z) = (4, 4, 3) to cylindrical coordinates. Give answers either as…

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Q: Let G be the solid in the first octant bounded by the sphere 2x? + 2y? + 2z? = 32 and the coordinate…

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Q: Exercise 2 Use spherical coordinates to evaluate f[[(9-x² - y³ ) dV , where E is the solid…

A: Introduction: When we perform a triple integral over a spherical region, it is convenient to follow…

Q: Describe the set of all points P = (x, y,z) satisfying x^2 + y^2 ≤ 4 in both cylindrical and…

A: Given,        x2+y2≤4

Q: Evaluate ⌠⌠(x+y)ds, where S is the cone whose parametric equations are x=ucosv, y=usinv, z=2u,…

A: Given  cone whose parametric equations are x=ucosv, y=usinv, z=2u, 0≤u≤3, 0≤v≤π/2 we find the given…

Q: Write down a parametrization r(u, v) for the portion of the plane x - y+ z = 3 that lies inside the…

A: r(u, v) = ( u cos v , u sin v,  3 - u cos v + u sin v)  Where u € [0, 1]           v€ [ 0,2π]

Q: Calculate the positive value of m so that the x+y+2z=m plane is tangent to the spherical surface…

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Q: Let G be the solid in the first octant bounded by the sphere 2x? + 2y? + 2z? and the coordinate…

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Q: Find an equation of the tangent plane to the parametric surface. x = u + v, y=6u^2, z = u − v. at…

A: Find an equation of the tangent plane to the parametric surface. x = u + v, y=6u^2, z = u − v. at…

Q: 它们也称 Use spherical coordinate to evaluate Vr² + y² + z² dz dy dx. 0,

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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: Convert the point (x, y, z) = ( – 1, – 4, 3) to cylindrical coordinates. Give answers either as…

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Q: Convert the following point from cylindrical to rectangular coordinates: (* ). 11a 6, (x, Y, z) =…

A: The given point in cylindrical coordinates are   6,11π6,9. We know that if cylindrical coordinates…

Q: The object shown in the figure is axially symmetric and its curved surface is described in…

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Q: Use Spherical coordinates to evaluate Cx*+ ya+22)² dV where Bis the B. ball with anter at the ongin…

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Q: A hole is drilled through the center of a sphere x2 + y? +z? = R², leaving a ring-shape solid. If…

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Q: The r in cylindrical coordinates must be positive or zero. O True O False

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Q: 5. Convert the integral 9-x2 9-x²-y² Vx? + y? + z² dzdydx to spherical coordinates then evaluate.

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Q: (b) Use spherical coordinates to evaluate l y²dV_where E is the solid hemisphere a? +y² + z² 0. E

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Q: Let B be the ball with center at the origin and radius 1 SIS 4(z² + y² + z*)dv = B

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Q: Find a vector parametric equation for the ellipse that lies on the plane z (x + 2 - cylinder x + y =…

A: Dear student. You have posted many parts, according to the policy we will answering the first part.…

Q: F in circular cylindrical coordinates.

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: use Cylindrical coordinates to the Vaume of the Solid bovnded by the parabolo ld z=16-x²-y? %3D

A: Introduction: A point with rectangular coordinates left(x,y,z right) in three-dimensional space R3…

Q: Find a parametrization for the line segment joining points (0, 2) and (4, 0) using the angle 0 in…

A: Given: The line segment joining (0, 2) and (4, 0). Do the construction as in below figure

Q: In cylindrical coordinates, the set {(r, 0, z): 0<r< 1, 0<0 <T, -1 <z < 1} is (a) a full right…

A: In the given cylindrical coordinates, r,θ,z Radius of the cylinder lies between 0 to 1. r=0≤r≤1r=1…