In Exercises 13–22, sketch the graph described by the following spherical coordinates in three-dimensional space. п 13. p = 3 14. ф %3D 15. 0 = 16. р %3D csc ф п 17. рсos ф %3D4 18. 1< p<2 sec 4, 0<ø< 19. 0 < p< 3 csc o 20. 0 < p< 1, < 6< m, 0 < 0 < 21. 0 < p cos 0 sin ø < 2, 0 < p sin 0 sin ø < 3, 0

Q: Match the surface to its corresponding equation in spherical coordinates. 4 2 3 4. %3D 2 1 а. -1 -2…

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Q: 1. Convert the equation of the sphere : x + y +6y+z? = 0 Into. a) Cylindrical coordinates (An…

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Q: The surface 10x – 9y = z2 can be described in spherical coordinates in the form p = f(0, 4) help…

A: Given 10x-9y=z2

Q: Match the surface to its corresponding equation in spherical coordinates. |p = 4 cos() 1.5 -1 -0.5 0…

A: To match the given surface to their given Equation in spherical coordinates.

Q: In Exercises 49-54, describe the given set in spherical coordinates.x 2 + y2 = 3z2

A: Given,           x2+y2=3z2  We have to describe it in spherical coordinate system.  We know that,…

Q: Match the surface to its corresponding equation in spherical coordinates. 37 4 -3 -2 -1 0 1 2 3 3…

A: To solve this we have to find the relation of equation

Q: Given the point (V3, ,-1) in cylindrical coordinates, what are the spherical coordinates (p, p, 0)…

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Q: Consider a point in Cartesian coordinates given by (-2, 2v3, 4). (a) Find the corresponding…

A: Given,

Q: 2. Convert the point (V6, , v2 ) from cylindrical to spherical coordinates. (12등, ) (b) (vZ;. )…

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Q: In Exercises 5-10, convert from rectangular to cylindrical coordinates.. (3, 3, 2)

A: Explanation The relation between rectangular coordinates x,y,z and cylindrical coordinates r,ϕ,z…

Q: In Exercises 13–22, sketch the graph described by the following spherical coordinates in…

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Q: Sketch the solid that has the given description in spherical coordinates           0 ≤   ≤ 2 , /4 ≤…

A: Concept: Calculus helps in understanding the changes between values that are related by a function.…

Q: Consider a point in Cartesian coordinates given by (3√√/3, −3, −8). (a) Find a corresponding…

A: The given Cartesian coordinates are: (x,y,z)=(33,-3,-8) Now, the Cylindrical coordinates is given…

Q: A Cartesian equation for the parametric curve x=24sin?e, y=21cos20, n ses 31/2 is given by O…

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Q: In three dimensions, the cylinder x? + z2 – 10x – 6z – 2 = 0 has radius k i +tj+ and the axis line…

A: Radius =6  r(t)= (5+6cos(thetha))i+tj+(3+6sin(thetha)k

Q: Sketch the set (described in cylindrical coordinates). r = 4

A: GIVEN r=4 we need to sketch the cylindrical coordinates

Q: Part 4 of 8 Since we want the portion of the sphere which is above this circle, we return to the…

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Q: (b) Find a parameterization, in spherical coordiantes, for the ellipsoid 4x2 + 9y2 + 2²/4 = 1 that…

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Q: By transforming into spherical polar coordinates, evaluate JJ) 1-x². ff - (- dxdydz , taken…

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Q: describe the given set in spherical coordinates  y2 + z2 ≤ 4, x = 0

A: y2+z2≤4,  x=0. Now consider, y2+z2≤4⇒x2+y2+z2≤4+x2⇒x2+y2+z2≤4             ∵x=0⇒ρ2≤4⇒0≤ρ≤2 Now since…

Q: Express the following points in cylindrical and spherical coordinates: (а) Р(1, — 4, — 3) | (b) Q(3,…

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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: Let P be the point (4, 1/3, 5) in cylindrical coordinates. Find the x-coordinate of P in Cartesian…

A: Formula: For a point P in three-dimensional space represented with cylindrical coordinates r, θ, z,…

Q: In spherical coordinates equation for the paraboloid z = 2- x - y is p(cos o- psin? $) = 2 Select…

A: We have to find out  spherical coordinate

Q: Let N be the lower hemisphere of the sphere of radius 5 and let H • Construct dS for 2. Try using…

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Q: 13. dy/dx = 2x, У (0) 3D —1

A: Solution: dy/dx =2x  ,    y(0)=-1

Q: describe the given set in spherical coordinates x2 + y2+ z 2 ≤ 1

A: Given: x2+y2+z2≤1 Spherical coordinates: x,y,z→ρ,θ,ϕ ρ2=x2+y2+z2

Q: 1. Sketch carefully the solid enclosed by the three cylinders x + y* – 1,x² + 2² = 1, and y + z² =…

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Q: Consider a sphere E with center at the origin and radius equal to 1, following the Beltrami-Klein…

A: Substitute the parametric coordinates of the line in the equation of sphere and solve to get the…

Q: Use spherical coordinates. Evaluate z dv, where E lies between the spheres x2 + y2 + z² = 1 and x2 +…

A: Using spherical  coordinate we can solve it very easily.

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: 1. Convert the point (-1,1, v2) from Cartesian to spherical coordinates. (a) (VZ. VZ) (b) (1., vZ)…

A: To convert the point (-1,1,√2) from cartesian coordinates to spherical coordinates.

Q: 1. Given a point (r, 0, z) = (2, 1/4, 1 /3) in cylindrical coordinates, what is its %3D rectangular…

A: We have to find the rectangular coordinates of given point in cylindrical coordinates.   According…

Q: Given the curve of intersection of the x² + 4y² -z = 0 which is a paraboloid and the plane 2x - z =…

A: Solution:-

Q: Which of the following is the rectangular coordinates of the point which is given by cylindrical…

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Q: A designer proposed using a paraboloid S,: x² +y² = z as the basis of a container design. However,…

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Q: 2. Convert the point (V6, , v2) from cylindrical to spherical coordinates. (e) (2VZ,품, 끌) (d) (vZ )…

A: The solution is given as

Q: Which of the following is the spherical coordinates of the point (0, v3, 1) which is given by…

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Q: Find the Cartesian coordinates of the point (6, 4. VIT) given in cylindrical coordinates

A: First we have to determine (r,∅,z) then calculate respective Cartesian co-ordinates

Q: The equation of a sphere of radius 3. centered at the origin in cylindrical coordinates is + = 9.…

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Q: Convert the point (x, y, z) = (5, 3, – 1) to spherical coordinates. Give answers as positive values,…

A: we have to convert the rectangular coordinates to the spherical coordinates   The given…

Q: 1. Consider a point in Cartesian coordinates given by (-2, 2v3, 4). (a) Find a corresponding…

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Q: 1. Convert the point (1,1, v2) from Cartesian to spherical coordinates. (a) (Vz. vz) (b) (1.#.v2)…

A: Option A is correct answer. Explanation is given below.

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

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Q: Convert the following point from rectangular to spherical coordinates: -5/2 -5/6 -5/2 4 4 (p, 0, 4)…

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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: Given that, 11-2-y 12x dzdyda = MT With the help of cylindrical coordinates find the value of m

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Q: Which of the following is the cylindrical coordinates of (-1, y/3, –2)? O a. (2, 플, -2) O b. (2, 폭,…

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Q: Convert the point from cylindrical coordinates to spherical co (3,2,0) (p, 0, 4) = || X

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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…