2 2 15. Eind. the Poiats.an.the.. surface.Xy 2=1 that.are closest.bothaorrqin.

Q: The surface described by the conditions 2 + y? + z² = 4, x 0 is the same as the surface described…

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Q: Find ervstion for the tangen plare to the Surface an Siven by x2y?3 =12 at the point Z-2,1,3)

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Q: The distance between the centers-of the following two spheres: x²-22x+y2-58y+z?=-961,…

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Q: Find the extreme values of ƒ(x, y, z) = x - y + z on the unit sphere x2 + y2 + z2 = 1.

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Q: Which of the following is the total length of the curve of intersection of the surfaces x2 + y? + 22…

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Q: I just need #20

A: Given,

Q: Ex.7 The area of the surface ∑ = {(x,y,z) €R® : (x² + ²) < 1, z = 9 + xy} is: (A) - 5 (B) 4개 2 (C)…

A: Using polar coordinates.

Q: 7. If the net was folded into a box, which sides represent the lateral surfaces? a f C e d

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Q: 5.4. F(х, у, 2) 2³), M is the outer surface of the sphere x² + y² + z² = a². %3D

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Q: 3. Determine the center and radius of the following sphere: x² + y² + z² - 2x - 4y + 8z - 15 = 0

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Q: 2. State the names of the following quadric surfaces. (a) The surface z = y² – 2x². (b) The surface…

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Q: When the plane x = 3 passes through the surface x² + y? + 2? = 64, the curve that forms from…

A: Given, the plane x = 3 passes through the surface x2 + y2 + z2 = 64 . The intersection of plane x =…

Q: Evaluate yds where S is the surface = x + 2y?, 0 <a < 1, 0<y S 2

A: Consider the surface, z = x + 2y²

Q: Use traces to sketch and identify the following surface 25x² + 4y? + z² 100.

A: Given: The surface 25x2+4y2+z2=100.

Q: sketch the given surface. x2 − y2 + 9z 2 = 9

A: Given, x2-y2+9z2=9

Q: (3) Consider the quadric surface SC R, having equation a2 + y? – 22 = 9. Find all lines through P =…

A: The quadratic equation is given by x2+y2-z2=9.  General equation of line is: x,y,z=a,b,c+tl,m,n…

Q: w.The given.surface.at. thespeeif 2.

A: Introduction:   We know that the equation of tangent plane to the surface z=f(x,y) at the point…

Q: Consider the surface shown in the following figure: If h, k, r, m, teR. A general equation that…

A: Solution is below

Q: 6. In Section 12.5, you learned that the distance from a point (ro, Yo, zo) to a plane ax+by+cz = d…

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Q: 4 The area of the surface S = {(x, Y, z) E R³ : z = 5 – x² – y², z > 3} equals (A) 4ñ 9. (B) 5* 13…

A: 4 Given S=x,y,z∈R3:z=5−x2−y2,z≥3.. We have to find the surface area of S At z=3 ⇒3=5−x2−y2⇒x2+y2=2…

Q: 2. Find the area of the part of the surface z = cylinder x2 + y² = 9. 3xy that lies within the

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Q: 4) Name a point that is coplanar with A, B, and C. b. E D a. D d. N C. F 3)

A: the given figure we have to name a point that is coplanar with A, B and C.

Q: A surface in R³ is defined by the equation 4z = x² + 4y².

A: Given:-                 The surface in  is given by  . Sketch the intersections (traces) of this…

Q: 10. Find the area of the portion of the sphere x2 + y² + z² = 16 between the planes %3D z=1, z=2.

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Q: 8. Find the surface area of the part of the sphere x2 + y? + 22 : = 4z that lies inside the…

A: The solution is given as

Q: sketch the given surface. x2 + y2 − z 2= 1

A: Given: x2 + y2 − z 2= 1

Q: sketch the given surface. y 2+ z 2 = 1

A: To sketch: The surface y2+ z2 =1 Concept used: The general equation of the cylinder whose base…

Q: 3.4.8 Show that the sphere x² + y² + z² = 1, z ≥ 0. JJ,z²dS=, where S is the surface of

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Q: Which is the equation of a sphere with a center at (1,0,-2) with a volume of 36(pi)(u^3)? a.…

A: We first defined the equation of sphere and centre,volume . Using this formula we have equation (a)…

Q: 4 Assuming that the curve ris thex + y +z = 0 intersection of the plane and the sphere , then the…

A: As per the question we are given a closed curve Γ , defined as the intersection of the plane x+y+z =…

Q: Find the point on the sphere x^2 + y^2 + z^2 = 8 that is closest to the point P(2, 1, 1)

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Q: (a) x² + 2x + 4y² + 16y + 9z? 19

A: Sketch and identify the surfaces: (a) x2+2x+4y2+16y+9z2=19.

Q: 7. Use a program to plot the surface generated by the following equation: 4x – 16y + z? = 16

A: we need to plot the following surface generated by, 4x2-16y2+z2=16

Q: Find the largest and smallest distances between the point P(1, 1, 1) and the sphere x² + y? + z? –…

A: Given circle is x2+y2+z2-2y+6z-6=0, and P(1, 1, 1) Let C be the center of the circle.…

Q: Evaluate ([(3xi +2yi)-d$ -d$ where S is a sphere x +y +z? =9.

A: To evaluate the below integral. ∫∫S3xi+2yj⋅ds Here S is a sphere x2+y2+z2=9

Q: Which of the following is a non-orientable surface? O a. all the other choices are orientable O b.…

A: orientable surface -  The surface for which we can define clockwise consistently.

Q: Find the standard equation of a sphere that has diameter with the end points given below. (3, 8,…

A: to find standard equation of sphere that has diameter with end points 3,8,-2,-1,4,10

Q: 47. Find the distance between the spheres x? + y² + z² = 4 and x? + y? + z? = 4x + 4y + 4z – 11.

A: The equation of the spheres are given:

Q: ce cut from the first octant by the cylinder z = 12 – 3y, and the plane x + y = 2

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Q: 2 Find the area of the ellipse cut from the plane z = 3x by the cylinder x² + y² = 16. Surface area…

A: Given plane z=3x and the cylinder x2+y2=16. The objective is to find the area of the ellipse cut…

Q: 8. Draw the figure and Find the area of the part of the sphere x? + y? + z? = 3z that lies inside…

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Q: Let be s a surface compaund by the union of s, qnd Sz An expression to get the Area of the Surface…

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Q: Find the center and radius of the sphere x? – 6x – 10+y? + 10y +z? – 20z = 0 OA C(-3,5,10), r = 10…

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Q: 11r If F(r) and o is the surface (x – 4)2 + y² + z² = 49 oriented 3 outwards, what is the value of…

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Q: 2. State the names of the following quadric surfaces. (a) The surface z = y² – 2x². (b) The surface…

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Q: Find the center and radius of the sphere. 2 4x + 4y + 4z + x + y+z= 25

A: Topic = Sphere

Q: Consider the sphere (x−3)2+(y−2)2+(z+1)2=32(x−3)2+(y−2)2+(z+1)2=32. The point P =(−1,2,3)(−1,2,3) is…

A: Given that, x-32+y-22+z+12=32 And the point on the sphere is p-1,2,3 To find another point on the…

Q: 1) A) Find the area of the portion of the sphere x? + y + =9 lying inside the cylinder x2 + y? = 3y.

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Q: Find the point(s) of intersection of the line l : ¯r(t) = ⟨−4, 3, 4⟩+ t⟨−5, 3, 4⟩ and the unit…

A: Solved below

Q: (3) Consider the quadric surface S C R, having equation a2 + y? - z2 = 9. Find all lines through P…

A: General equation of line from point 3,-3,3 is x,y,z=3,-3,3+tl,m,n.  Substitute it in the quadratic…