cribe the surface with equation x + y° + z? + 8x + 4y + 2z – 43 = 0 surface is a sphere with center ( i i i ) and

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: (b) Sketch the trace of the surface z = 2x? – y? when x = -1. Label your axes, and give the…

A: Given surface is  z=2x2-y2          (i) By putting x=-1 in (i), the surface becomes z=2-y2 The graph…

Q: Find an equation of the surface of revolution by revolving the plane curve 3y = √(9- [(x-1)] ^2)…

A: We need to find the equation of the surface. Please find step by step solution below:

Q: a) Find the center of the sphere satisfying the equation, x2 + y2 + z2 - 2x + 4y + 2z = 10.…

A: The given equation of sphere,   x2+y2+z2-2x+4y+2z=10

Q: Identify the type of surface represented by the equation z2 x2 %3D 10 10 6. Parabolic cylinder…

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Q: Identify the type of surface represented by the given equation. 를 - 2.2 2 8. O Parabolic cylinder…

A: The given equation is z22-x28=y2. As we know that the general equation of the parabolic cylinder is…

Q: 2.a. Write the equation of the surface r? + y? = 4y in cylindrical coordinates. b. Classify the…

A: To convert to the cylindrical coordinates, we need to make the following substitutions: x=rcos(θ);…

Q: Find the points on the surface x² −yz = 5 that are closest to the origin.

A: Let the point P be (x,y,z). The distance between the point P and origin is given by the formula…

Q: Identify a generating curve on the XZ-plane for the surface of revolution with equation x? + y? + Z?…

A: We need to identify a generating curve on the xz-plane for the surface of the revolution with the…

Q: Consider the equation below. x² – y2 + z² – 4x – 2y – 4z + 7 = 0 - Reduce the equation to one of the…

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Q: Determine the characteristics of the equation z = p? -q? and find the integral surface which passes…

A: Given partial differential equation is z=p2−q2 We have to find he characteristics of the equation…

Q: Find the points on the surface represented by x2 + y? + z2 - 4x – 6y + 2z = -10 which are closest to…

A: To find - Find the points on the surface represented by x2 + y2 + z2 - 4x - 6y + 2z = -10 which are…

Q: Sketch the section of the surface at y = 0. 9x^2+4z^2=36

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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 given surface. x2 − 4y2 = z

A: Given: x2-4y2=z Divide the equation both sides by 4. x24-4y24=z4x222-y21=z4 The equation…

Q: Identify the surface 2x² + 4y? – 1=0. A. An elliptic cylinder. B.Ahyperbolic cylinder. OC. None of…

A: We will solve the problem

Q: find an equation of the form r = f (θ , z) in cylindrical coordinates for the following surfaces.…

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Q: cribe the surface with equation 2 +y +? + 8x + 6y + 2z - 10 = 0 surface is a sphere with center ( i…

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Q: Identify a generating curve on the XZ-plane for the surface of revolution with equation x? + y2 + z?…

A: Given: Surface of revolution with the equation x2+y2+z2=e2x To find: Identify a generating curve on…

Q: sketch the given surface. x = 1 + y 2+ z2

A: sketch the given surface. x = 1 + y 2+ z2

Q: (e) x = 4 – z²

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: For the surface x? + y? = 2z? a) Find an equation in cylindrical coordinates

A: In this question, the concept of conversion of the coordinate system is applied. Cartesian…

Q: Find the equation of spheres passing through the circle x+y+z'-6x-2z+5 =0, y = 0 and touching the…

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Q: Find the point on the ellipsoid x2 + y2/4 + z2/9 = 1 for which x + y + z is largest.

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Q: find an equation of the form r = f (θ , z) in cylindrical coordinates for the following surfaces.…

A: Given: The surface, x2+y2+z2=4.

Q: Match the surface to its corresponding equation in cylindrical coordinates. 2z 3z %3D = 6 = 36 – 22…

A: To find- Match the surface to its corresponding equation in cylindrical coordinates. r = 2z r2 = 3z…

Q: Sketch the section of the surface at y=0. z = /2+x² + y?

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

A: Given: x2 + y2 − z 2= 1

Q: Sketch the curve of intersection of the surfaces. The ellipsoid 2x + 2y° + = 288 and the paraboloid…

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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: Find the center C and the radius a for the spheres x2 + y2 + z2 - 6y + 8z = 0

A: To Determine: Find the center C and the radius a for the spheres  Given: we have an equation…

Q: Find the equation for the sphere centered M(2,-3,2) tangent to the D:6x-3y+2z-11=0 plane

A: we have to find the equation for the sphere centered 2,-3,2 and tangent to the plane 6x-3y+2z-11=0.

Q: 1 Find the surface area of the part of the hyperbolic paraboloid z = (x² - y²) that lies inside the…

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Q: The surface defined by the equation z= 4x2 + y2 is called an elliptical paraboloid. a. Write the…

A: Given, function

Q: Sketch the graph of the equation in xyz coordinate system and identify the surface 8x? + 4y? – z2 =…

A: Sketch the graph for the given surface.

Q: Sketch the curve of intersection of the surfaces. The ellipsoid 2x + 2y² + z? = = 24 and the…

A: We have to write the intersection curve

Q: Identify a generating curve on the XZ-plane for the surface of revolution with equation x? + y2 + Z?…

A: Solution-

Q: Consider the Equation:  x2 + y2 + z2 + 8x - 6y + 2z + 17 = 0 1. Show that the equation represents…

A: x2 + y2 + z2 + 8x - 6y + 2z + 17 = 0

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: Find an equation of the form p = f(0, $) in spherical coordinates for the surface. x2 - y2 = 36 p =…

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Q: Find an equation in cylindrical coordinates for the surface represented by the rectangular equation…

A: we have to find an equation in cylindrical coordinates for the surface represented by the…

Q: Choose the equation that represents the graph of the cylindrical surface below O2 + y? = 1, = 5 O…

A: We have plotted the graph:- second option

Q: Evaluated the counter integral 9,+z² - z-1 dz ,where C 1. The circle z| = 0.5 2. The circle |z+1-i=…

A: Given contour integral is  ∮Cezz3+z2-z-1dz We can write it as ∮Cez(z+1)2(z-1)dz Poles of…

Q: The equation of the sphere with radius r = V75 and center C(2,1, – 1) is (a) x² + y² + z² + 4x + 2y…

A: The general equation of a sphere with radius r and center a,b,c is x-a2 + y-b2 + z-c2 = r2

Q: Find the center and the radius of the sphere. x^2+y^2+z^2-6x+3z=0

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Q: Find the traces for the given surface: 16x? +16y² – 9z = 0. Then sketch and identify the surface.…

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Q: 4. Consider the equation 16y" - 4 + 2² = 16. By first deseribing all of its traces, sketch the…

A: Given,  The equation, 16y2 -4x2 + z2 = 16

Q: Find an equation for the surface generated by revolving the curve about the y-axis. y = 2x , (z = 0)…

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Q: Parametrize the intersection of the surfaces using t = z as the parameter. (If there are multiple…

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Q: Identify the surface by completing the squares. x +16y² – z? – 14x + 32y + 8z = 0 O A hyperboloid of…

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