Find the point lying on the intersection of the plane x + y +z = 0 and the sphere x2 + y2 + z? = 25 with the largest z-coordinate.

Q: Explain why the curve of intersection of the surfaces x + 3y? – 2z2 + 2y = 4 and 2x? + 6y? – 4z2 –…

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Q: What is an equation for the largest ball centred at (0,0, 1) that can fit in the paraboloid z = 3 -…

A: To find the equation for the largest ball centered at (0, 0, 1) that can fit in the below equation…

Q: parametrizes the portion of the sphere x² + y² + z² = 9 that is above the xy-plane and below the…

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Q: 5a. Consider the right square pyramid with a horizontal plane intersecting the pyramid halfway up…

A: The horizontal plane will be parallel to the base of the pyramid.

Q: Classify the surface: 1-z = 3y? + 4z? ,2

A: Given : The surface 1 - x = 3y2 + 4z2   To classify the given surface.

Q: Find the area of the surface. The part of the plane z = 9 + 2x + 5y that lies above the rectangle…

A: Given: The part of the plane z=9+2x+5y that lies above the rectangle0, 9×1, 6. To Find: Area of…

Q: Find an equation of the sphere with center (2, 1,−3) that is tangent to the plane x −3y + 2z = 4.

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Q: Find the area of the surface. The part of the plane  z = 3 + 2x + 5y  that lies above the rectangle…

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Q: Find the area of the part of the sphere x2 + y2 + z2 = 4z that lies inside the paraboloid z = x2 +…

A: Given, x2+y2+z2=4z  and  z=x2+y2 Equation of the sphere and paraboloid in cylindrical coordinates is…

Q: Find the center C and the radius a for the sphere 1. 3x2 + 3y2 + 3z2 + 2y - 2z = 9 2. x2 + y2 + z2 -…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Evaluate ff. xyz ds, over that part of a sphere of two units radius and centre at the origin Which…

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Q: Sketch the curve of intersection of the surfaces. The ellipsoid 2x + 2y + = 3 and the paraboloidz =…

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Q: 2. Find the area of the part of the sphere x² + y² + z² = 4z that lies inside the paraboloid z = x²…

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Q: Find the maximum volume of a box that is resting on the xy-plane with one vertex at the origin and…

A: Given the plane is 3x+4y+2z=12

Q: Find the area of the surface. The part of the sphere x2 + y2 + z2 = 16 that lies above the plane z =…

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Q: Find the centroid of the portion of the sphere x2 + y2 + z2 = a2 that lies in the first octant.

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Q: Q2: A cube of edge 24mm is resting on the top of a frustum of cone of base diameter 60mm and top…

A: We are asked to draw the isometric view of the solid.

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: Find the area of the surface of the part of the plane 3x + 2u + z = 6 that lies in the first octant.

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Q: Find the area of the cap cut from the top of the sphere x2 + y2 + z2 = 1 by the plane z = sqrt(2)/2.

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Q: What is the highest point on the ellipse that is the intersection of the plane z+y+ 2z = 2 and the…

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Q: 2. The portion of a cylinder of radius 3 centered along the y-axis that lies between the planes y =…

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Q: Find the surface area of the part of the plane z = 4+ 7x + 6y that lies above the rectangle [1, 6] ×…

A: We can use integral calculus to find the surface area of the part of the plane above the given…

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

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Q: Find all points on the isometric dot plane, Ax,1 yl, with x and y integers, that are ex- actly V133…

A: a)The distance from origin to point x,y is 133. b)The distance from origin to point x,y is 217.

Q: Find the center and the radius of the sphere that has the given x2 + y2 + z2 + 10x – 7y + 2z + 26 =…

A: Given a equation of the sphere , x2+y2+z2+10x-7y+2z+26=0 To fin the center and the radius of the…

Q: Find the surface area of the part of the plane 7+ 2x + 5y that lies above the rectangle [1, 4] x [0,…

A: Given that  Z=7+2x+5y To find the area of the surface of the plane that lies above the rectangle

Q: Find the point lying on the intersection of the plane x + y + 4 z = 0 and the sphere x2 + y2 + z2 =…

A: Determine z from the equation of plane.

Q: Show that the maximum value of a2b2c2 on a sphere of radius r centered at the origin of a Cartesian…

A: Let fa,b,c=a2b2c2 subject to a2+b2+c2 =r2  The gradient equation is…

Q: classify the quadric surface given by equation and determine its standard form.−8x 2 − 8y2 + 10z2 +…

A: We have the quadratic surface : -8x2-8y2+10z2+32xy-4xz-4yz-24=0…

Q: Classify the quadric surface given by equation  and  determine its standard  form. x2 + y2 + 2z2 −…

A: The quadric surface given to us is: x2+y2+2z2-2xy+4xz+4yz=16 This is compared to the general form of…

Q: Find the point lying on the intersection of the plane x + y +z = 0 and the sphere x2 + y? + z? = 25…

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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: Find the surface area of the part of the plane 3x + 2y + 4z = 24 that lies in the first octant…

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Q: What is the highest point on the ellipse that is the intersection of the plane z +y+ 2z = 2 and the…

A: I am going to solve the given problem by using the Lagrange's Multiplier method to get the highest…

Q: A mirror for a reflecting telescope has the shape of a finite paraboloid of diameter 0.3 meters and…

A: Equation of a circular paraboloid  f=r24d here, f= focal length along the axis of symmetry from the…

Q: Find the area of the surface. The surface cut from the “nose” of the paraboloid x = 1 - y2 - z2 by…

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Q: Find the area of the surface. The part of the plane z = 7 + 5x + 2y that lies above the rectangle…

A: The given equation is, z=7+5x+2y The partial derivatives are, fx=5fy=2

Q: Classify the quadric surface given by equation  and  determine its standard  form. x2 + y2 − z2 − 2x…

A: x2 + y2 − z2 − 2x − 4y − 4z + 1 = 0

Q: Find the area of the surface. The part of the plane  z = 4 + 3x + 2y  that lies above the rectangle…

A: Consider the part of the plane that lies above the rectangle .

Q: Find the points on the surface y2 = 64 + xz that are closest to the origin. %3D (х, у, 2) 3 (smaller…

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Q: classify the quadric surface given by equation and determine its standard form.−x 2 − y2 − z2 + 4x y…

A: Given quadric Surface is         -x2-y2-z2+4xy +4xz+4yz =3 Comparing it to the general form,…

Q: Find the area of the cap cut from the top of the sphere x2 + y2 + z2 = 1 by the plane z = √2/2.

A: Given equation of sphere is    x2+y2+z2=1     And the equation of plane is  z=22=12 But we know that…

Q: Find the surface area of the part of the plane 3x + 3y+ z = 9 that lies above the triangle formed by…

A: In the question we have to find the surface area of the plane.

Q: Find the extreme values of ƒ(x, y, z) = x2yz + 1 on the intersection of the plane z = 1 with the…

A: consider the following equations  f(x,y,z)=x2yz+1                                  (1)h(x,y,z)=z-1…

Q: The surface that is linear with the three variables, x, y, and z is called cylinder plane sphere O…

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Q: Find the area of the surface. The part of the plane z = 8 + 5x + 2y that lies above the rectangle…

A: Area of the surface z=f(x,y) A(s)=∬1+fx2+fy2f(x,y)=8+5x+2yfx=5fy=2

Q: Find the surface area of the part of the plane z = 4 + 6x + 2y that lies above the rectangle [1, 4]…

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Q: 3) Which type of quadric surface listed in Table 2 below is 4x² + y² + 4z² – 4y – 24z + 36 = 0?

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.