Show that the maximum value of a2b2c2 on a sphere of radius r centered at the origin of a Cartesian abc-coordinate system is (r2/3)3.

Q: Find the dimensions of the rectangular box of maximum volume that has three of its faces in the…

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Q: 3. Use Lagrange Multipliers to find the dimensions of the closed right cylindrical can of smallest…

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Q: B4. Find the dimensions of the right circular cylinder of maximum lateral surface area which can be…

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Find the dimensions of the rectangle of largest perimeter that can be inscribed inthe ellipse x2/a2…

A: To find the dimensions of the rectangle of largest perimeter that can be inscribed in the…

Q: A long metal sheet with a width of L meters is formed into a gutter by bending up two of its sides…

A: We will use the basic knowledge of 3D solid geometry and applied differential calculus to answer…

Q: Find the maximum value that ƒ(x, y, z) = x2 + 2y - z2 can have on the line of intersection of the…

A: Given and planes are

Q: Determine the points on the surface y2+z2−x=8 that are closer to the origin.

A: Consider the given surface. y2+z2−x=8z2=8−y2+xf(x,y)=8−y2+x

Q: Find the minimum and maximum squared distance between the sphere x² + y² + z² = 9 and the point…

A: We have to find the minimum and maximum squared distances between the sphere x2+y2+z2=9 and the…

Q: Sketch the surfaces PARABOLOIDS AND CONES z = 8 - x2 - y2

A: Consider the equation of the surface, z = 8 - x2 - y2

Q: Find the dimensions of the rectangular box of maximum volume with faces parallel to the coordinate…

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Q: Find the points on the cone z2 = x² + y² that are closest to the point (1,-1,0) %3D

A: Given that, z2=x2+y2 and the point is (1, -1,0). Form the equation of distance as follows.…

Q: A cone-shaped drinking cup is made from a circular pieceof paper of radius  R by cutting out a…

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Q: Find the area of the vertical wall whose base is the semicircle {(x, y) | x² + y² = 1 and y>0} and…

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Q: Find the equation of the sphere of radius 8 centered at (1, 3, 6). O x² + y² +z² = 46 O x² + y² + z²…

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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 dimensions of the rectangle of maximum area that can be inscribed in a circle of radius r =…

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Q: 82. Use Theorem 6.10 to prove that a sphere of radius 5 has surface area 1007.

A: Given ,radius of sphere=5 We know, surface area (S) of a sphere of radius r units is given by:…

Q: Find the maximum volume of a box inscribed in the tetrahedron bounded by the coordinate planes and…

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Q: A surface is called bounded if there exists M > 0 such that everypoint on the surface lies at a…

A: Explanation: The possible Quadric surfaces are Spheres, Ellipsoids, Hyperboloid of one sheet,…

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: The sphere x² + y² +z² = 100 has the center (0,0,0) and a radius of length 50. Select one: True…

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Q: Find the area of the cap cut from the sphere x2 + y2 + z2 = 2 by the cone z = √(x2 + y2).

A: to find the area

Q: The minimum vertical dimension (B) for the junction box shown in the Figure is _______

A: Given vertical dimensions of diodes are  3+2+2(1/2) = 7+(1/2) inches Vertical dimensions can fit…

Q: Find the points on the sphere at which the minimum and maximum distances between the sphere…

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Q: Sketch the surfaces PARABOLOIDS AND CONES x = 4 - 4y2 - z2

A: The given equation is x = 4 - 4y2 - z2

Q: Find the dimensions of a rectangular box of maximum volume such that the sum of the lengths of its…

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Q: a

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Q: A rectangle, R, has length L = 8 and width W = 3. What is the maximum area of the rectangle, Q, that…

A: We need to find maximum area.

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: A closed rectangular box with faces parallel to the coordinate planes has one bottom corner at the…

A: Let x , y, z donate  the length, width and the height of the rectangular box.  Volume of the box is…

Q: An Inscribed rectangle Is bounded by the x - axls and the semicircle y =V25-x2. What length and with…

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Q: Show that the rectangular box of maximum volume that can be inscribed in the sphere x^2 + y^2 + z^2…

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Q: Find the dimensions of the rectangular box of maximum volume that can be inscribed inside the sphere…

A: Given sphere is

Q: Classify the quadric surface ² - y² - x² + 4x = 5. 2 य

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Q: Find the area of on of the triangle that can drawn between the planes 3x – 6y – 2z = 15 - and 2r + y…

A: For any triangle that will lie between two planes, one point has to lie on a plane and the other two…

Q: Use Lagrange multipliers to find the dimensions of a box with volume 1000 cm3 that has minimal…

A: the surface area of the box is  S=2xy+2yz+2xz................(1) the volume of the box is given by…

Q: A farmer with 120 meters of fencing needs to enclose a rectangle area into three equal pens with…

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Q: The quadric surface 2 = x² + is called

A: We know that this is the equation of hyperboloid from the general equation of hyperboloid.

Q: Find and classify (local maximum, local mi points of f(x,y) = x2 - x²y + 2y². Show all supporting…

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Q: A rectangle is inscribed with ts base on the z-axis and its upper comers on the parabola y= 12-r Fre…

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Q: Find the area of on of the triangle that can drawn between the planes 3x – 6y – 2z = 15 and 2r + y -…

A: The equations of the two planes are: 3x-6y-2z=152x+y-2z=5 As, 5,0,0 satisfies the equation of plane…

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

A: The surface cut from the '' nose '' of the paraboloid x=1-y2-z2 by the yz plane .…

Q: What is a flat surface that extends infinitely in all directions?

A: Plane.

Q: What is the surface of the box formed by the net above

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

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Q: Find the point lying on the intersection of the plane x + + z = 0 and the sphere x2 + y2 + z2 = 25…

A: According to the given information, it is required to find a point lying on the intersection of the…

Q: An open rectangle box with volume 2m2 has a square base .express the surface s of the box as a…

A: Please find hand written solution.

Q: 2) Find the area of the part of the surface z = x2 + 2y that lies above the triangle with vertices…

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