62. A rectangular box is inscribed in the region in the first octant bounded above by the plane with x-intercept 6, y-intercept 6, and z-intercept 6. 6. (x, y, z) -y a. Find an equation for the plane. b. Find the dimensions of the box of maximum volume.

Q: 4. Find the volume of the wedge cut from the first octant by the cylinder z = 12 – 3y², and the…

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Q: 13) Find an equation of the plane that is through the point (1.1.2) and makes minimum volume in the…

A: The equation of plane is given as, z-z0=ax-x0+by-y0 The points (1,1,2) is given Now substituting for…

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

A: Let say that(a,b,c) is point in plane 4x+3y+z=12 and it is one vertex of requested rectanglar box.…

Q: Find the volume of the largest rectangular box in the first octant with three faces in the…

A: The given equation of plane is : x+2y+3z=6 x=6-2y-3z                   …(1) Volume of a rectangular…

Q: Find the centroid of the region with the indicated boundaries: The parabola y² = 4x, the Y-axis,…

A: We use the formula  x=MyM=∫abxfx-gxdx∫abfx-gxdxy=MxM=∫ab12fx2-gx2dx∫abfx-gxdx Now, fx=4, gx=4x, a=0,…

Q: Find the volume of the largest rectangular box in the first octant with three faces in the…

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Q: Find the volume of the largest rectangular box in the first octant with three faces in the…

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Q: 4. Find the volume of the wedge cut from the first octant by the cylinder z = 12 - 3y2, and the…

A: We have to find volume.

Q: Find the volumes of the regions. The wedge cut from the cylinder x2 + y2 = 1 by the planes z = -y…

A: Given Data The equation of a cylinder is x2+y2=1. z=-yz=0   Determine the interval of x and y,…

Q: 5. Find the surface area of the portion of the surface z = 2x + y? that is above the triangular…

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Q: 3. Find the volume of the solid that lies between the paraboloid z = x² + y² and the sphere x2 + y²…

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Q: Find the volume of the largest rectangular box in the first octant with three faces in the…

A: We have to find the volume of the largest rectangular box in the first octant with three faces in…

Q: Find the minimum distance from the point to the plane x – y + z = 12. (Hint: To simplify the…

A: According to bartleby guidelines when student ask more than one question the expert should answer…

Q: Describe in words the region in R' represented by the equation x² + y² – 10y + z² + 2z = 0 O A…

A: we have to check the region of the given equation in R^3 is

Q: 10. Find the centroid of the area bounded by the parabolas x 2y and x - 2x - 2y = -5, and y-axis

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Q: Its base is with the y = x ² + 1 parabola, coordinate axes and the line x = 1 When sections…

A: Let R be the given region bounded by y=x2+1, x=1, x=0 and y=0. If S is a solid and suppose that the…

Q: The base of a three-dimensional figure is bound by the line x = -y2-2y +3 on the interval [0, 1].…

A: Option(4) is true

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

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Q: Find the surface area of the portion of the half ball with radius a which cuts off by the cylinder…

A: The equation of a ball with radius a is x2+y2+z2=a2. The surface area of the function z=fx,y over…

Q: Find the area of the region cut from the plane x+4y+8z=9 by the cylinder whose walls are x=y2 and…

A: Given, x+4y+8z=9 x=y² x=18−y² Therefore, The surface is  f=0 with f= x+4y+8z-9

Q: Find the area of the surface of the part of the cylinder ? + 2² = 4 that lies above the square in…

A: For the given part of the cylinder  x2+z2 =4  which lies above the x-y plane at the vertices…

Q: 3. Find the centroid of the region bounded by the parabola y? = 4x, the y-axis, and the line y = 4.

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Q: Determine the relative dimensions of a rectangular box without a lid and with a volume of 36u ^ 3 if…

A: To find- Determine the relative dimensions of a rectangular box without a lid and with a volume of…

Q: What is the center of gravity of the region bounded by the graphs of equations y = x2 -2x+1, y =…

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Q: A rectangular box has three of its faces on the coordinate planes and one vertex in the first octant…

A: Given,The box's volume is  V = xyz  but we know that   z = 4 − x2 − y2V = xyz    = xy ( 4 − x2 − y2…

Q: Compute for the volume of the solid formed bounded by the equations (y- 4)2 = x - 3, x-10, y-4, and…

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Q: A box, used to package men's shirts, is in the shape of a square-based prism and its to have a…

A: Given Data: The volume of the square-based prism is: V=8400 cm3 The equation of surface area is:…

Q: Find the centroid of the region bounded by the graphs of the inequalities

A: Given information: y≤14x2          ...(1)x-42+y2≤16              ...(2)y≥0                ...(3)

Q: What is the solid formed when the area bounded by

A: Given: 2x+y=2 The  coordinate axis is revolved about the y axis. To find: What is the solid form.

Q: Find the area of the region cut from the plane x + 2y + 2z = 5 by the cylinder whose walls are x =…

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Q: Find the volume of the largest rectangular box in the first octant with three faces in the…

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Q: 2. Find the centroid of the region bounded by the parabola y=x² and the line y=4.

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Q: Calculate the volume of the rotating object that occurs if the area in the first quadrant is bounded…

A: Calculate the volume of the rotating object that occurs if the area in the first quadrant is bounded…

Q: 6. Show that when a hole of radius a is bored through the center of the sphere of radius b, the…

A: Given: The radius of the sphere is b. The radius of the hole is a. We have to show that the volume…

Q: 1. Find the surface area of the part of the sphere x+ y +z = 4 that lies above the plane z =1.

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Q: 3. Find the volume of the tetrahedron in the first octant bounded by the coordinate planes and the…

A: Given

Q: Find the area of the part of the sphere x2 + y2 + z2 = a2 that lies inside the cylinder x2 + y2 =…

A: answer is A = a2(π -2) detailed solution with explanation is given below

Q: (A) Find the surface area of the portion of the half ball with radius a which cuts off by the…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the volume of the largest rectangular box in the first octant with three faces in the…

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Q: 13- Find the volume V of tetrahedron bounded by the coordinates planes and the plane z = 6 - 2x + 3y

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: 7. Find the area of the portion of the plane z = 2 y that lies directly above the circle x+(y-1) =1…

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Q: \ Use optimization to find the maximum volume of a box with one corner at the origin and the…

A: Assume, V be the volume function representing the volume of the box. l, b, h be the dimensions of…

Q: The volume of the solid generated when the region at the first quadrant bounded by the curve y = x²…

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Q: 9) Find the center of mass of the plate of uniform thickness and density formed by the curves:…

A: To find the solution

Q: The area in the first quadrant bounded by a parabola 12y = x2, the y=axis, and the line y = 3,…

A: Given:       Parabola x2=12y                      y=x212              line y=3 The parabola and line…

Q: 7. Find the area of the portion of the plane z = 2y that lies directly above the circle x +(y-1)² =1…

A: we have to find area of the portion of plane .and coverting the problem in polar coordinate makes it…

Q: A cylindrical shampoo container is to have volume 750 cm³. Shampoo V%3DTT r?h 759cm3 ) Determine the…

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