Determine t he volume of t he largest rectangular box in the first octant with three faces in the coor dinate planes, one vertex at the origin, and its opposite vertex in the plane r+3y+6z = 36.

Q: Find the point on the plane 5x + 4y + z = 11 that is nearest the origin. What are the values of x,…

A: First we find the distance(d) between a point (x,y,z) on the plane and the origin .Then form a…

Q: Q6) Find the area of the portion of the cylinder x2 + y2 = 6y that inside the %3D sphere x² + y? +z²…

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Q: i Which of the following regions are simply-connected? a) the half-plane lying above the x-axis b)…

A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Aforce F: 2i+j-3K is applied to a space craft with Velocig V. 3L-J- Express FasThe Sum of aretor…

A: F = 2 i + j - 3k,v = 3 i -j

Q: Q5/ Find the volume of the Tetrahedron that is determined by three edge vectors â = [1, 0.-3), 5=…

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Q: O Find the equ.of Plane that contains p(o,3) and Parallel co the X-2 Plane and PerPendicular to the…

A: We have to find equation of plane with given conditions.

Q: Use Lagrange multipliers to find the volume of the largest rectangular box in the first oc- tant…

A: We need to find volume.

Q: Find whether the planes below intersect, and if so, where they intersect using Gaussian elimination.…

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Q: Q2. Find the volume of the sphere x² + y +z = a (In Cartesian coordinate system). %3D

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Q: Find c > 0 c > 0 such that the area of the region enclosed by the parabolas y = x 2 − c 2 y = x 2 -…

A: To find the value of c given area between the curves.

Q: 1.Find the area of the triangle in the xy-plane with vertices A(n,,n2, n2),B(m,,m2,m3),C(r,,r2, 13).

A: Please see the explanation below

Q: Find the dimensions of the largest rectangular box in the first octant (x, y, z > 0) with one corner…

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Q: 14. Find the volume of the parallelepiped having i + 3j + 2k, 2i + j- k and i- 2j + k be the edges.…

A: The edges of the parallelopiped is given to be a=i+3j+2k, b=2i+j-k, c=i-2j+k. To find the volume.…

Q: • Find the area of the portion of the Sphere x² + y² + 2²² = 9 between the planes Z=1 and 2 = 0.…

A: The given equation of  plane is x2+y2+z2=9. The polar coordinates are x=rcosθ & y=rsinθ. The…

Q: V Z the tetrahedron cut off from the first octant by the plane 6 2

A: NOTE: Refresh your page if you can't see any equations. . the limit of z is

Q: Find the area of the surfaces The portion of the cone z = √x2 + y2 that lies over the regionbetween…

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Q: WY bisects ZXWZ and ZXYZ. Complete the proof that AWXY E AWZY. Y. W

A: Given that WY bisects ∠XWZ and ∠XYZ. We know that when a line bisects an angle, it means it divide…

Q: Q.5. Let a, a₂? and b 3. For what values of his b in the plane spanned by a, and

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Q: Use Lagrange multipliers to find the volume of the largest rectangular box in the first octant with…

A: To find the value when the volume is the greatest possible value under the given constraints

Q: Find the surface area of the portion of the sphere x2 + y2 + z2 = 25 inside the cylinder x2 + y2 =…

A: Recall:  The formula of surface area is S=∫∫S1+∂z∂x2+∂z∂y2 dA

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

A: Given, equation of the plane is  7x + 6y + 2z = 18 => 2z = 18 - 6y - 7x Therefore, z = ( 1/2)(18…

Q: Find the area of the surface. The portion of the sphere  x2 + y2 + z2 = 100  inside the cylinder…

A: To find the area of surface

Q: The solid enclosed by the sphere x² +y² +z? = 4a* and the planes z = O and z = a.

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Q: Z • W Y. T. U. 10. What is the intersection of the two planes? 11. Are points T, Z, U, and W…

A: To answer the given questions using the given figure.

Q: Find the volume of the prism whase base is the triangle in te Xy-plane bonnded by the X-axis and the…

A: To find- Find the volume of the prism whose base is the triangle in the xy-plane bounded by the…

Q: Q6/ Find the volume of the parallclogram-sided determined by: u- -3i +7j +5k, v -3i + 7j-3k, and w-…

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Q: Find the distance between the parallel planes – 2z + y + : = 0 and 10z – 5y – 52 – 36 = 0. NOTE:…

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Q: Find the trace of the plane 9x – 9y + 11z = 5 in the coordinate xz-plane. (Use symbolic notation and…

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Q: 14. How many points P(x,y) on a Cartesian plane satisfy the following conditions? A. One. B. Two. C.…

A: We have to find no. of points that will satisfie the given conditions.

Q: Use Lagrange multipliers to find the volume of the largest rectangular box in the first octant with…

A:

Q: Thevolume of the body is given by The touwo surfaces Z=8-3 (x44) 2.

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Q: The olid lies betcween planes perpendicular 4o the X=axis at x=0 and X=7,The Cross sections…

A: Concept -we have a given two plane and perpendicular to x axis from x=0 to x=7 , We have to find…

Q: SSx x dA; R is the portion of the disk x +y s 16 in the second quadrart

A: According to the given information, it is required to find the value of the given integral.

Q: Find the center C and the radius r of the sphere S: x2 + y2 + z2 + 4x + 8y – 8z =-11

A: A geometrical object which is in the shape of ball is called sphere. Outer surface of sphere is…

Q: XydA, D is the triangular region with Vertices (0,0), Cu,0], and Cor) SketchD onthe XY planel

A: 8/3

Q: lo. find a point in the plane x+2y+3z=13 nearest to the point (1,1) usung the methed of Lagrange's…

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Q: H.W: Find volume of box (parallelepiped) determined by u = i+ j- 2k , v = -i -k and w 2i + 4j - 2k…

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Q: 4) The solid lies between planes perpendicular to the x-axis at x = 0 and x = 6. The cross sections…

A: Given: y=-5x  to the parabola y=5xAs we can see in the diagram is given below.

Q: Use Lagrange multipliers to find the volume of the largest rectangular box in the first octant with…

A: Given,  Plane x + 3y + 4z = 9

Q: III. Consider the parabola C: 2 - 4 = -(x - 2)² on the xz-plane. 2. Sketch the portion of the…

A: Given,  Parabola :C: z-4=-(x-2)2 on xz-plane We have to draw or sketch the portion of cylinder…

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

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Q: Two art Students are cstsed to create avase Using the snape shown below as a ad basis. One decidea…

A: The surface area using the pappus theorem is A=2πR·L. Here, R is the distance of the axis of…

Q: 4 2 + Find the area of the portion of the Sphere x² + y² +2²= 9 between the planes Z=1 and 2 = 0.…

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Q: Find the area of the surface. The portion of the paraboloid z = 16 - x - y in the first octant

A: The given surface is the portion of the paraboloid z=16-x2-y2 in the first octant. The surface area…

Q: Let T be the tetrahedron with vertices (5, 0, 0), (0, 2, 0), (0, 0, 5) and the origin. Write II|…

A: Given T is a tetrahedron with vertices (5,0,0) , (0,2,0), (0,0,5) and  (0,0,0)…

Q: Find the area of the surface. 12. The part of the sphere x2 + y2 + z2 = 4z that lies inside the…

A: Solution:GivenSphere:   x2+y2+z2=4zParaboloid: z=x2+y2To find the area of the…

Q: SSx x dA; R is the portion of the disk x + ys 16 in the second quadrart

A: I use polar conversion method

Q: 1. Determine the value of a so that A= 2i +aj +k and B= 4i-2j-2k are perpendicular a. 1 unit b. 2…

A: 1. Determine the value of a so that A= 2i +aj +k and B= 4i-2j-2k are perpendicular. We have, A= 2i…

Q: Determine whether the planes are parallel, perpendicular, or neither. (a) P1:2r - 3y – 8z – 2 = 0…

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