I want to solve this questionQ) Use Lagrange multiplier to find the largest product of three positive numberx,y,z can be if x+y^2 +z^2 =16

Q: Use Lagrange multipliers to find the distance from the point (3, 0, -1) to the plane 6x - 4y + 7z +…

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Q: An open top box is to be made from 48 m of wood with dimensions x, y and z as shown in figure. Using…

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Q: The center and radius of 4x2 +24x + 36 + 4y?-8y 100 is O Center: (3,-1); radius = 26 %3D O Center:…

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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: Use Lagrange multipliers to find the highest point on the curve of intersection of the surfaces.…

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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: 4.x² + y = 4

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Q: Find the minimum distance from the point (8, 3, 4) to the plane x - y + z = 4. (Hint: To simplify…

A: Let ax+by+cz+d=0 is a plane  Then distance from the  a point (xo,yo,zo) is D= |axo +byo +czo…

Q: Find the maximum volume of a rectangular box with faces parallel to the coordinate planes if one…

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Q: Use Lagrange multipliers to find the dimensions of the box with volume 216 cm3 that has minimal…

A: According to the given information, it is required to use Lagrange multiplier to find the dimension…

Q: As a hardworking student, plagued by too much homework, you spend all night doing math homework. By…

A: First we consider the volume of small disk and integrate this across the given region to get the…

Q: Bounded by the coordinate planes and the plane 3x + 2y + z = 6

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Q: Use Lagrange multipliers to find the dimensions of the box with volume 216 cm3 that has minimal…

A: Given: The volume of the box is 216cm3 . Calculation: Let the dimensions be x, y and z. The volume…

Q: SET UP the necessary equations to find the point on the intersection of the surfaces x2 + 4y2 + 4z2…

A: The solution are next step

Q: Find the distance between the planes x + 3y – 2z = 3 and 2x - y - z = 4. %3D

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Q: Show that the sum of the squares of the distances from a pointP = (c, d) to n fixed points (a1, b1),…

A: Here, the objective is to show that the sum of the squares of the distances from a point P = (c, d)…

Q: Hex reasoned that a moving point traces out a line segment, and that a line segment moving parallel…

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Q: Differentiate, and make sure to show all your work: y = exin(2z) %3D

A: The given question is taken from the derivative of the function in which we have to find the…

Q: The point on the plane 2x+y+z=1 that is closest to the point (1, 2, 3) is (a, b, c). Then a+b-2c= O…

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Q: find a formula for the area of triangle in the xy-plane with vertices at (0,0), (a1,a2) and (b1,b2).…

A: To find a formula for the area of triangle in thexy-plane with vertices at (0,0), (a1,a2) and…

Q: A rectangular pen is built with one side against a bam. # 200 mof fencing are used for the other…

A: Given: A rectangular pen is built with one side against a barn.

Q: Use the method of Lagrange Multipliers to find the dimensions of the rectangle of maximum area with…

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Q: 2 b) Prove that Imz=0, larg z - 41= 4, 2-ž =0, 1Z-il=1Ztil are different equations all describing…

A: If we let z=x+iy then We will show that y=0 which is the equation of real axis.

Q: 2. Find a unitvedctor with positive z-component porpendcular to the plane 2xt2y-2=3 Z-C

A: We will find out the required value.

Q: find the engle of intersection between 2x - 4y + 4z = 7 and 6x + 2y – 3z = 2 .

A: Consider the given planes: 2x-4y+4z=7So,n1→=2,-4,46x+2y-3z=2So,n2→=6,2,-3

Q: 24) By using Lagrange multiplier find a point in the plane x+2y+3z=13 nearest to the point (1,1,1)

A: We have to find a point in the plane x+2y+3z=13 nearest to the point 1,1,1 by using Lagrange…

Q: wz bisects 2XZY and 2X = ZY . Which choice of method can be used to prove AXWZ = 4YWZ ?

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Q: 4. Use the method of Lagrange Multipliers to find the point on the plane r+y- 2 = 5 that is closest…

A: Given: The plane equation is x+y-z=5 and the point is -3, 5, 4.

Q: 8 A rectangulaer garden with an area of 30m is Surrounded by a grass border Im wide on two Sides and…

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Q: For this exercise we will use the fact (see Exercise 32 in Section'6.5) that the moments of a…

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Q: Find the minimum distance from the point (8, 3, 4) to the plane x - y + z = 4. (Hint: To simplify…

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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: 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: Use Lagrange multipliers to find the dimensions of the right circular cylinder with maximum volume…

A: To determine the dimension of the right cylinder, let r be the radius of the base of the cylinder…

Q: Find the minimum distance from the point (0,0,0) to the plane 9x+4y+z=5.

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Q: Compute the intersections of the curve xy = 1 and the lines x +y = 5/2, x+y = 2, x+y = 0, x=0 , x=1…

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

Q: An open top box is to be made from 48 m of wood with dimensions x, y and z as shown in figure. Using…

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

Q: Consider a rectangle of sides x and y with fixed perimeter of 40 units. Find the maximum and minimum…

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Q: Find the volume of the parallelepiped whose edges are represented by: A=2i-3j+4k , B=i+2j-k and C=…

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Q: 2. A right circular cylindrical container with volume 167 cm³ is to be made. Use the method of…

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Q: Find the families of characteristics of the PDE (1-x²)w„ - u,, = 0 in the elliptic and hyperbolic…

A: Pde

Q: As a hardworking student, plagued by too much homework, you spend all night doing math homework. By…

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Q: As a hardworking student, plagued by too much homework, you spend all night doing math homework. By…

A: Given: The region bounded by y=2x2, x=0, x=2 and y=0.

Q: nospital of ground and three rants are to be provided. The Iis (300 * 30O) m. Find numb fire…

A: Please refer to the image below

Q: Use Lagrange multipliers to find the dimensions of the right circular cylinder with maximum volume…

A: Given that  a right circular cylinder with surface area = 24π square unit.   As volume is to be…

Q: A right circular cylindrical container with volume 167 cm³ is to be made. Use the method of Lagrange…

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.