Q2. Use the Method of Lagrange Multipliers to find the dimensions of the closed right circular cylindrical can whose volume is 16n ft' and having smallest surface area.

Q: 2. For the same problem, use Lagrange multipliers to maximize the volume V ryz under the constraint…

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Q: 4. Find the area of the plane region that lies below the line y = 2x and between the parabolas y =…

A: The area between two curves y=f(x) and y=g(x) within the x-limits x=a to x=b is given by:…

Q: Find the point on the planez = x + y + 1closest to the point P = (1, 0, 0). Hint: Minimize the…

A: Let Q(x,y,z) be the point closest to the point P. Let D be the distance between these two points.…

Q: Using Lagrange multiplier, find the minimum value of f(x,y) = 3x +ly on the circle x2 + y2 = 1. Give…

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Q: Use the method of Lagrange multipliers to find the minimum distance from the origin (0, 0) to the…

A: We need to use the method of Lagrange's multiplier to determine the minimum distance from the point:…

Q: Draw the given optimization problem and solve. Find the dimensions of the closed cylinder volume…

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Q: Help with #4

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Q: The temperature in degrees centigrade (°C) at each point (x, y) on a curve 2x + y = 3 is given by…

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Q: Luke `needs to build a shed to store his family's moisture vaporators. The shed must have a volume…

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Q: A silo (base not included) is to be constructed in the form of a cylinder surmounted by a…

A: Calculate the curved surface area of hemisphere and cylinder.

Q: Find minimum distance from the surface x² – y? – z² = 1 (Lagrange Multipliers) to the origin.

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Q: The surface of many airfoils can be described with an equation of the form Thickness max y = =…

A: As per the question we are given the general form of the equation y = f(x) of the surface of a…

Q: We must build a cylindrical tank of 1000 m3 so the two ends are hemispheres.If the material used for…

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Q: Find the minimum distance from the point (6, 0, 9) to the plane x – y + z = 5. (Hint: To simplify…

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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: 4. By revolving the semicircle x = cost, y = sint (0 <t< ) about the x-axis, show that the surface…

A: Equation of semicircle with radius r is x=rcost, y=rsint We know the formula for surface area for…

Q: 2. Use the method of Lagrange multipliers to show that for x, y ≥ 0, we have z"+"> (²+)" 2

A: Introduction: For minimizing a multi-variable function under some certain constraint or constraints,…

Q: Consider a circle of radius 2 centered at the origin. Use the Lagrange multiplier method to find the…

A: It is given that circle is of radius 2 and centered at origin. The function isfx,y=3x-y+5.

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: 2. For the same problem, use Lagrange multipliers to maximize the volume V = xyz under the…

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Q: An inner-city revitalization zone is a rectangle that is twice as long as it is wide. The width of…

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Q: · What is the shortest distance from the surface xy + 6x + z = 41 to the origin? distance =

A: The surface is given as , xy+6x+z2=41 find the shortest distance from the surface to the origin.

Q: The area bounded by the parabolas (x − 2)^2 − 9py=0 and y^2=9p(x−2) is to be revolved around x = 2.…

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Q: Find the minimum distance from the point to the plane x - y + z = 6. (Hint: To simplify the…

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Q: 5. What is the maximum vertical distance between the line v1+2 and the parabolh v for

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Q: A cylindrical orange juice container has metal bases of radius length 1 in. and a cardboard lateral…

A: The radius of metal bases = 1 in. The height of cylindrical container = 3 in. So the total area of 2…

Q: You need to construct a cylindrical container with a circular base and no top, having a total…

A: Given Total surface area with no top =27π square inches Radius is r and height is h. We have to find…

Q: Find the minimum values of the function (x, y) = x² + 2y² that lic on the cirele x² + y² =1

A: Given : Function fx,y = x2 + 2y2  Circle x2 + y2 = 1   To find : Minimum values of the given…

Q: Given a cylinder with radius r cm and height h cm has a fixed surface 270n cm². Find the maximum…

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Q: find the maximum value that f(x, y, z) = x^2 + 2y - z^2 can have on the line of intersection of the…

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Q: The temperature of points on an elliptical plate r +y´ + xy <l is given by T(1,y) = 10( + y°). Use…

A: From Lagrange's multiplier, ∂T∂x=λ∂g∂x⇒20x=λ(2x+y)   ............(1)∂T∂y=λ∂g∂y⇒20y=λ(2y+x)…

Q: Find minimum perpendecular distance between given paraboles. y = x2 + 1 y = x - x2

A: To find the minimum distance between 2 parabolas

Q: . Use the method of Lagrange multipliers to show that for x, y > 0, we have a" +y" > (팔1)" 2

A: We will first try to minimise (xn + yn)/2 using Lagrange multipliers then show that its minimum…

Q: What should the dimensions of the box be in order to minimize the surface area?

A: Let,Breadth of the box = b = xLength of the box = l = 2b = 2x        (according to question)Height…

Q: Determine the shortest distance from the surface xy+3x+z2=12 to the origin.

A: Given surface equation is

Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and y =…

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Q: As a petrochemical engineer, you are required to design a conical container (without a cover) to…

A: The shape of the container is conical, so, the surface area of the container will be S=πrr2+h2,…

Q: What is the shortest distance from the surface xy+3x+z^2=12 to the origin?

A: Let (x ,y, z) any point on surface. We have to minimize function f(x,y,z) = x2 + y2 + z2 under…

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

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Q: Solve the following maxima and minima problems: A silo consists of a right circular cylinder…

A: When we place right circular cone on top of a cylinder, the curved surface…

Q: A company is constructing an open-top square- based rectangular tank that will have a volume of…

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Q: A manufacturer needs to make a cylindrical can that uses 100 square centimeters of material.…

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Q: 2. Noemi had a 3 × 5 ft² piece of plyboard. She needs to have it cut it into a parabolic shape that…

A: The plyboard has dimensions 3×5 ft2 So, the area of the board is 15 ft2 The area of the shape needed…

Q: In a chemical plant, it is required to construct a cylindrical container (without a cover at the…

A: Note: Surface area of a cylinder without cover at the top is S= πdh + (π/4)d2 Where h is the height…

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

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Q: - You are designing a 1000 cm³ right circular cylindrical can whose manufacture will take waste into…

A: Given that the volume of the right circular cylinder is V=1000 cm3 We know that the volume of the…

Q: 4 Determine the surface area of a funnel that is generated by revolving the graph of 1 y = f(x) =…

A: Given  y=fx=x3+112xand interval 1,2

Q: Use Lagrange multipliers to find the minimum distance from the curve or surface Line: x − y = 4 to…

A: To Find: Use Lagrange multipliers to find the minimum distance from the curve or surfaceLine : x-y=4…