Thermal nuclear reactor is subject to the constraint P(a,b,c) = 2m B, a constant. Find the ratios of the sides of the %3D rectangular parallelepiped reactor of minimum volume.

Q: Use Lagrange multipliers to find the maximum and minimum values of f(x,y)=2x−4y subject to the…

A: Given a function : f(x,y)=2x-4y subject to the constraint (say g(x, y)) : x2+3y2=84 We have to use…

Q: Find the maximum values of f(x,y) = 81x² + y² subject to the constraint 4x? +y² = 1 (Use the…

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Q: Find the maximum value of r + y subject to the constraint a2 + y? = 18.

A: The function is given by fx, y = x+y                                          ..........1 The…

Q: Use Lagrange multipliers to find the maximum area of a rectangle inscribed in the ellipse x2 y2 + =…

A: According to the given information, it is required to find the maximum area of rectangle that is…

Q: Use Lagrange multipliers to find the maximum and minimum values of f(z, y) = 4r² + y² subject the…

A: Given,           f(x,y) = 4x3 + y2  -1           Constraint : 2x2+y2=1 -2

Q: vertex of parabola : (-2,1)= (h,k) x=a(y-k)²+h ✓ (-1.5, -2.3) (j,4.2)

A: Given Vertex of parabola h, k=-2, 1 Equation of parabola x=ay-k2+h Points of intersection of line…

Q: A natural gas company is laying an underground natural gas pipeline in a new subdivision on both…

A: Solution: Let cost for laying underground = P      cost for laying underwater = 2P

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Q: Find the minimum value of f(x,Y)=34x2+25y2 subject to the constraint x2+y2=196 %3D

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Q: Find the minimum value of f(x,y)=66x2+9y2 subject to the constraint x2+y2-784

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Q: 18. A) Complete the square for y = 2x² − 12x – 14 B) Determine the coordinates of the vertex. Is it…

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Q: Rae plans to build a rectangular pig pen against one of the walls of her barn. If she has 18 meters…

A: let l be the lengthlet w be the widthThen l+2w=18⇒l=18-2wLet Area of the rectangular pig pen be…

Q: Find the maximum and minimum values of the given quadratic form, 2x + 6y? subject to the constraint…

A: To find the maximum and minimum values of fx,y=2x2+6y2…1 subject to the constraint x2+y2=1.…

Q: Find the relative extrema using lagrange multipliers. F(x,y) = 16x0.70.3 Constraint: 2x+ y = 25

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Q: about 12 ounces of fruit juice requires a volume of 113 cubic inches for its packaging. How  should…

A: Question : About 12 ounces of fruit juice requires a volume of 113 cubic inches for its packaging.…

Q: 4. What is the axis of symmetry of the parabola y = x = 7 x= -14 y = 28 Ox=28 O x²14x+28?

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Q: Find maximum and minumum values of f(x, y, z) = 8x – 16y + 40z subject to the constraint x? + y? +…

A: The given function is; f(x,y,z) = 8x-16y+40z

Q: Use Lagrange multipliers to find the minimum value of f(x,y) x2 – y? subject to the constraint 2y –…

A: According to question, fx, y = x2 -y2,subject to the constraint 2y-x2 = 0,let gx, y = 2y-x2

Q: Use Lagrange multipliers to find the maximum and minimum values of f(x, y) = 4x – 3y subject to the…

A: Recall: Method of Lagrange Multipliers :1.)Solve the system of equations                ∇f(x,y)…

Q: Find maximum and minumum values of f(x, y, z) = 2 - 4y + 10z subject to the constraint a? + y? + z?…

A: If f is our function and g is the constraint. We can use Lagrange multiplier, c to equate the first…

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Q: An open top rectangular tank with square bases is to have a volume of 10 cubic meters. The material…

A: To find out the most economical height.

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Q: A triangle has variable sides x, y, z subject to the constraint such that the perimeter P is fixed…

A: As per given question  We have to determine the maximum possible area for the triangle

Q: The maximum value of f(x, y) subject to the constraint g(x, y) = 280 is 5500. The method of Lagrange…

A: Consider the given information:

Q: . Find the minimum value of C = 3x + 5y subject to %3D 4x +3y > 240 4x + y > 120 y > 0

A: 4x+3y≥240 divide both sides by 240 4x240+3y240≥240240 x60+y80≥1 compare this equation with the…

Q: The temperature of a planetť's atmosphere is a function of altitude relative to the mesosphere, a,…

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Q: Find the two values of c such that the area of the region enclosed by the parabolas y = x² – c² and…

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Q: Use Lagrange multipliers to find the maximum and minimum values of f(x, y) = 2x + 7y, subject to the…

A: Use La Grange method

Q: bétween the spheres and 2- + Y 4 if the dênsity at any point is equal to the square of its distance…

A: Given: The solid lies above the cone 3z=x2+y2 and between the sphere x2+y2+z2=1 and  x2+y2+z2=4  The…

Q: Use the method of Lagrange multipliers to find the maximum and minimum values of the function…

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Q: Find maximum and minumum values of f(x, y, z) = 7x – 14y + 35z subject to the constraint x? + y? +…

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Q: Find the minimum value of f(x,y)=48x²+30y2 subject to the constraint x2+y2=361 %3D

A: Given that fx,y=48x2+30y2 Let, gx,y=x2+y2 Then, fx=96xfy=60ygx=2xgy=2y

Q: A triangle has variable size x.y.z subject to the constraint such that the perimeter is fixed to…

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Q: Maximize z= 14x, +3x,

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Q: Use the method of Lagrange multipliers to find the maximum and minimum values of f(x, y) = 5xy…

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Q: Find the minimum distance from the point (4, 2) to the parabola y2 = 8x. A 4/3 B) 2/7 © V3 D 2/3

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Q: Use Lagrange multipliers to find the maximum and minimum values of f(x, y) = 4x – 2y subject to the…

A: Use Lagrange multiplier to find the maximum and minimum values of f(x, y) = 4x - 2y subject to the…

Q: Use Lagrange multipliers values exist. to find the maximum and minimum values of f(r,y). 4x 3y…

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Q: In "Blingblong Takes the World", a famous online role-playing game, the titular character's total…

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Q: find the ends of the latus rectum, axis of symmetry of x2+20y=0

A: Given  x2+20y=0 Find the ends of lactus rectum and axis of symmetry.

Q: N-N-OUT manufacturer of food-storage containers makes cylindrical can with a volume of 500…

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Q: A rectangular field is to have an area of 900 sq. m. This is to be enclosed and divided into three…

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Q: The are of a rectangle is 100 cm2 and one of its sides is x cm. Find the minimum perimeter possible.

A: Let us consider a rectangle with length l unit, breadth b unit Then area of this rectangle= lb…

Q: Find the points on the ellipse x2/25 + y2/100 = 1 that are furthest away from the point (2,0).…

A: The given equation of the ellipse is:x225+y2100=1which can be written as4x2+y2=100⇒y2=100-4x2…

Q: A rectangular field is to have an area of 900 sq. m. This is to be enclosed and divided into three…

A: Let's find.

Q: Find the minimum value of f(x,y)=48x2+30y2 subject to the constraint x2+y23D361

A: Since you have asked multiple questions in a single request we would be answering only the first…