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Q: Use Lagrange multipliers to find the minimum distance from the curve or surface to the indicated…

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Q: Use Lagrange multipliers to find the minimum distance from the curve or surface to the indicated…

A: To find the minimum distance from the given curve to the point using Lagrange multipliers method.…

Q: If ƒx(a, b) = ƒy(a, b) = 0, does it follow that ƒ has a local maximum or local minimum at (a, b)?…

A: To determine: Whether the function f follows that it has a local maximum or local minimum at a point…

Q: 5. What is the maximum vertical distance between the line y = x + 2 and the parabola y = x² for – 1…

A: The given equations are, y = x + 2       ....(1)  y = x2            ....(2) To find the maximum…

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: 3. A piece of wire 36 in. is cut into two parts, one of which is bent into the shape of an…

A:

Q: Consider the following problem: A farmer with 750 ft offencing wants to enclose a rectangular area…

A: Given, The farmer have 750 ft of fencing.

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

A:

Q: What is the maximum vertical distance between the line y = x + 51 and the parabola y= x² over the…

A: Given: The line y=x+51 and the parabola y=x2 To find: Maximum vertical distance between given line…

Q: Find the absolute maximum of f(x,y) = 6x²y² + 4y2 + 4x2 bounded by y = x, y = 0 and x = 2. %3D

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Q: find the point on the line y=2x+10 that is closest to the orgin, (0,0) What is the minimum distance?

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Q: What is the maximum vertical distance between the line y = x + 2 and the parabola y = x2 for −1 ≤ x…

A: Consider the given line

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: (c) cut from each corner of length x cm, a maximum volume for the resulting open-top cake tin will…

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Q: What is the shortest distance from the surface xy + 15x + z2 = 204 to the origin? distance =

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Q: Full working plz, Thank you.

A: Suppose, I is the real image of an object O and let d be distance between the image and the…

Q: What is the shortest distance from the surface ry + 15x + z2 = 204 to the origin? distance =…

A:

Q: ` What is the shortest distance from the surface xy + 9x + z² = 76 to the origin? distance =

A: z2+9x+xy=76z2=76-9x-xy   ---- Eq 1Let P(x,y,z) be a point on the given surface. We know that…

Q: Find a cubic tunchion feo=ax34 bx'textd that has a local maximum valve of 3 at X=-2 and a local…

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Q: Let g(x, y) = 3x²y + y³ - 27y

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Q: Find the minimum distance from the parabola x – y = 0 to the point (0, 3). Minimum distance = %3!

A: At P(x,y), the point of shortest distance the slope of the line from P to (0,3) must be…

Q: All boxes with a square​ base, an open​ top, and a volume of 200ft^3 have a surface area given by…

A: We differentiate S(x) with respect to x. S(x)=x2+800xS(x)=x2+800x-1S(x)=2x-800x-2S'(x)=2x-800x2

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: What is the minimum vertical distance between the parabolas y = x² + x en y = x – x²?

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Q: A manufacturer wants to design a rectangular box with a square base and an open top. (In other…

A: Let  side of square = x  height of box = y    surface area = area of base + 4 * area of side face…

Q: Find the minimum distance from the point (6, 1, 6) to the plane x - y + z = 6. (Hint: To simplify…

A: To find the minimum distance from the point (6,1,6) to plane x - y + z = 6. By using formula,…

Q: Find the point on the parabola y = x^2 closest to the point (−3, 0)? and give the minimal distance?

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Q: A rectangle has one corner at the point (0,0), a second corner on the posit below. What is the…

A: Let the length of the rectangle be "y" and breadth be "x". The expression for the area of the…

Q: Find the minimum distance from the parabola x − y2 = 0 to the point (0,3) Minimum distance =

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Q: Two factories are located at the coordinates (-x, 0) and (x, 0), and their power supply is at (0,…

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Q: Find the minimum distance from the point (6, 0, 5) to the plane x - y + z = 3. (Hint: To simplify…

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Q: Use calculus to show that the maximum possible area of a triangle with one vertex at (0, 0) and the…

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Q: Find the altitude of a rectangular close box with volume 100 with length twice the width so that the…

A: We can find the altitude of the box by using the second derivative test.

Q: A tube of lip balm has a height of 2.75 inches and a diameter of 0.75inches.  a. if the cap on the…

A: Part (a):Diameter of the lip balm tube, d = 0.75 inches. Thus, the radius of the tube is r = d/2 =…

Q: Find the local minimum ond local moximunm Cit exists) for the funetion fex,ys = 2x? + y? + 8x -by…

A: We have to find the local maximum and local minimum of the functionf(x,y)=2x2+y2+8x-6x+20 we denote,…

Q: What is the shortest distance from the surface xy + 6x + z² = 48 to the origin? distance =|

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Q: A farmer with 120 meters of fencing needs to enclose a rectangle area into three equal pens with…

A:

Q: A piece of wire 10 m long is cut into two pieces. One pieceis bent into a square and the other is…

A: To find: The way to use the wire such that the area enclosed by the triangle and square would be…

Q: Abox of volume 60m3 with a squan botHom and no top IS constructd out of 2 diffennt materi als. The…

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Q: Let R be a rectangle with sides measuring x > 0 and y > 0 and perimeter equal to 14. What is the…

A: x = length of rectangle R ; x>0y = width of rectangle R; y>0A = Area of RA = xy…

Q: If f(x, y) is continuous, then it must have an absolute maximum in the region x? + y² < 1. True…

A: Given: f(x,y) is continuous Region R is an open circle centre at origin and radius 1 ie x2+y2 &lt; 1…

Q: Find the rectangle of the maximum area that can be inscribed in a right triangle with legs of length…

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Q: 4. Four identical bricks are stacked up on top of each other. Each has a length of a and a mass of…

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Q: What is the maximum vertical distance between the line y = x + 29 and the parabola y = x² over the…

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Q: 3. Car B is 100 miles directly east of car A and begins moving north at 50 miles per hour. At the…

A: Solve the given problem

Q: What is the maximum vertical distance between the line y = x + 38 and the parabola y = interval [–…

A: Given line equation is y=x+38 Given parabola equation is y=x2 From the above two equations x2-x-38=0…

Q: Find the minimum distance from the cone z= to the point (6, 6, 0).

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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…