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

Q: Identify and sketch the surfaces x2 + y2 - z2 = 4

A: Given, The surface is x2 + y2 - z2 = 4

Q: What is the shortest distance from the curve x^2+xy+y^2=16 to the origin?

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Q: Find the area of the surface formed by revolving the portion in the first quadrant of the graph of…

A: Rearrange the given equation to find y in terms of x and thus f(x). Plot the curve and find the…

Q: Find the points on the surface y2 36 + xz that are closest to the origin. (х, у, 2) (smaller…

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Q: 2 The length of the curve y = 312 between x = 0 and x = 1 is 3 %3D %3D

A: Answer is 4√2/3 unit.

Q: Find the minimum distance from the point (3, 0) to the circle x2 + y2 = 4.

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Q: What is the length of the latus rectum of the curve x2=-12

A: Answer

Q: 6. Find the area of the surface generated when y = v4x + 6 is revolved about the x- axis on the…

A: 80π

Q: Find the minimum distance from the point to the surface z = √4 - 2x - 2y. (-2, -2, 0)

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

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Q: 3. For curve y ==x +4x2 - 12x , locate the possible maximum and minimum %3D points.

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Q: What is the total length of the curve of intersection of the surfaces x2 + y2 + z2 = 4 and y2 + 2z2…

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Q: Find the area of ​​the rotating surface that occurs by turning circle x2+y2=4 around line x=2 .

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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: Sketch the surface: x + 2y + 3z = 12.

A: First find the intersection of plane with axis then draw the plane.

Q: Find the points on the surfaces x^2-yz=25 that are closest to origin

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Q: Find the point(s) on the surface xyz = 1 closest to the origin.

A: Given, g(x,y,z): xyz=1 distance from origin is  d=x2+y2+z2 f(x,y,z)=x2+y2+z2  square of distance…

Q: Find the minimum distance from the point (−2, −2, 0) to the surface                     z = √(1 − 2x…

A: We have to find the minimum distance from the point (-2,-2,0) to thesurface z=1-2x-2y

Q: Find the minimum distance from the point to the plane x - y + z = 9. (Hint: To simplify the…

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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: What is the shortest distance from the surface xy +12x +z^2 =144 to the origin?

A: To find the shortest distance from surface xy +12x +z2 =144  to origin.

Q: The area of the surface obtained by rotating the curve y = 25-x² , -4 sx<4 about the x-axis is

A: Area of the surface rotated about x -axis is, a≤x≤b,…

Q: dentify the length of the curve 9y2 = 4x² from x = 0 to x = 3. %3D

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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…

A: Given plane is x-y+z=5 and the point is (6,0,9) normal to the plane is (1,-1,1)

Q: Find the points that are minimum to the origin and lie on the lines of intersection of planes: y +…

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Q: Find the minimum distance from the cone z = 2x2 + y2 to the point (-6, 4, 0).

A: To find the minimum distance first write distance function. Which is the square distance from  .

Q: Find the points on the surface y2 = 4 + xz that are closest to the origin. (Enter your answers from…

A: Consider the given surface equation y2=4+xz.  The distance d between the origin 0,0,0 and any point…

Q: The equation of a curved road is given as y = 100+6x–0.015x² +0.0000111? Determine the places where…

A: The equation of the curved road given is: y=100+6x-0.015x2+0.00001111x3 Measure of the "Sharpness of…

Q: The slope of the surface z = xy² in the x- direction at the point (2, 3) is O 12 O 8 O 1 O 9 O 10

A: The slope of the surface z = f(x,y) in the x-direction at (x0,y0) is given by [∂z/∂x](x0,y0) =…

Q: Find the length of the curve 3x = (y² + 2)³/2 from y = 2 to y = 3 %3D

A: Use length of curve formula:-  for a given curve x = f(y) from y=y1 to y=y2 length of curve,…

Q: Find the shortest distance from the point (0,2,3) to the plane x+2y+z=1

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

A: Given surface equation is

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

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis.  y = Square root…

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Q: Find the length of the curve. 3/2 y = (4 – x2/3 )2 %3D from x = 1 to x = 8 %3D %3D

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Q: The slope of the surface z = xy2 in the x-direction at the point (2,3) is ______, and the slope of…

A: Given, surface, z = xy2Differentiating the z with respect to x assuming y as constant,∂z∂x = y2×1 =…

Q: Find the points on the surface y2 = 64 + xz that are closest to the origin. %3D (х, у, 2) 3 (smaller…

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Q: Find the minimum distance from the point to the surface z = V7 - 2x – 2y. (Hint: To simplify the…

A: We need to find the minimum distance from the point A (-2,-2,0) to the surface z = 7-2x-2y…

Q: Find the minimum distance from the point (2, 1, 9) to the surface x + y + z = 9.

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Q: Sketch the section of the surface at y = 0. 4 2 -2 -6 -4 -6 -4 4 6. -61

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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: Q1 Find extrema point of the Surface 2-ペ-S-12x+3}+2

A: Consider the given function  z=x3-y3-12x+3y+12 Find partial derivatives of the function with respect…

Q: Find the area of the segment of a sphere formed by revolving the graph of y = V9 - x2, 0 sxs 2,…

A: We need to find area.

Q: Find the exact area of the surface obtained by rotating the curve about the y-axis: y = 3 + 5x2 ; 3…

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Q: Find the minimum distance from the surface x2 -y2 -z2= 1 to the origin.

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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: The area of the surface obtained by rotating the curve y = 36-x2, -6<xS6 about the x-axis is

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Q: Find the area of the surface generated by revolving the curve y=2/x 18xs2, about the x-axis.

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Q: nd the minimum distance from the point to the surface z = V7- 2x - (-2, -2, 0)

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