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

Q: Explain why the curve of intersection of the surfaces x + 3y? – 2z2 + 2y = 4 and 2x? + 6y? – 4z2 –…

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Q: 4. Find the equations of the line tangent to the intersection of the surfaces z = x´ + 2y and

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

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

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 minimum distance from the point to the plane x-y+z=3 at (1,-3,2)

A: We will find the minimum distance from the point to the plane x-y+z=3 at (1,-3,2) in the following…

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

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Q: 4. At the point (0, 0) the graph of y 4.x2 has greater curvature than does y 2x2.

A: These equation represents parabola,then Radius of curvature: K=  y'' /([1+(y')²]^3/2)

Q: 3/2 Find the length of the curve. y = (x* +4)" OSxs2

A: see below the answer and calculation

Q: Sketch the surfaces 1. 9x2 + y2 + z2 = 9  2. 4x2 + 9y2 + 4z2 = 36

A: Using graphing calculator to graph them. 9x^2 + y^2 + z^2 = 9

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

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Q: The area of the surface obtained by rotating the curve y = 1sxse about the line x = 42 is

A: Given that y= 1/x  + x3 /12 and find the surface area. Here i attached solution of this question.

Q: Determine the points on the surface y2+z2−x=8 that are closer to the origin.

A: Consider the given surface. y2+z2−x=8z2=8−y2+xf(x,y)=8−y2+x

Q: Find the points on the surfaces z = V² + y? and z = 2 – x/2 having the shortest distance to the…

A: We know that the two given surfaces will intersect at some curve whose equation can be obtained by…

Q: Find the minimum distance from the point (4, 0, 6) to the plane x − y + z = 3.

A: Find the minimum distance from the point (4, 0, 6) to the plane x − y + z = 3.

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

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Q: Find the points on the surface xy2z3=2 that are closest to the origin.

A: Given, xy2z3=2We have to find the point on the given surface that are closest to origin.let the…

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: 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: The area of the surface obtained by rotating the curve y = V9-x2, -1sxs1 about the x-axis is mit…

A: Use formula of surface area about x axis

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 total length of the loop of the curve 6y² = x(x – 2)² between x = 0 and x = 2. %3D

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Q: 5. Consider the two curves y = x° - 3x + 20x + 88x² + 71x – 74 and y = 2a+ 50x – 22x + 42.x + 31. |…

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Q: Sketch the surfaces 1. x2 + y2 = 4  2. x2 + 4z2 = 16

A: The given surfaces are sketched using online 3D calculator.

Q: Find the exact area of the surface obtained by rotatingthe curve about the x-axis. 9x =y2 + 18 ,  2…

A: Consider the curves, 9x=y2+18,  2≤x≤6 Differentiate the given curve with respect to “y” then,…

Q: Find the minimum distance from the point (-6, -6, 0) to the surface z = O√√559 O 3√61 09 O√773 O√69…

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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: Find the equation of the surface of revolution of x = z2 about the x-axis.

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Q: Compute the length of the curve x = 2y3 + 1/(24y) from y = 1 to y = 3.

A: Given: x=2y3+124y1≤y≤3

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: The area of the surface obtained by rotating the curve y = v64-x2, -2 <x < 2 about the x-axis is

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Q: Find the areas of the surfaces generated by revolving the curve x= 2sqrt(4-y), 0≤y≤15/4

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Q: FIND THE LENGTH OF THE CURVE 9y = x(x – 3)´ from X = 1 to x = 4 %3D 10

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

A: Given surface equation is

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 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: Find the area of one side of the “winding wall” standing orthogo-nally on the curve y = x2, 0 &lt;=x…

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

A: To find the minimum distance

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

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Q: 2. Find the shortest distance from the point (2,0) to the curve: (a) y = 3x – 1 (b) y = x^2 (c) x^2…

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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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Q: Find the minimum distance from the point to the surface z = √4 - 2x - 2y. (Hint: To simplify the…

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Q: Find the points on the surface 2 2 xY + 100 that are closest to the origin.

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