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

Q: Explain why the curve of intersection of the surfaces x2 + 3y2 − 2z2 + 2y = 4 and 2x2 + 6y2 − 4z2 −…

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Q: Find the area of the surface generated by revolving the curve y = sqrt(x + 1) , 1 <= x <= 5 about…

A: Given that the surface is generated by revolving the curve y=x+1 , 1 &lt;= x &lt;= 5 about the x -…

Q: 13. Find the area of the surface generated when the curve y = -, on [2,4] is rotated about the…

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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: Obtain the DE based on given conditions solve for item 1 only.

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Q: Find the minimum distance from the point to the plane x - y + z = 3.

A: Now, formula of shortest distance of the plane ax+by+cz=d passing through the point (l, m, n) is,

Q: A frustum of a cone is generated by revolving the graph of y = 2x on the interval [2, 8] about the…

A: GIVEN FRUSTUM cone generated by revolving  the graph of y=2x on interval [2,8] about x axis  we need…

Q: Find the area of the plane region bounded by y = x2 - 4x and y = x(2 - x)

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Q: 4.x² + y = 4

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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: Jategrate h (x.y) = (x+y)i+(-x)j over the closed curve that begins at (-1, 0), goes along the x-axis…

A: we will use green theorem here to solve this question

Q: 2. The surface area of the surface generated by revolving the curve y = x, -1 < x<1, about the…

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Q: Calculate the point on the surface z =1 - x2 - y2 that has a maximum value for the sum of its…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = √5 -x, 3 ≤ x…

A: We know that surface area obtained by rotating the curve y=f(x) about x axis between x=a &amp; x=b…

Q: .Find the area of the surface generated from revolving the curve y = x3 ++4 from x = 1 to x = 2…

A: Function is the unique relation where each x is mapped to unique y. It can be of many type,…

Q: 3. Find the area of the surface generated by revolving the curve = 2/1- y (-1 < y < 0) X about the…

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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: 5- Find the area of the surface generated by revolving the curve X= (y*/4) +1/ (8y²),1<y <2 ,about…

A: Given:function: x=y44+18y2Interval: 1≤y≤2To find : Area of surface generated by revolving the curve…

Q: 9ху. Use hyperbolic functions to parametrize the intersection of the surfaces x - y = 49 and z =

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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 minimum distance from the point (2, –6, 6) to the plane 2x - y + z = 0.

A: NOTE:- the distance between a plane say px+qy+r z +s=0 and a point say u, v, w is d= p u+q v+r…

Q: Find the exact area of surface obtained by rotating the curve about the x-axis. y=sqrt(5-x)    3<…

A: Given curve is y=5-xdydx=-125-x Now, area of the surface obtained by revolving y=f(x) from x=a to…

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

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Q: What is the radius of curvature at point (1, 2) of the curve 4x – y2 = 0.

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Q: 4. Find the area of the surface obtained by rotating the curve x²/3 + y>/3 = 1, 0 <y<1 about y-axis.

A: If the curve defined by the parametric equations x=x(t), y=y(t)  with a≤t≤b , is rotated about the…

Q: 3 Find the Minimum distance from the origin to the plane X+2y-z=5

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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 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 area of the surface obtained by revolving the graph of x = y³ on the interval [0,1] about…

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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 areas of the surfaces generated by revolvingthe curves about the given axes. x = √4y - y2,…

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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: :y² + z² — ² by first sketching at least three cross sections in each of the 4. Graph the surface 1…

A: A quadric surface is a graph of an equation in the three variables x, y and z in a three dimensional…

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

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Q: 6. Find the area of the surface formed by revolving about the curve defined by y = x2 - x2, 1<x<3…

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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: find the points of the surface x^2-y^2+z^2=1 which corresponds to the extreme value of…

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Q: area of the surface obtained by rotating the curve y=x^3, x ∈ [0

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

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Q: Q/ Find the points have minimum distance from the origin to the surface. xyz²=1

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

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Q: find the areas of the surfaces generated by revolvingthe curves about the given axes. x = √y, 2 ≤ y…

A: We first find dx/dy

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 areas of the surfaces generated by revolvingthe curves about the given axes. y = x3/3, 0 ≤…

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Q: 1 Find the points have minimum distance From the origih to the Surface xyz =1.

A: Using the lagrangian ultiplies Let For critical points,

Q: Find the minimum distance from the point (0, 0, 4) to the surface  z = (1-2x-2y)^1/2   (Round your…

A: Solution: