Find the minimum distance from the point (0, 0, 4) to the surface  z = (1-2x-2y)^1/2   (Round your answer to two decimal places.)

Q: Q3/ Find a center of mass of a thin plate of density 8 = 3 bounded by the lines x = 0, y = x, and…

A: Given region bounded by x=0 , y=x and parabola y=2-x2    in first quadrant

Q: Find the center of mass of a thin plate of variable density  d(x) = 4x2 covering the region bounded…

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Q: find the center of mass of a thin plate of constant density d covering the given region. The region…

A: Given: y=2x2-4x and y=2x-x2 Graph:

Q: find the center of mass of a thin plate of constantdensity d covering the given region. The region…

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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: Find the 'slope' of the tangent line to the curve of intersection of this surface 3z = 36-9x –4y?…

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Q: The area of the surface obtained by rotating the curve y = 21 x + 1, 0sx< 42 about the x-axis is

A: Given:- y = 21x+1 To find:- Are of rotation about x axis [0, 42]

Q: * = Vy +5,

A: We have to evaluate the area of the surface generated by revolving the curve  x=y+5 between the…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. 1 1 <x < 1 y =…

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Q: Find the moment of inertia of the region between the parabola y=4-x^2 and the line y=1-2x from x=0…

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Q: Find the surface area cut from the cone 2x2 + 2y2 = 5z2, z &gt; 0, by the cylinder x2 + y2 = 2y

A: To find the surface area cut from the cone 2x2 + 2y2 = 5z2, z &gt; 0, by the cylinder x2 + y2 = 2y

Q: Find the area of the surface generated by revolving the curve about the y-axis. y=4-x², 0≤x≤2.

A: In this question we have to find the area of the surface generated by revolving the curve about the…

Q: Find the center of mass of a thin plateof density δ = 3 bounded by the lines x = 0, y = x, and the…

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Q: Find the area of the surface obtained by rotating the curve y=4x3 from x=0 to x=2 about the x-axis.…

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Q: 3. Find the area of the surface generated from revolving the curve y =x ++4 from x = 1 to x = 2…

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Q: Find the centroid of the region cut from the first quadrant by the curve y = 1/sqrt(x + 1) and the…

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Q: A container with a height of 3/2 is made by rotating the curve y = 3/2x^2, Osx<1, about the axis x =…

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Q: Find the area of the surface obtained by rotating the curve y = 4x + 4, 0 < x< 8, about %3D the…

A: To find- Find the area of the surface obtained by rotating the curve y2 = 4x + 4, 0 ≤ x ≤ 8, about…

Q: A thin plate of constant density k, bounded by the parabola y=3x² and the line y=3 has a mass 4k.…

A: If mass of a region R bounded between y=f(x) and y=g(x) from x=a  to x=b  Then there two moments,…

Q: Determine the maximum highest point (x, y,=) the surface on z = 1+ 4x + 4y- x* - y*

A:

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 a unit normal to the surface x'y + 2xz = 4 at the point (2,-2,3).

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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 exact area of the surface obtained by rotating the curve x = (1/3)y^3, 0 &lt;= y &lt;= 1,…

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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: Find the points on the surface ry + yz + zr - r - z = 0 where the tangent (5) plane is parallel to…

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Q: 9. Determine the position of the centroid of a sheet of metal formed by the curve y = 4x - x² which…

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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: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = + 2 бх

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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 area of the surface obtained by rotating the curve x = 3 (y + 2)3/2, 1 <y< 2, about the…

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Q: Find the curved surface area of the solid generated by revolving the part of the curve y=x² from…

A: Given curve is                                               y=x2 from     (0, 0) to (6, 6) Rotation…

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 generated when the curve y = x* 1 + ,on [1,2] is rotated about the…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. 1 + 2x 1 < x< 1…

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Q: Find the area of the surface generated by revolving the curve y= 2 sqrt(1-x), from x=-1 to x=0,…

A: The volume of the solid generated by a region under y=f(x) bounded by the x –axis and vertical lines…

Q: ) Find the points on the ellipsoid 6x² + y² + 3z² = 4 where the tangent plane is parallel to the…

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Q: Find the areas of the surfaces generated by revolving the curves about the indicated axesx = t + √2,…

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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: The curve y = (64x – 4x³ )m bounds the shaded section on top and the x-axis on the bottom. Determine…

A: Given curve, y=64x-4x3 The shaded region is shown as: Formula for the centroid x, y in a region is…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. x = 5 + 4y2,…

A: We use the formula S=2π integration of y √(1+x'2)dy from 1 to 2

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

A:

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: x=y"2 -y², 1<y<3 about the y-axis 3°

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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: Find a point on the ellipsoid 3x2 + y2 + 3z2 = 1 where the tangent line is parallel to the plane…

A: Given: The equation of ellipsoid is 3x2+y2+3z2=1 and the equation of the plane is -12x+2y+6z=0.…

Q: Find the center of mass of a thin plate of constant density δ covering the given regions. The…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. (y2 + 2)3/2, 2 <…

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.