Determine the surface of revolution of arc y³+y=x²+6x on the interval [-5,-1] if it is revolved about y= -3

Q: The equation of the area of the plane region bounded by y = x^3 and the lines x = 1 and y =0 is…

A: Detail solution written below

Q: The equation of the tangent plane to the surface x² 8 at the point (-2, 1, 3) is Select one: 1/2…

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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: 7. Sketch the surface 15zs9-x' - y² and x'+y' <1

A: To find:

Q: The equation of the tangent plane to the surface at the point (-2, 1, 3) is Select one: = -(x-2) +…

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Q: Find the equation of the tangent plane to th surface 3x? + 5y? + 4z2 = 24 at the point (1, –1,2). 1.…

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Q: Find all equations of the tangent line to the common curve of the two surfaces with equations z = x²…

A: follow next step

Q: 4.) Find an equation for the plane tangent to the surface 9x² +4y² +9z² = 34 at the point (1,2,-1).

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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 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 all points of horizontal and vertical tangency to the curve: x = 3cos 0 y = 3sine

A: for Horizontal tangent put dydθ=0 for the vertical tangent put dxdθ=0

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 an equation of the tangent plane to the surface at the given point. x2 + y2 − 4z2 = 21,    (−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 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: Consider the curve C parametrized by x = -1 + 6 sin t and y 6 cos t for -n <t< 9n. %3D Then C is a…

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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: Find the minimum distance from point (2, 5, -1) and plane 3x + 4y + z = 10.

A: Given query is to find the minimum distance.

Q: Find the center of 2 circles tangent to g² + y² = 100 at (6,-8) having a radius of 15 units O…

A: Use the following formulae, to obtain the solution. The slope of a line passes through the points…

Q: The value of the line integral I- [Adl where A-(2x+y)£+(y-x)ý along the parabola y=x^2 and form…

A: Evaluate: I=∫A.dl              ...(1)WhereA=2x+yx∧+y-xy∧

Q: Find az/ay for a level surface x2 - y2 + z2= c at the point (-3,8,8). Give your answer correct to…

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Q: Find the area and centroidal distances of the curve that lies between the equations y=4-x^2 and…

A: Consider the region bounded between the curves is as shown in the figure below: Here, the objective…

Q: Find the length of the longest straight line that lies entirely within the surface: This will from…

A: (d) To find: The length of the longest straight line that lies entirely within the surface. Given…

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

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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: Given a surface f(x,y) = -3x2 + (4)y2. Find the derivative in the direction of v = at the point (1,…

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Q: Find the tangent plane to the surface 8x2+y2+4z2 = 25 at the point ( 1, -1, 2 )

A: To find: The equation of the tangent plane at the point  1,-1,2. The given function for the surface…

Q: Find an equation of the tangent plane to the surface x² + 2y² + z² = 175 at the point (5, -5, 10). O…

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Q: Sketch the surface x = 2y2 +3z2

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Q: find the slope of the tangent to the curve of intersection of the surface 3z=√36-9x²-4y² and the…

A: Consider the surface 3z=36-9x2-4y2and the plane x=1 at the point 1,-2,113.The objective is to find…

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: Describe the traces of the curve x2 + 9z2 = 9 in the vertical planes (those parallel to the…

A: The traces of a surface are the cross-sections created when the surface intersects a plane parallel…

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

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Q: Determine the surface of revolution if the arc y^3 + y = x^2 + 6x on the interval [−5, −1] is…

A: The curve will appear like this

Q: Find an equation of the tangent plane to the surface at the given point. 5x2 + 2y2 + 5z2 = 73,    P…

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Q: Find an equation of the tangent plane to the surface at the given point. x2 + y2 − 7z2 = 27,   (−3,…

A: Differential equations are those equations of mathematics that involve dependent variables ,…

Q: The circle of radius 1 centered at (-3, 4,1) and lying in a plane parallel to the yz-axis is a)…

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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: 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 an equation of the tangent plane to the surface x-xyz 56 at the point (-4,5,2). Select one:…

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Q: Show that the surfaces S1 : 4x + y° + 9z² = 108 and S2 : xyz = 36 are tangent at the point (3, 6,…

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

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Q: Sketch the section of the surface at x = 0. y - 252 = 25 -12- -8 12 -6 -4 -6 12 -4 -8 -12 6 4 4 -6-4…

A: topic - hyperbola y2-25z2= 25 is a hyperbola with vertex are (0,5,0) and (0,-5,0)

Q: find the slope of the tangent to the curve of intersection between 6z=3squareroot(20-x^2) and the…

A: the cylinder equation is given by  and the plane is given by  We want to define each variable in…

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: Sketch the graph of -x + 9y² – 4z² = 36 and identify the surface. %3D

A: Given a function in terms of x, y and z. Here x and y are independent variables and z is a dependent…

Q: What is the surface generated by a straight line which moves along a fixed curve, and which remains…

A: To determine the name of the surface generated by a straight line which moves along a fixed curve,…

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 the tangent lines as directed. To the ellipse x²+2y²=9 perpendicular to the line 4x-y=6

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.