The circle x² + (? − 1) 2 = 1 is rotated around the line y = x-3. A torus is formed as a result of the rotation. Calculate the surface area of the resulting torus. (Hint = Pappus Theorem)

Q: Prove that an object thrown at an acute angle of elevation travels along a parabolic path, if wind…

A: To show that the path is parabolic                 ux=u cos θuy=u sin θax=0ay=±g

Q: Sketch the section of the surface at x = 0. y? – 42? = 4

A: Given

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Q: Find the area of the resulting surface if an arc of a parabola y = x? from (1,1) to (2,4) is rotated…

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Q: 17. Concentric with the circle (x – 2)² + (y – 1)² = 4 and passes through (4, –1) %3D

A: Given, Concentric with (x-2)2+(y-1)2=4 and passes through (4,-1) General equation of circle is…

Q: Calculate 8-z -dz, z(4-z) where C is the circle of radius 7, centre 0, negatively oriented.

A: C : circle with radius 7 and centre 0, negatively oriented  f(z) = (8-z)/(z(4-z)) Singularity of…

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Q: Use transformations to show that circle A with radius r is similar to circle A' with radius r'. A'

A: .

Q: Q2 Calculate 8- z dz, z(4 - z) where C is the circle of radius 7, centre 0, negatively oriented.

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Q: Find the area of the resulting surface if an arc of a parabola y = x² from (1,1) to (2,4) is rotated…

A: Given

Q: Q2 Calculate 8- z dz, z(4-z)* where C is the circle of radius 7, centre 0, negatively oriented.

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Q: The intersection between the surface x + y + z = - 1 and the circle x2 + y2 = 1,z = 0 is

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Q: BG and BH are tangents that intersect circle M at points G and H, then A. MZGMH = 120° B. BG = BH C.…

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A: "For a point moving with uniform circular motion, the distance traveled per unit timeby the point is…

Q: Set up and simplify (but do not evaluate) : 3x ds, where C is the arc of the circle r2 + y² = 4 from…

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Q: .If C is the circle (traversed once counterclockwise) of radius 2 with center at z = 0, %3D 7e?…

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Q: 6) Find the area of the surface generated when the upper portion of the circle x + y? = 100 on the…

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Q: If the infinite curve y = e-6x, x > 0, is rotated about the x-axis, find the area of the resulting…

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Q: Describe the projections of the circle r(t) =〈sin t, 0, 4 + cost〉onto the coordinate planes.

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Q: Use transformations to show that circle A with radius r is similar to circle A' with radius r'. A A'

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Q: What is the definition of a parabolic cylinder?

A: The parabolic cylinder functions are the solutions to the differential equation d2ydx2 + ax2 + bx +…

Q: Circle to the center of C is a origin Coordina tes and radius 4

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Q: 5. plot x?-y?=z (Elliptic paraboloid) in 3D.

A: Note: According to bartleby we have to answer only first question please upload the question…

Q: 6. Prove (by plot) the equation (x²+y²=16) is the circle in 2D , and cylindrical in 3D.

A: We will answer the first question since we don't answer multiple questions at a time. Please…

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

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

Q: If the infinite curve y = e-2x, x 2 0, is rotated about the x-axis, find the area of the resulting…

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Q: A circle is specified in parametric form by x=7+3cosθ y=−8+3sinθ What are the coordinates of the…

A: Given : A circle is specified in parametric form by  x=7+3 cosθy=-8+3 sinθ To Find : What are the…

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Q: The arc of the parabola y = x? from (1, 1) to (2, 4) is rotated about the y-axis. Draw the surface…

A: Given: Equation of parabola : y= x2  Arc of parabola passes through (1,1) and (2,4).

Q: True or False: Given secant AB goes through the center of circle H and intersects the circle at…

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Q: Suppose the center of a circle is at (3, - 2) and a point on the circle is at (6, – 1). The radius…

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Q: Problem the circle xây? a? otatad about the x- escis, fnd the Jolume of the Solid geverated 2.

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Q: . (a) Show that as (x, y)→ (0, 0) along any straight line y = mx, or along any parabola y = kx², the…

A: Given : f(x) = x³y/(2x^6+y²)  To find : To prove that limit exist along parabola

Q: Consider the curve C which is the intersection of the surfaces shown in the attached figure.

A: To evaluate the below integral. ∫Cx−y−2zds

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Q: 7. Determine if line AB is tangent to the circle. Show your work. B 6 12 16

A: Use circle property

Q: Calculate 8 - z 'zp- z(4 - z) where C is the circle of radius 7, centre 0, negatively oriented.

A: In this question we have to find the Integration.

Q: In R', the equation x² + y + z? = 4 describes a sphere of radius 2. Select one: True O False

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Q: Evaluate ds where C is the upper half of the circle centered at the origin with radius 1 with the…

A: Draw the curve C:  Here, we divide C in two parts:  C1 represented by the curved part C2…

Q: Calculate 8-z dz, z(4 - z) where C is the circle of radius 7, centre 0, negatively oriented. (2ー2

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Q: rea of the closed region det

A: Given, the equation of the circle is                                        (x+2)2+(y-3)2=4

Q: Calculate 8-7 dz, z(4- z) where C is the circle of radius 7, centre 0, negatively oriented.

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Q: Consider the circle with center (h, k) and radius length r. If the circle contains the point (c, d),…

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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.