ABC is rotated around the line x=0 to produce a solid. What describes the shape of the solid?

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Q: Convert z = 9x2 - 9y2 to cylindrical coordinates.

A: The objective of the question is to convert the given equation in Cartesian coordinates (x, y, z) to…

Q: Sinlxy). lnx dx 19141 to be investipa te the uniform Convergence of ne parametric intepral)

A: Given integral is, ∫01sinxylnxxdx Since, the given integral is improper integral so applying the…

Q: Describe the region in polar coordinates.

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Q: Convert to cylindrical coordinate. 1. z = x2 + y2

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Q: Find length of the cardioid r-a03from 0 0 to 0 t %3D

A: To find Length of cardioid r=aθ3  where θ=0 to θ=π

Q: The shape of y = V that has been reflected across the origin. Preview

A: To find:

Q: 21 6) x-1. y

A: Given query is to write the equation in the form of rectangular form.

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Q: The parametric equation for the y-axis is:

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Q: gure to the right as the parameter. (x, y) 12 ind parametric equations for the particle's motion.…

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Q: 2- Write two examples about converting from rectangular (x,y) to polar form(r.)

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Q: In an open space, Thomas throws a ball at an angle of 70° to the horizontal with an initial velocity…

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Q: How do you solve this using polar coordinates?

A: We will find out the required result.

Q: Evaluate ²y dA where D is the top half of the disk, centered at the origin with radius 2.

A: The given integral is ∬x2ydA over the region D where D is the top half of the disk centered at the…

Q: √2-1₁² √4-x²-1,² ITI S y=0x=y=z=√x² + y² arctan() dzdxdy ||

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Q: Try to sketch by hand the curve of intersection of the circu- lar cylinder x + y² = 4 and the…

A: Given, Circular cylinder, x2+y2=4 Parabolic cylinder, z=x2

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.