Does the origin lie on the polar curve r = 1 – 3cose ? Explain.

Q: Use the integration capabilities of a graphing utility to approximate the area of the surface formed…

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Q: Transform the polar equation r = 3 sin(0) to an equation in x and y. %3D

A: Converting the polar equation to rectangular equation

Q: What is the area of the area Outside the polar curve r= 1+ cosoo and inside the polar curve r=3 cos…

A: Given : Polar curves Cardioid r = 1 + cos θ, Circle r = 3 cos θ     To find : Area of the outside…

Q: Find the points at which the polar cone irc4coso, has horizontal and vertical tungent liner.

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Q: Sketch the polar curve r= Jcos 20 and r = 2cos0. %3D

A: To sketch the polar curve r = cos 2θ   and r = 2cos θ

Q: Which of the following is the surface area of the solid body created by rotating the given…

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Q: Find the polar coordinates of a point with Cartesian coordinates (x, y) %3D 2

A: Given: The given Cartesian coordinates are x, y=932, -92. Let the corresponding polar coordinates be…

Q: 1.What type of polar curve is named for a heart? For a snail? For a ribbon?2. What is the difference…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: (x, y) of the point with polar coordinates What are the Cartesian coordinates (r, 0) = (4, 5 ) ? O…

A: Given (x, y) = 4, π6

Q: Use the parametric equations of an ellipse, æ = 2 cos(0), y = 5 sin(0), 0 < 0 < 27, to find the area…

A: Given :  x=2cos(θ), y=5sin(θ),  0≤θ≤2π The area under the curve can be written as:…

Q: Plot the polar curve r(0) = on [0,57].

A: Given that,  r(θ)=θπ on 0,5π

Q: Under what conditions can you find the length of a curver = ƒ(θ), a ≤ θ ≤ b, in the polar coordinate…

A: step 1 :           Conditions to find the length of the curver = f(θ) , ∝ ≤ θ ≤ B* The curve r =f(θ)…

Q: Convert the polar curve r=6cos(θ)+6sin(θ) to Cartesian coordinates. choose the correct ones from the…

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Q: Identify the surface whose equation in spherical coordinates is given by p= 2 cos o

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Q: Sketch the polar curve 0=1

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Q: Find the area of the region enclosed by one love of the curve with the polar equation r=2sin3θ.

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Q: Sketch the surface represented by the parametric equations x = cos³ t and y=sin³ t with 0st≤n/2.…

A: Given: x=cos3t and, y=sin3t we have to find the surface area by rotating about x-axix. Suppose the…

Q: Find the area of the surface formed by revolving the polar equation over the given interval about…

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Q: Sketch the region in the plane consisting of points whose polar coordinates satisfy the given…

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Q: What are the rectangular coordinates of the point with polar coordinates (r, 0) = (-10, (x, y) Enter…

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Q: What are the polar coordinates (r, 0) of the point with Cartesian coordinates (x, y) = (v2, – V2) ?…

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Q: Convert the point(r,o) from polar to nectangular COordinates ( Ca,s

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Q: Show that every vertical line in the xy-plane has a polar equation of the form r = a sec u.

A: The relation between polar coordinates r,u and rectangular coordinates x,y is x=rcosu…

Q: Use polar coordinates to integrate under z=xy above the first quadrant of the unit circle on the xy…

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Q: Use the formula for the arc length of a curve in parametric form to derive the formula for the arc…

A: Given arc length of a curve in parametric form

Q: What is the polar equation of a circle of radius Va? + b centered at (a, b)?

A: General equation of a circle is given by - x-h2+y-k2 = r2              ..............(1)where,h, k =…

Q: 7T What are the rectangular coordinates of the point with polar coordinates (r, 0) = [2, ? 4 (х, у)…

A: Given: r,θ=2,7π4

Q: (b) Test the symmetricity of the curve r 11cos 20 about the y -axis. Then, sketch the polar curve,…

A: Given curve is r=11cos(2theta)

Q: Find polar Ir>0 and Os0<2T. Coordinates of the points such that

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Q: Determine the arc length of the curve formed by the polar equation r = 4 cos 0 - 4. 2T 2п 2√/2 √1 -…

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Q: Identify the surface whose equation in spherical coordinates is given by p = 2 cos o %D

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Q: Show that the parametric equations x a cosh u cos v, y b cosh u sin v c sinh u represent a…

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Q: What are the polar coordinates (r,θ) of the points of intersection of C1 curve with polar equation…

A: It is given that, It s known that at the point of intersection equation of both curves satisfies…

Q: 1. What are the rectangular coordinates of the point with polar coordinates (r, 0) = (10, 45°)?

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Q: Express the polar equation r=2 sin 0 in cartesian coordirates.

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Q: Identify the surface whose equation in spherical coordinates is given by p = 8 cos %3D

A: The given equation in the spherical polar co-ordinates is ρ=8cosϕ. In spherical polar co-ordinates,…

Q: Sketch the curve r=0 in polar coordinates for: i. (0 <=0) ii. (-∞0 <0<∞ )

A: In a polar coordinate system, a point is represented with coordinates (r,θ). The radial coordinate r…

Q: Use the Distance Formula to approximate the distance between the two points in polar coordinates. 5,…

A: We are going to solve

Q: Convert the point Cr,e)f from polar to nectangular COordinates (xx) 5T 3. ब्लज( कथावक 2)(a,)

A: To convert the given point from its polar form to rectangular form

Q: Describe the test for symmetry with respect to the polar axis.

A: The graph of a polar equation is symmetric with respect to the polar axis if replacing r, θ with r,…

Q: What are the polar coordinates (r, 0) of the point with Cartesian coordinates (x, y) = (V2, -V2) ? ㅇ…

A: Given cartesian coordinates:x,y=2,-2To find: polar coordinates r,θ

Q: Give a parametrization of the left half portion of the polar curve described by the equation r = 3.

A: Give a parametrization of the left half portion of the polar curve described by the equation r = 3.

Q: Find the polar coordinates of a point with Cartesian coordinates (x, y) =

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Q: Qz: sketeh in polar %3D

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Q: Determine the polar moment of inertia and the polar radius of gyration of the shaded area shown with…

A: Solution:- At x = 2a, y = 2a  y1=k1x2  2a=k12a2 k1=12a At x = 0; y = a y2=c+k2x2 c = a…

Q: Identify the surface whose equation in spherical coordinates is given by p= 6 cos

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Q: how to find  Find the exact length of the polar curve. r = θ2,    0 ≤ θ ≤ 7π/4

A: The polar curve I given as, r = θ2,    0 ≤ θ ≤ 7π/4.The formula to calculate the exact length of…

Q: converts from cartesian coordinates (x, y) to polar coordinates (r, theta).

A: To convert Cartesian coordinate of any point (x, y) to polar coordinate (r, θ) We will use x = r…

Q: Find the tength of the curve over the given interval Polar Equation Interval

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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.