Homework 2: Find the areas of the regions in the following Exercises: 1. Shared by the cardioids r= 2(1 + cos 0) and r= 2(1 - cos 0) %3D -COThen) 20 CeThen)

Q: 37. Figure A, the small hexagon, was dilated with the origin as the center of dilation to create…

A: Here hexagon A is dilated to creat hexagon B.

Q: Find the area of the region Inside one leaf of the three-leaved rose r = cos 3 theta

A: Given an  equation of petal rose : r=cos3θ We need to find the area of the region inside one leaf.

Q: Find the area inside the circle r=−3acosθ and outside the cardioid r=a(1−cosθ), a>0

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Q: If the area inside the cardioid r = 5 + 5 cos 0 but outside the circler = 3 cos 0 is A , then what…

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Q: . r= 2a cos e %3D

A: We have to find the area enclosed by the given polar curve: r=2acosθ ; 0≤θ≤2π

Q: Find the area inside the 'figure eight'r = 1+ cos 20 and outside the circle r = 1.

A: Area inside r = 1 + cos2θ and outside r = 1 is shown by shaded region.

Q: r= 6+4cos(theta) A. Limacon without loop B. Cardioid Which one is it?

A: The solution is given by using the definitions of the limacon and there types Ans :  Limacon without…

Q: The area inside one or more of the three interlocking circles r = 2a cos θ, r = 2a sin θ, and r = a…

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Q: The area common to the circle > = 3 and the cardioid r = 3(1 - cos 9).

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Q: The area of the region common to both circles r=16sin(0) and r=8 is:

A: Area is calculated as shown below

Q: c) Find the total area inside r = 2+ cos (20) and outside r = 2 + sin (20)

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Q: The area of the region inside r = 6 cos 20 the rose and outside the circle = 3/2

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Q: r = 5 + 2 cos0 : %3D circle rose inner loop cardioid dimpled convex O spiral lemniscate

A: Solution ) limacons  equation  r = a ± b cos θ If  a > b   = dimpled  a = b = cardioid b > a =…

Q: Find the area of the region that lies inside the first curve and outside the second curve. r2 = 32…

A: The given curves are. r2=32 cos2θ and r=4 To find the area of the region inside r2=32 cos2θ and…

Q: а) The diagram below shows a sector AOB of a circle with center O and radius r cm. ( cm 72° i)…

A: Given sector AOB of a circle with radius 'r',  a) The ends of sector makes as angle 72° Formula for…

Q: Ql find chromatic number of

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Q: Sketch the graph of the limacon r = 3 – 2 cosθ and the circle r = 2. Shade the region that is inside…

A: The objective is to sketch the graph of the limacon r = 3 – 2 cosθ and the circle r = 2. Shade the…

Q: 2) Given y = Cos x and y= 20 Period 28 D Period = X Degrees y= Cosx 1

A: Given  y=cosx and y=2cosπx the period of a cos function is 2π so period=2π/b =2π which implies that…

Q: Find the area of the region inside the cardiod r = 2+2 cos 0 and inside the cardiod r = 2 2 cos 0 -…

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Q: Find the area of the region inside the circler= -6 cos e and outside the circle r=3. The area of the…

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Q: 4. (a) The following diagram shows two sectors, POQ and ROS. 0Q is x cm and OS is (x + 1) cm. Angle…

A: As per honor code, we are entitled to solve only one question at a time so I am providing you the…

Q: 2. 4. 1. 3. 4. To find the blue shaded area above, we would calculate: = area %3D xp(x)f a. Where:…

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Q: (A) Find the Area :r= a (1+ Cos e)

A: It is given that

Q: 50. y = (1 – cos x) sin x

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Q: 1. Find the area of one leaf rose r=a cos 2B

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Q: In Exercises 17-20, find the area of the shaded region in Figures 16-19.

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Q: Find the area of the shaded region. r = sin(20) r = 4+3 cos (8)

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Q: Luse the Half Anola Forula cos2

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Q: Find the areas of the regions Inside the lemniscate r2 = 6 cos 2θ and outside the circle r = √3

A: Given that: r2=6cos2θ,     r=3 To calculate the points of intersection,   Set the given equation…

Q: Find the area of the region enclosed by one loop of the graph of the equation r = 5 cos 30. Draw the…

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Q: Name: Section: i+ (4t - 3)k E = sint i tcost K 3. %3D

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Q: find area Inside the circle r = -2 cos 0 and outside the circle r

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Q: 53. y = 1 y = cos?x cos*x

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Q: Shared by the circle r = 2 and the cardioidr = 2(1 – cos 0)

A: (24) Given curve is r=2 and the cardioid  r=21−cosθ. We have to find the area bounded by the region…

Q: Find the area of the region inside the circle r=-4sin(theta) and outside the circle r=2

A: Given, the area of the regionis inside the circle r=-4sinθand out side the circle r=2.

Q: posulate

A: For first diagram one side is same for both the triangles  and an angle is equal for both the…

Q: Find the area enclosed by one leaf of the rose r = 12 cos 3u.

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Q: ind the area inside the circle r = cos 0, but outside the circle r =| = 1/2. Sketch the graphs…

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Q: Find the area inside the circle r=6cos(theta) and outside the cardioid r=2(1+cos(theta)) Area=

A: Given that,  Equation of the circle is r=6cosθ Equation of the cardioid is r=21+cosθ Now, consider…

Q: Graph the cardioid r=3 (2+2 cosθ), and then find the area of the region inside this the cardioid.

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Q: Differentiate. 3 – cot(x) y' = Need Help? Read It Watch It

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Q: Find the area of the shaded region. r = 44 cos 0 r = 44/3 sin 0 NOTE: Enter the exact answer.

A: Use polar coordinates

Q: Question 16 Calculate the sum of x, y, and z in degrees. [Image 16 ] (4z + 6)° 106° 2y O 124 O 99 O…

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Q: Hawad Findthe areas fak the fallowing regions 2 Area af the region insidethecircle (r=1) and outside…

A: Given

Q: Find the area lying outside r = 2 cos 0 and inside r = 1+ cos e. Area =

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Q: Solve for the area common with r = 2+5cos(2*theta ) and r = 5sin(theta). Illustrate the graph.

A: Double integral is used to integrate the function of two variable over two-dimensional region.…

Q: 7. Sketch the graph of the limacon r= 3-2 cose and the circle r = 2. Shade the region that is inside…

A: Given r=3-2cosθr=2

Q: 7. In the diagram below of circle A, diameter MP = 26, m¿GAI = 30° and radii GA and Al are drawn.…

A: Explained below

Q: Find the arca of the shaded region y=r-24 O -4.5 O 4.5 O Not enough information O None of the above

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Q: The spray from a watering hose spans 30°, reaching both a cluster of tulips and a daisy, which are…

A: Sine Rule states that if A, B and C are angles of a triangle with opposite side a, b and c…

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.