If C is a circle of radius 7 centered at the point ( 4, -2 ), then evaluate $ (7y – esin (2) ) dæ + (12æ – sin(y³ + y)) dy. | value = T

Q: 3. What is the length of the curve r = cos3 (-) where 0 < 0 <: sos

A: See the attachment

Q: Let P(cos t, sin t) be a point on the unit circle x2 + y2 = 1 in the first quadrant. Show that t is…

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Q: 1. Find the total length of the curve r = 4(1 - sin 0) from 0 = 90° to 8 = 270° and also the total…

A: The given problem is to find the total length and the perimeter of the given curve. Given curve…

Q: Find the length of the curve r(t) (e" cos(2t), e" sin(2t), e"), -2 sts 2 %3D

A: I am attaching image so that you understand each and every step.

Q: Let F(x, y) = 4yi + (2æ + ev* ); Calculate ,F · dr, where C is the circle of radius 2 centered at…

A: Given that F(x,y)=4yi+2x+ey2j The objective is to calculate ∫CF.dr where C is the circle of radius 2…

Q: 5. Tangent B. Determine the center and radius of each circle: 6. x2 + y2 =16 7. (x-2 )2+ y2 - 13 8.…

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Q: If C is a circle of radius 8 centered at the point ( 0, 5 ), then evaluate pain(2dr + (11æ sin(y*…

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Q: 2. KS is tangent to the circle at T. Secant KR contains P, the center of the circle. PR and PT are…

A: Firstly draw a circle with center P Now draw a tangent KS at point T

Q: Find the length of arc of the curve y = In r from r = 3 to r= 9. 8

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Q: 4. Let C denote the circle |z – 2i| = 1, taken in the usual counterclockwise orientation. Compute by…

A: Given: Let C  denote the circle z-2i=1 z-2i=1x+iy-2i=1x+iy-2=1 So, Centre of circle will be 0,2 and…

Q: 2.2 Prove that e? dz] < 3 +++1 where C is the arc of the circle |2| = 3 from z = 3i to z = -3.

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Q: Find the length of the curve r(t) = (cos 3t, sin 3t, 2t3/2),0 sts 3. %3D

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Q: The unit circle x² + y=1 can be wrriten in parametric form as x = cos(0) and y : = sino. dy and…

A: Follow the procedure given below

Q: Express the circle specified by x = 2 cos(0) y = 1+ 2 sin(0) in Cartesian coordinates and find the…

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Q: A- Using Simpson s Rule to estimate the area of the circle (r-4), c (1, 0) with (n=4). B- Prove…

A: The equation of a circle having center C(1,0) and radius r=4 is given by: x-12+(y-0)2=42…

Q: 1. Use Green's Theorem to evaluate |F. dr, where F(r, y) = (3y- esin, 7x + Vy + 1) and C is the…

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Q: Suppose an arc of length s lies on the unit circle x + y = 1, starting at the point (1,0) and…

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Q: If C is a circle of radius 3 centered at the point ( 3, -4 ), then evaluate £(3y – ein(=) ) dz +…

A: The integral is given by ∮C3y-esinxdx+10x-siny3+ydy Where, C is a circle of radius 3 centered at the…

Q: 13. Let C be the unit circle |z| = 1, described in the positive sense. Determine the %3D value of c…

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Q: Express the circle specified by x = 2 cos(0) y = 1+2 sin(0) in Cartesian coordinates and find the…

A: Given: x=2cos θ y=1+2sin θ Now, x2=cos θ and y-12=sin θ Squaring both: x22+y-122=cos2θ+sin2θ…

Q: Given the cardioid r= 3(1+cosθ) 0 ≤ θ ≤ 2π Determine in wich points the cardiod has vertical…

A: Differentiate the equations r=31+cosθ and x=rcosθ with respect to θ, to find drdθ and dxdθ.…

Q: The curve y V4 – x², – 1 < x < 1, is an arc of the circle x² + y? = 4Find the area of the = 1…

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Q: Verify Green's theorem for $[xy² dx + x²y dy], where y is the circle x? + y² = 4.

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Q: If C is a circle of radius 9 centered at the point ( -5, 5 ), then evaluate $ (2y – esin ( x ) ) dæ…

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Q: Find the length of the curve. r(t) = (9t, 3 cos(t), 3 sin(t)), -5 sts 5

A: To determine the length of the curve.

Q: B. Find the length of the circle of radius r defined parametrically by x = r(v1 – sin t) and y =…

A: We need to find the length of the circle which is parametrically defined as below.

Q: C is the part of the circle of radius 3 in the first quadrant from (3,0) to (0,3) and F = (1, -y),…

A: Given, C is part of circle of radius 3 in the first quadrant from (3,0) to (0,3) and F=[1,-y] The…

Q: ) Let C be the arc from the point (3,0) to the point (0,3) on the circle x² + y² = 9. The value of…

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Q: Express the circle specified by x = 2 cos(0) y = 1+ 2 sin(0) in Cartesian coordinates and find the…

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Q: Consider a curve given by Ř(t) = (2 cos t, 12t + 3, -2 sin t). Let f(t) be a function such that f(1)…

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Q: Express the circle specified by a = 2 cos(0) y = 1+2 sin(0) in Cartesian coordinates and find the…

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Q: Evaluate |*(x + 7) – 2y ds where C is the circle of radius 1 centered at (-3,0) and lying on the…

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Q: 2.2 Prove that e zp- 3 where C is the arc of the circle |2| = 3 from z = 3i to z = -3.

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Q: Express the circle specified by x 2 cos(0) y = 1+ 2 sin(0) in Cartesian coordinates and find the…

A: Note: Equation of a circle with radius r and center at (h, k) is given by (x-h)^2 + (y-k)^2 = r^2

Q: Express the circle specified by x = 2 cos(0) y = 1 + 2 sin(0) in Cartesian coordinates and find the…

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Q: Use Green's Theorem to evaluate - – In(x² + y²))dx + 2 tan¬²(y/x) dy, C is the circle (x - 4)² + (y…

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Q: 2. Use Green's theorem to evaluate fe e-x³ dx + (5x + sin(y²)) dy, where C is the circle x² + y² = 4…

A: Please see the below picture for detailed solution.

Q: Find the exact length of the curve. x = 9 cos(t) − cos(9t), y = 9 sin(t) − sin(9t), 0 ≤ t ≤ pi

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Q: Express the circle specified by r = 2 cos(0) y = 1+ 2 sin(0) in Cartesian coordinates and find the…

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Q: Express the circle specified by x = 2 cos(0) y = 1 + 2 sin(0) in Cartesian coordinates and find the…

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Q: The curve C is the circle of radius 19 contained in the plane z = 19 and centered around the z-axis,…

A: …

Q: Show that = sin t if t>0 and C is the circle z] = 3. 2mi Jz+1

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Express the circle specified by x = 2 cos(0) y = 1 +2 sin(0) in Cartesian coordinates and find the…

A: Given that,   x=2 cosθ and y=1+2 sinθ

Q: If x = 8cos3theta and y = 8sin3theta, find the total length of the curve swept out by the point…

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Q: Using the definition, find the length of the circle of radius r defined parametrically by x = r cos…

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Q: (a) Evaluate sin 2z -dz, 3z -ĝi where C is an anticlockwise unit circle centred at the origin.

A: Follow the procedure given below.

Q: The DE for the family of circles of radius 9 is: A [1+ (y')²]³– 81=0 B [1+ (y')²]²- (» )²-[1+…

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Q: Find the length of the curve. r(t) = (3t, 3 cos(t), 3 sin(t)), -3 sts 3

A: For the curve r(t) = f(t) , g(t), h(t)On the interval [a, b]The length is given by L =…

Q: If C is a circle of radius 3 centered at the point (-4, 2 ), then evaluate £ (2y - eh (=) ) da + (6z…

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Q: If C is a circle of radius 6 centered at the point ( 3, -2 ), then evaluate 6y – esin ( z ) ) dæ +…

A: Given if C is a circle of radius 6 centered at point 3,-2 then  We have to evaluate…

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.