12: A tangent to the circle x² + y? = 5 at the point (1,2) and th circle x? + y² – 8x + 6y + 20 - A) Touches B) Cuts at real points C) Cuts at imaginary points

Q: 22 Calculate 8 - z dz, where C is the circle of radius 7, centre 0, negatively oriented.

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Q: A circle has its center at (3,-2) is tangent to the line 3x+4y-26=0. Compute the point of tangency…

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Q: In the given figure, CF and BF are tangents to crcle A and intersect at F, a point on circle E. BF…

A: Given Figure:

Q: 2. Find the coordinate of the points on the cardioid r=1- cose at which there is a horizontal…

A: We are given the polar curve: r = 1- cosθ use formula:         x=r cosθy=r sinθ then,  dxdθ=-sinθ+2…

Q: A sphere in the first octant is tangent to the three coordinate planes. What is the radius of the…

A: Given:- A sphere in the first octant is tangent to the three coordinate planes To find:- Radius of…

Q: Use Green's theorem to evaluate 2y3 dx – x³y2 dy, where C is the positively oriented circle of…

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Q: Suppose surface #1 is defined by o =45° , 0 <ps9, 0 < z< 6 and surface #2 is defined by 0 =56.3° The…

A: given:

Q: Let C denote the circle of radius 1 in R2 centered at the origin, oriented counterclockwise. for…

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Q: Use Green's Theorem to find SF ·dř where F = (y³, –x³) and C is the circle x² + y² = 3. %3D %3D

A: The given vector is  F = y3i - x3j

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

A: Mathematical methods used to solve equations or evaluate integrals or solve differential equations…

Q: 4) The lemniscate curve (x2 + y² )² = 4(x² – y²) was discovered by Jacob Bernoulli in 1694, who…

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Q: Demonstrate that the circles (x- 2)² + y² = 2 and x? + (y – 2)? = 2 share tangent at point (1,1),…

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Q: Verify Green's Theorem where F1=y^2-7y , F2=2xy+2x and the curve C is a circle x^2+y^2=1

A: Given: F1=y2-7y , F2=2xy+2x and C is a circle i.e., x2+y2=1 As, we have:…

Q: b) Calculate again an approximate value of the length L of the curve arc from the previous…

A: The distance (d) between two points (x1,y1) and (x2,y2) is given by the equation;…

Q: The distance from a point P1(x1, Y1) to the line ax + by +c = 0 is laxi + by, + c] Va? + b2 Use this…

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Q: Consider the curve C parametrized by x = -1 + 6 sin t and y 6 cos t for -n <t< 9n. %3D Then C is a…

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Q: Calculate the area of the circle r = 3 sin θ bounded by the rays θ = π/3 and θ = 2π/3.

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Q: If C is the line segment that first connects point 2 to point i, and then the spring piece that…

A: Consider two regions C1 and C2 then these can be defined as follows, Thus, C=C1UC2 The conjugate…

Q: Let F=-yi+xj and let C be a curve consists of the line segment C₁ from (0,0) to (4,0) followed by…

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Q: 9. Given: a circle with a center O and a straight line with a point M on it (they do not intersect).…

A: solution is given below....

Q: 16 6xy ds, where C is the right half of the circle x² + y² = 4. Evaluate the line integral

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Q: Verify Green's Theorem in the plane for F = -3y³i+ (3x3 + cos y)ĵ where C is the circle x² + y² =…

A: In this we have to verify green theorem.

Q: By using Green's theorem evaluate (4.ry – y') dr + (x + 3ry) dy where C is a closed curve starting…

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Q: Evaluate  ∫C (3y + exsinx) dx + (8x - ln(y3+2)) dy, where C is the circle x2 + y2 = 9  with positive…

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Q: 56 Consider points P and Q in the x-y plane, with P = (1,0) and Q = (0,1). The line integral 2|(xdx…

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Q: 17. Evaluate OF . • dr where C is the circle x +y² = 1, z = 0 and F=yi+zj +xk.

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Q: Use Green's theorem to evaluate $ 2y3 dx – x3y² dy, where C is the positively oriented circle of…

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Q: Let C be the line segment connecting 0 to ni. Then f. 1-e2z dz =

A: we have to find integration

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: Two tangent segments are drawn to sphere Q from external point E. Where A and B are the points of…

A: Given, E is an external point, and A and B are the points of tangency on sphere Q. The tangent of a…

Q: Evaluate fc 2x ds, where consists of the arc of the parabola y= x2 from to followed by the vertical…

A: The given line integral is ∫C2xdS where C is the arc of the parabola y=x2 from (0,0) to (1,1) and…

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

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Q: From the vertex (0, c) of the catenary y = c cosh(x/c) a line L is drawn perpendicular to the…

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Q: Consider a semicircle of radius 1. Let l be the line segment from one endpoint of the semicircle to…

A: Consider a semicircle of radius 1. Let l be the line segment from one endpointof the semicircle to…

Q: Tangents are drawn to the concentric circles x^(2)+y^(2)=a^(2) and x^(2)+y^(2)=b^(2) at right angle…

A: We have to Show that locus of their point of intersection is a 3rd concentric circle and find its…

Q: Let C be the curve of intersection of length of C from the origin to the poi

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Q: Let C be the arc of the circle |z| = R from -R to R. %3D Where R is a positive integer greater than…

A: We will solve this question only using the ML Inequality which is an elementary concept in complex…

Q: 6.2 Finl the Voune of the Selid enclosed by the curves y=eX, y=0 x=0,'= "about the x-axs.

A: Given: y=ex, y=0, x=0, x=1 From the given curves the bounded region is as shown below; Apply the…

Q: Let C consist of the part of the circle r +y = 4 from (2,0) to (0,2), Followed by the line segments…

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Q: By using Cauchy's integral formulas evaluate sin Tz2 + cos TZ² dz (z + 1)(z – 2) C and e2z dz (z –…

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Q: b. the length of the tangents from the point (2, 5) to the circle x +y² -14x-2y+34= 0

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Q: Verify Green's Theorem in the plane for F = -3y³i+ (3x3 + cos y)j where C is the circle x2 + y? =…

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Q: Use either a computer algebra system or a table ofintegrals to find the exact length of the arc of…

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Q: Use Green’s theorem to evaluate the line integral 2x2y dx + 6x3 dy, where C is the circle x2+y2 = 4,…

A: The answer is as follows:

Q: Q5. Prove that the circle {(r, y), x² + y? = 1} is not homeomorphic to the interval [-1, 1].

A: Here we can prove this question using topological property connectedness.

Q: Prove that the lengths of the two tangent segments to a circle from a point outside are equal. Use…

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

Q: find the volune of the selid generated by revolving regron bounded by the graphts of dhe ģiven…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: 2. Circles with fixed radius r and tangent to the y-axis.

A: Solution is given below:

Q: 17. It is a line coplanar with the circle and intersects it at one and only one point. A. secant B.…

A: if a line is coplanar with the circle this mean that circle and the line are on the same plane and…

Q: 8 Find the distance from (1, 0) to (0, 1) along (a} a straight line (b) a quarter-circle (c) a…

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