Use Green's Theorem to evaluate the integral (x² - y)dax + 3xdy where C is the circle x² + y² = 1 oriented counterclockwise. NOTE: Enter the exact answer. #7 f (x² − y) dx + 3xdy -

Q: Q3: Evaluate z + 1 $c (z6 + 5z5 + 4z¹) (z + 4) dz where C is the circle |z1| = 5

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Q: Use Desmos to graph y=sqrt(2−x). Find the maximal area of a rectangle with the following properties:…

A: use the demos to graph the function and draw a rectangle according to the given instructions as we…

Q: Find the values of a for which the point (a-1,a+1) lies in the larger segment of the circle…

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Q: Find the values of a for which the point (a-1,a+1) lies in the larger segment of the circle…

A: The point a-1, a+1 lies in the larger segment of the circle x2+y2-x-y-6=0 made by the chord whose…

Q: Let f (2) = . Let C be the circle |2| = 2 in the counter-clockwise direction. What is | f (z) dz?…

A: This problem based on Cauchy's Integral formula. See the solution.

Q: i æ² + y? = 30 and (x + 1)? + (y – 1)² = 6 | ii (æ + 3)? + (y – 2)² = 9 and (x + 7)? + (y + 1)? = 4…

A: (i) The given circle is: x2+y2=30        ....1x+12+y-12=6       ....2

Q: P(t) denotes the point on the unit circle U that corresponds to the real number t.

A: The x-coordinate of any point on the unit circle represents cosine value and y-coordinate represents…

Q: Write a paragraph explaining how the distance formula giving the distance between two points (x1,…

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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: Let C be the circle given by x² + y² = 1. Evaluate √(-2x²y + cos x)dx + (2 xy² + y²e³)dy going in…

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Q: 2. Write the equation of the following circle ingeneral form and standard form. Show your work. (-4,…

A: Given query is to find the equation of the circle in stany and general form.

Q: Find the values of a for which the point (a-1,a+1) lies in the larger segment of the circle…

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Q: Let C be the upper half (yzo) of the circle x² + y2 = 16 from (4,0) to (-40). √ (ax 2-3y) ds =

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Q: Use Green's Theorem to find (8y + x) dx + (y + 2x) dy, where C: The circle (x - 4)2 + (y-3)2 9 541…

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Q: The radical center does not existif the circles are concentric TRUE FALSE

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Q: If the radical axis of the circles x² + y² + 2 gx + 2 fy+c= 0 and 2x² + 2y² +3x+8y +2c=0 touches the…

A: The radical axis of the given circles             x2+y2+2gx+2fy+c=0and      x2+y2+(3/2)x+4y+c=0 is…

Q: (b) Evaluate 2 + 5z zdz, 22 — 2х — 3 - where C' is a circle |z + 2| = 2.

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Q: O COsZ Sc (5 dz T. 4 2

A: Consider the equation, z-π2=1 This equation represents a circle plotted on the Argand Plane, with…

Q: e2z dz, I (z+ 1)* (b) Where C is a circle |z| = 3

A: The given integration is ∮ce2zz+14dz where c is the circle z=3 Here the pole z=-1,which is of order…

Q: Please show how the following Figure can be linearly separated by mapping from the features (X1, X2)…

A: In many machine learning scenarios, data points that are not linearly separable in the original…

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: M2. Let C be the positively oriented circle |z1|-2 in the complex plane. Which of the following is…

A: Given C is the positively oriented circle  in the complex plane. We need to find the value of line…

Q: Find the values of a for which the point (a-1,a+1) lies in the larger segment of the circle…

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Q: Integrate counterclockwise dz, C the circle with z2 + 16z + 63 center –7 and radius 2. dz z² + 16z +…

A: Use Cauchy Residue theorem to evaluate this integral.

Q: enter-radius form of the equation of t

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Q: Find the number of common tangents to the circles x\power{2}+y\power{2}+2x+8y-23=0 and…

A: For x2+y2+2x+8y-23=0 ,C1≡(-1,-4),r=210for x2+y2-4x-10y+9=0,C2≡(2,5),r=25now C1C2=distance between…

Q: Two circles have equations of x2 + y2 – 4x – 4y + 4 = 0 and x2 + y2 – 4x + 8y + 4 = 0. Compute the…

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Q: ㅠ Use Green's theorem to find: where C is the circle x² + y² = 4 going counter-clockwise. -8T […

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Q: Use Green's Theorem to evaluate §+(x² - y²)ẩx + xảy, where C is the circle x² + y² = 9. Select one:…

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Q: If the radical axis of the circles x² + y² + 2gx + 2 fy+c= 0 and 2x² + 2y² + 3x +8₂ touches the…

A: Given: Here the radical axis of the circles given x2+y2+2gx+2fy+c=02x2+2y2+3x+8y+2c=0 we have to…