@ 7. Show that $ i 2π e² dz = sino where C is the circle |z| = 20. z²+w² 2

Q: Suppose R is the shaded region in the figure, and f(x, y) is a continuous function on R. Find the…

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Q: b) Use Greens theorem to findf x² ydx – xy?dy where C is the circle x? + y? = 4 going counter clock…

A:

Q: Evaluate ∫ C ( 2 + x^2 y ) d s , where C is the upper half of the unit circle.

A: We have to evaluate the line integral: ∫C2+x2yds where C is the upper half of the unit circle.

Q: 4. What is the equation of a line parallel to the diameter of circle A, with a center at (-5,7) and…

A: Given query is to find the line which parallel to the given line.

Q: 7. The radius of the circle whose equation x + 6x + y – 6y – 7 = 0 is

A: Your answer Radius =5

Q: Use the Distance Formula to show that the circle with center (0, 0) and radius length r has the…

A: Given: x2+y2=r2 Formula used: OA=x-02+y-02

Q: The general equation of the circle is x²+y²+Dx+Ey+F=0,where D,E and F are real numbers? True or…

A: We know that, the general form of the equation of a circle is x2 + y2 + 2gx +2fy + c = 0. Here, the…

Q: Evaluate 12x-7 dz where (2213) (2-1)² Cis the circle Z = 2

A: Approach to solving the question:  Detailed explanation:

Q: Which projection of (cost, cos 2t,sin t) is a circle?

A: Which projection of (cost, cos 2t,sin t) is a circle?

Q: 2. The circle, if the center of the circle of radius 3 lies on the line x + 2y = 4 and it is tangent…

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Q: rotate the point (2,8) by the (3/5,4/5) about the origin (0,0). (3/5,4/5) is on the unit circle.

A: Given data, Point A(2,8)

Q: 3. The distance between two distinct points (x1, y1) and (x2, y2) is given by the formula

A: Given: Points x1, y1 and x2, y2

Q: 18. The equation of a circle with center on the y-axis and passing through the origin and the point…

A: It is given that the circle is passing through the origin (0,0) and the point (2,3). As the general…

Q: Find the radius and center of a circle with the equation x2 + y2 + 4x – 8y = 16.

A: Given: Equation of circle x2 + y2 + 4x - 8y = 16 To find out: Radius and center of circle.

Q: 6. Show that the line with equation y = 3x – 5 is a tangent to the circle with equation x² +y? + 2x…

A: Equation of line : y=3x-5 Equation of circle : x2 + y2 +2x -4y -5=0 We have to prove that the line…

Q: Write the equation in standard form of the circle whose center is at (0, 0) and that is tangent to x…

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Q: Find the distance d between the points (1, 3) and (5, 6).

A: Our Aim is to find the distance between the points (1,3) and (5,6).

Q: 8. Is the point (2, –7) on the circle defined by (x + 6) + (y + 1) = 100?

A: Given the equation of a circle, x+62+(y+1)2=100                   ...(1)