Please try to answer both B and C part of the question. 6. Evaluatež dz, whereti-clockwise din(b) C is the semicircle z = 2 + 3i + 5e",34Tin the anti-clockwise3direction.[Hint: Try using polar system].(c) C is the semicircular path from (0,0) to (4, 4) with radius 2/2 and centerat (2,2).[Hint: Express the equation of the semicircle in a similar formgiven in 6(b)].

Answered: Image /qna-images/answer/146bed32-f36d-438e-b318-bcd25eacb2fe.jpg

Answered: 6. Evaluate ž dz, where ti-clockwise…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section: Chapter Questions

Problem 18T

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Similar questions

Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?
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Find the equation of the tangent plane to the hyperboloid in 2 sheets x2 - y2 - z2 = 4 at the point (3,2,4).
Sketch the surfaces CYLINDERS z = y2 - 1
Find the center C and the radius a for the spheres 3x2 + 3y2 + 3z2 + 2y - 2z = 9
Find the equations of all spheres in R3 of radius R = 3 passing through the point (7 ,8, 9)that their centers lie on the z-axis.
What is the size of the largest segment parallel to the y axis inside the ellipsoid determined by the equation below? 4x2+5y2+3z2+6x+8y+5z−4=0
The parametric curve x=2sin(t)+2, y=3cos(t)-2 describes a clockwise traveling vertical ellipse with centered at (2,-2). T or F?
Find an equation in spherical coordinates whose graph is the parapoloid Z=(X^2)+(Y^2)
1. Consider the area enclosed between the circle x^2 + y^2 = 4, the line y = 3, y = x, and y = -x. (a) Express these Cartesian equations as polar equations.
Suppose that a cylindrical container of radius r and height L is filled with a liquid with volume V , and rotated along the y-axis with constant angular speed ω. This makes the liquid rotate, and eventually at the same angular speed as the container. The surface of the liquid becomes convex as the centrifugal force on the liquid increases with the distance from the axis of the container. The surface of the liquid is a paraboloid of revolution generated by rotating the parabola y = h + ω2x2/2g around the y-axis, where g is gravitational acceleration and h is shown below. (You can take g=32ft/s2 or 9.8m/s2). Express h as a function of ω. (2) At what angular speed ω will the surface of the liquid touch the bottom? At what speed will it spill over the top? (3) Suppose the radius of the container is 2 ft, the height is 7 ft, and the container and liquid are rotating at the same constant angular speed ω. The surface of the liquid is 5 ft below the top of the tank at the central…

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