Solve the problem.Let M =  and N = . Show that  where R is the region bounded by the unit circle C centered at the origin. Why is Green's Theorem failing in this case?

What will be an ideal response?


Answers will vary. Notice that M and N are not defined at (0,0), which is contained inside the region R.

Mathematics

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Find the center and radius of the circle with equation . ?

A. Center: (7, 2)Radius: 5 B. Center: (-7, 2)Radius: 25 C. Center: (7, -2)Radius: 25 D. Center: (7, -2)Radius: 5 E. Center: (-7, 2)Radius: 5

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Test the equation for symmetry with respect to the specified axis, line, or pole.r = 4 - 4 cos ?; the y-axis 

A. Symmetric about the y-axis B. May or may not be symmetric about the line y-axis

Mathematics

Provide an appropriate response.The following graph represents the speed of a truck as a function of time.  a.What is the speed of the truck at 14 seconds?  b. Identify and interpret the intercepts.

A. a. 40 mph. b. (8, 40); (24, 40) At 8 and 24 seconds, the speed is 40 mph. B. a. 30 mph b. (0, 0); (32, 0) At 0 and 32 seconds, the speed is 0 mph. C. a. 40 mph b. (0, 0); (32, 0) At 0 and 32 seconds, the speed is 0 mph. D. a. 40 mph b. (0, 0) At 0 seconds, the speed is 0 mph.

Mathematics

Graph the parabola and label the vertex. Find the y-intercept.y = -32 - 4

A. vertex , y-intercept (0, 22.75)

B. vertex , y-intercept (0, -22.75)

C. vertex , y-intercept (0, -22.75)

D. vertex , y-intercept (0, -22.75)

Mathematics