Show the area formula for polar coordinates gives the expected answer for the area of the circle r=a centered at the origin
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Show the area formula for polar coordinates gives the expected answer for the area of the...
3. Polar Coordinates. (a) Given a rectangular coordinate point (x, y), how do you compute the equivalent polar coordinates: (r, 0)? (b) Given a polar coordinate (r, o), how do you compute the equivalent rectangular coordinate: (x, y)? (c) Consider the drawing in Figure 1. Compute the coordinate of each small circle. (d) What if the circle is centered at the point (cx, cy) (and not the origin). How does the formula change?
a) Write the iterated integral in rectangular coordinates that gives the surface area of the graph of x + y2 + 2z = 1, R = {(x,y) x² + y² 1} b) Evaluate this integral by changing to polar coordinates.
Use a double integral in polar coordinates to find the area of the region bounded on the inside by the circle of radius 5 and on the outside by the cardioid r=5(1+cos(θ))r=5(1+cos(θ))
6) a) Find the area of the circle (x-3)+ y'- 9 using polar coordinates b) Find the area of the region below the cardioid r = 1 + cos(9) and above y = 1x1. 6) a) Find the area of the circle (x-3)+ y'- 9 using polar coordinates b) Find the area of the region below the cardioid r = 1 + cos(9) and above y = 1x1.
If you can show work to prove your question that would be greatly appreciated. Polar coordinates: 13. Describe the following curves: a./ r = 3, b./ r cos 0 = 3 c./ r sin 0 = 3 14. Convert from polar to rectangular coordinates: a./ r = 2 sino b./ r = 2 cos cos 15. Convert from rectangular to polar: a./ y=x2, b./ eV +2+y2 = 1 c./ ry = 1 Area calculation in polar coordinates. - sin
a- find equation in terms of polar coordinates that represent the figure b - determine the area contained within the circle given in part (a) by using tbe definite integral c- use def of the derivitive in polar coordinates to find points (r, (theta)) on the circle where vertical tangent line exists 4 OE 6 4 12 4 -4.
a) The origin in polar or cylindrical coordinates as compared to the rectangular coordinate system ______________________ A. is fixed. B. none C. follows particle. D. is body centered. b) If r = q 2 and q = 2t, find the magnitude of r and q when t = 2 seconds. A. 4 cm/sec, 2 rad/sec2 B. 8 cm/sec, 16 rad/sec2 C. 16 cm/sec, 0 rad/sec2 D. 4 cm/sec, 0 rad/sec2 c) Cylindrical or polar coordinates are a suitable choice for...
just make circle questions which 2,(b) and 3,(i) thank you 2. (Polar Coordinates: Polar Plots). (a) Consider the curve given in polar coordinates (i) Use a scientific calculator to fill in the following table with the (approximations of) values of the function r(0) on π, π r(e) (the approximations of the values r(e) must be good to at least two decimal places). (i) Use the graph paper for the polar coordinate system (attached to the assignment sheet) to plot the...
5. (a) Give an equation in polar coordinates that represents the circle below y 4 4 6 (b) Find the area contained within the circle given in part (a) by using the definite integral for area in polar coordinates Use the definition of the derivitive in polar coordinates to find the points, (,0), on the circle where vertical tangent lines exist
5. (a) Give an equation in polar coordinates that represents the circle below y 4 4 6 (b) Find the area contained within the circle given in part (a) by using the definite integral for area in polar coordinates Use the definition of the derivitive in polar coordinates to find the points, (,0), on the circle where vertical tangent lines exist