Good morning, please tell us how to graph on a map the graph that is seen in the image with those colors and their areas for the following exercise:

1. Draw the graph and find the area of ​​the region that is inside the cardioid r=2+2 cosθ and outside the circumference r=3

Calculate the area of ​​the region common to the two regions limited by the following curves:

r1= -6*cos(θ) Circle
r2= 2-2*cos(θ) Cardioid

Good morning, please, how do I graph the vector that you see in the image ( Addition and Subtraction)? I have seen that there is an option called VectorSumPlot but I don't care about the graph or the result.

Good morning, I am trying to graph the length of the curve but Maple gives me an error. Please if someone can tell me how I can graph the curve in 2d and 3d.

plot([t*sin(t), t*cos(t), (2*sqrt(2))/3*t^(3/2),t, t = 0 .. Pi]) -> error

Good evening, how do I get Maple to graph and shade the intersection area of ​​the curves? Can someone please tell me how to do this? I have used implicitplot but I don't know how to shade the area.

Good morning, please, could you tell me how to graph this solid of revolution using implicitplot and shade the intersection zone as seen in the graph.

x=y-y^2

x=y^2-3

Around x=2