Consider the region bounded by the curves 2. y = 3 + x , y = 3, and x = 2. find the volume of the solid obtained by rotating this region about the axis y = 3.

units cubed

Step-by-step explanation:

Let's look at a point (x,y) on the line y=3+x. The height between (x,y) and the x-axis is y.  We want the distance from the axis of rotation which is y=3 so the height (or distance between) point (x,y) on y=3+x and y=3 is y-3.  

y-3 is the radius in terms of y.

(3+x)-3=x is the radius in terms of x.  I replaced y with 3+x since we have y=3+x.

The area of the circle I drew is

To find the volume we must integrate the area of the circle we found between the bounded lines x=0 and x=2.

units cubed

step-by-step explanation:

two pairs of adjacent sides are of equal length. this implies that one diagonal divides the kite into congruent triangles, and so the angles between the two pairs of equal sides are equal in measure. it also implies that the diagonals are perpendicular.

the ordered pairs for the given function are of the form