Question

R is bounded by the x axis, the y axis, and the line x=3 - y

Answer 1

sure looks like a triangle to me.

Answer 2

The area of the region is pretty simple since it's a triangle. If you graph it, it has endpoints at (3,0) and (0,3), telling us the dimensions of the triangle. Thus, the area of the region is (3*3)/2 = 9/2 = 4.5 square units

You don't give a revolution axis for the volume, so I'm assuming you just wanted the area of the region.

Answer 3

Could be x axis, could be y axis, no difference. However should say particularly if the axis is at some odd angle :)

Answer 4

But it also might not be either axis! Perhaps the lines x=5 or y=4 for instance. That volume would change.

Answer 5

[AI-generated answer — Explain Bot]

To determine the boundaries of the region R, we need to find the equations of the x-axis, y-axis, and the line x=3-y.

1. The x-axis is the horizontal line where y=0.
Equation: y = 0

2. The y-axis is the vertical line where x=0.
Equation: x = 0

3. The line x=3-y represents a diagonal line passing through the point (3,0) and (0,3).
To find the equation of this line, we can rearrange the equation to isolate y:
x = 3 - y
y = 3 - x

Now we have the equations for the boundaries of region R:
x-axis: y = 0
y-axis: x = 0
line x=3-y: y = 3 - x

By graphing these equations, you can visually see where the boundaries lie and how the region R is bounded by the x-axis, y-axis, and the line x=3-y.