Question

Sketch the region enclosed by the graphs of:
x = 0, 6y – 5x = 0, and x + 3y = 21.
Find the area.


Find the volume of the solid formed when the region is revolved around the y-axis.

Answer 1

Hello again!
From the previous problem, you know that the line x=0 is vertical. I'd suggest you draw it.

The other two lines are just that: lines. But their slopes are neither infinity nor 0. What is the fastest way you can think of of drawing the lines 6y – 5x = 0, and x + 3y = 21?

It's important that you be able to identify accurately the coordinates of the points where these graphs intersect. There will be 3 such intersections.

From this point on, how may I help you further?

Answer 2

The main thing is that I don't know how to graph those points. I just don't know.

Answer 3

x=0 is just a vertical line. Any point on this line has the x-coordinate 0, and the y-coord. could be any real number.

x + 3y = 21 is just a little bit more of a challenge. My suggestion in this case is to find the x- and y-intercepts. To find the x-int., let y = 0, producing x = 21; then the x-intercept is (21,0). To find the y-int., let x = 0, producing 3y=21, or y=7. Then the y-intercept is (0,7).

Answer 4

Please graph x = 0 now, along with the two intercepts (21,0) and (0,7). Once you've done that, draw a line through (21,0) and (0.7); this line represents x + 3y = 21.