Find the volume of the solid of revolution formed by rotating about the x--axis the region bounded by the given curves.
f(x)=x-4, y=0, x=4, x=10.

Step-by-step explanation:

For this case we are interested on the region shaded on the figure attached.

And we can find the volume with the method of rings.

The area on this case is given by:

And the volume is given by the following formula:

For our case our limits are x=4 and x=10 so we have this:

And if we do the integral we got this:

And after evaluate we got this:

6mm^3 or .6cm^3

      216

      /   \

  36     6

  /   \     /

6     6   6

factor trees are nice.

unless you made a typo, the answers are both a and c.

step-by-step explanation:

1.5/3 is .5 whereas 3/9 is .3333333 not proportional

22/33 is .66666 and 4/6 is also .66666 proportional

2/4 is .5 whereas 142/213 is .66666 not proportional

14/7 is 2 and 7/3.5 is also 2 proportional

you could've also checked it by doing this simple division:

if the larger fraction divides with the smaller fraction to equal 1, it is proportional. so let me show you what i mean:

when i divide 22/33 by 4/6 i get 1, so we know it is proportional, and it is the same with 14/7 and 7/3.5. now if i divide 3/9 by 1.5/3 i get .66666 so therefore we know it is not proportional.

there are many ways to do this so i wanted to show you some possible ways.