Answer:
3π square units.
Step-by-step explanation:
We can use the disk method.
Since we are revolving around AB, we have a vertical axis of revolution.
So, our representative rectangle will be horizontal.
R₁ is bounded by y = 9x.
So, x = y/9.
Our radius since our axis is AB will be 1 - x or 1 - y/9.
And we are integrating from y = 0 to y = 9.
By the disk method (for a vertical axis of revolution):
![\displaystyle V=\pi \int_a^b [R(y)]^2\, dy](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V%3D%5Cpi%20%5Cint_a%5Eb%20%5BR%28y%29%5D%5E2%5C%2C%20dy)
So:

Simplify:

Integrate:
![\displaystyle V=\pi\Big[y-\frac{1}{9}y^2+\frac{1}{243}y^3\Big|_0^9\Big]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V%3D%5Cpi%5CBig%5By-%5Cfrac%7B1%7D%7B9%7Dy%5E2%2B%5Cfrac%7B1%7D%7B243%7Dy%5E3%5CBig%7C_0%5E9%5CBig%5D)
Evaluate (I ignored the 0):
![\displaystyle V=\pi[9-\frac{1}{9}(9)^2+\frac{1}{243}(9^3)]=3\pi](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V%3D%5Cpi%5B9-%5Cfrac%7B1%7D%7B9%7D%289%29%5E2%2B%5Cfrac%7B1%7D%7B243%7D%289%5E3%29%5D%3D3%5Cpi)
The volume of the solid is 3π square units.
Note:
You can do this without calculus. Notice that R₁ revolved around AB is simply a right cone with radius 1 and height 9. Then by the volume for a cone formula:

We acquire the exact same answer.
Well, a linear function is proportional, a straight line (on a graph). And the numbers must not have the same answer. For instance, if the X input is 5, and the Y output is 7. And then another X input is 5, and the Y output is 8, that's non-linear.
So, the Answer would be the third graph. This is because the X values are steadily increasing, and so are the Y values.
For the X and Y values, for each time X increases by 1, Y increases by -8. This is, linear because both sides are constantly and evenly increasing.
Prime numbers are numbers that we can only divide by 1 and it self.
example- 2 can only be divided by 2 and 1
composite numbers are numbers we can divide by two or more numbers
example- 4 can be divided by 1,2 and 4.
Answer:
c
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
-3x-2
-2x+11
+3x +3x
-2
x+11
-11 -11
-13
x