Answer:
The volume of the solid is 
Step-by-step explanation:
In this case, the washer method seems to be easier and thus, it is the one I will use.
Since the rotation is around the y-axis we need to change de dependency of our variables to have 
. Thus, our functions with 
as independent variable are:
For the washer method, we need to find the area function, which is given by:
![A=\pi\cdot [(\rm{outer\ radius)^2 -(\rm{inner\ radius)^2 ]](https://tex.z-dn.net/?f=A%3D%5Cpi%5Ccdot%20%5B%28%5Crm%7Bouter%5C%20radius%29%5E2%20-%28%5Crm%7Binner%5C%20radius%29%5E2%20%5D)
By taking a look at the plot I attached, one can easily see that for a rotation around the y-axis the outer radius is given by the function 
and the inner one by 
. Thus, the area function is:
![A(y)=\pi\cdot [(\sqrt{y} )^2-(y^2)^2]\\A(y)=\pi\cdot (y-y^4)](https://tex.z-dn.net/?f=A%28y%29%3D%5Cpi%5Ccdot%20%5B%28%5Csqrt%7By%7D%20%29%5E2-%28y%5E2%29%5E2%5D%5C%5CA%28y%29%3D%5Cpi%5Ccdot%20%28y-y%5E4%29)
Now we just need to integrate. The integration limits are easy to find by just solving the equation 
, which has two solutions 
and 
. These are then, our integration limits.
Answer:
21
Step-by-step explanation:
Using alternate interior angles, we can conclude that angle C is equal to X (the 3rd, unmarked angle in the center triangle)
To find that 3rd angle, we can do 180 - 105 - 54. This is because all angles in a triangle must equal 180. Using this, we find that angle C is equal to 21. By the law, X must also equal 21.
Answer:
the answer is c
Step-by-step explanation:
Answer:
Cone Volume = (PI * radius^2 * height) / 3
Cone Volume = (PI * 6^2 * 12) / 3
Cone Volume = 452.3893421169 cubic inches
Source: http://www.1728.org/volcone.htm
Step-by-step explanation:
Answer:
b) 18,342
Step-by-step explanation:
18,342 es divisible por 6 porque es divisible por 3 y es divisible por 2
