Given:
The radius, r=4x
The height,
![h=21xy^2](https://tex.z-dn.net/?f=h%3D21xy%5E2)
To find the volume of the cone:
The volume of the cone formula is,
![V=\frac{1}{3}\pi r^2h](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%20r%5E2h)
Substitute the values of r and h in the above formula we get,
![\begin{gathered} V=\frac{1}{3}\pi\times(4x)^2\times21xy^2 \\ =\frac{1}{3}\pi\times16x^2\times21xy^2 \\ =\pi\times16x^2\times7xy^2 \\ =112\pi x^3y^2 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20V%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%5Ctimes%284x%29%5E2%5Ctimes21xy%5E2%20%5C%5C%20%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%5Ctimes16x%5E2%5Ctimes21xy%5E2%20%5C%5C%20%3D%5Cpi%5Ctimes16x%5E2%5Ctimes7xy%5E2%20%5C%5C%20%3D112%5Cpi%20x%5E3y%5E2%20%5Cend%7Bgathered%7D)
Hence, the volume of the cone is
![V=112\pi x^3y^2](https://tex.z-dn.net/?f=V%3D112%5Cpi%20x%5E3y%5E2)
Thus, the correct option is option D.
Answer:
x=2
Step-by-step explanation:
Answer:
C. f(x) = 5·log(x +1)
Step-by-step explanation:
To shift the graph of a function g(x) to the right by "h" units, replace x in the definition with x-h. That is, g(x-h) will be the same graph, but shifted right by h units.
Here, we want h=-1. That is, we want the shift to be the opposite of right 1 unit. So, the shifted function is ...
g(x-(-1)) = g(x+1)
For g(x) = 5·log(x), the shifted function will be ...
f(x) = g(x+1)
f(x) = 5·log(x+1)
B is correct because
4 + 16 < 28