I guess you mean
![\sec^6x(\sec x\tan x)-\sec^4x(\sec x\tan x)=\sec^5x\tan^3x](https://tex.z-dn.net/?f=%5Csec%5E6x%28%5Csec%20x%5Ctan%20x%29-%5Csec%5E4x%28%5Csec%20x%5Ctan%20x%29%3D%5Csec%5E5x%5Ctan%5E3x)
On the left side, we have a common factor of
, so that
![\sec^6x(\sec x\tan x)-\sec^4x(\sec x\tan x)=\sec^5x\tan x(\sec^2x-1)](https://tex.z-dn.net/?f=%5Csec%5E6x%28%5Csec%20x%5Ctan%20x%29-%5Csec%5E4x%28%5Csec%20x%5Ctan%20x%29%3D%5Csec%5E5x%5Ctan%20x%28%5Csec%5E2x-1%29)
Recall that
![\sec^2x=1+\tan^2x](https://tex.z-dn.net/?f=%5Csec%5E2x%3D1%2B%5Ctan%5E2x)
from which it follows that
![\sec^5x\tan x(\sec^2x-1)=\sec^5x\tan x\tan^2x=\sec^5x\tan^3x](https://tex.z-dn.net/?f=%5Csec%5E5x%5Ctan%20x%28%5Csec%5E2x-1%29%3D%5Csec%5E5x%5Ctan%20x%5Ctan%5E2x%3D%5Csec%5E5x%5Ctan%5E3x)
Answer:
108 cubes
Step-by-step explanation:
A rectangular prism with a volume of 4 cubic units is filled with cubes with side lengths of 1/3 . How many 1/3 unit cubes does it take to fill the prism?
Step 1
We find the volume of the cubes
Side length = 1/3 units
Volume of a cube = Side length ³
Hence,
(1/3 units)³ = 1/27 cubic units
Step 2
A rectangular prism with a volume of 4 cubic units.
The number of 1/3 unit cubes that would fill this rectangular mrism is calculated as:
4 cubic units ÷ 1/27 cubic units
= 4 ÷ 1/27
= 4 × 27/1
= 108 cubes