The answer would simplify to 1/6.
Answer:

Step-by-step explanation:
Consider the given differential equation is



Taking all variables on right sides.


Let as assume,
and 
Find partial derivatives
and 
and 
Since
, therefore the given differential equation is exact.
The solution of the exact differential equation is






Answer:
The maximum height of the prism is 
Step-by-step explanation:
Let
x------> the height of the prism
we know that
the area of the rectangular base of the prism is equal to


so
-------> inequality A
------> equation B
-----> equation C
Substitute equation B in equation C

------> equation D
Substitute equation B and equation D in the inequality A
-------> using a graphing tool to solve the inequality
The solution for x is the interval---------->![[0,12]](https://tex.z-dn.net/?f=%5B0%2C12%5D)
see the attached figure
but remember that
The width of the base must be
meters less than the height of the prism
so
the solution for x is the interval ------> ![(9,12]](https://tex.z-dn.net/?f=%289%2C12%5D)
The maximum height of the prism is 
2km=2000m
25m=25m
2500cm=25m
3000mm=3m
Hence the longest is 2km=2000m
Answer:
313 ft
Step-by-step explanation:
If 12in = 12 ft
313in = x
= 313 ft