Answer:
The upper limit for the height of the prism is 
Step-by-step explanation:
Let
x------> represent the height of the prism
It is known that
the area of the base of the prism must not exceed


thus
-------> inequality A
------> equation B
-----> equation C
Insert equation B into equation C

------> equation D
Substituting equations B and D into inequality A
-------> using a graphing tool to solve the inequality
The resultant solution for x lies in the interval---------->![[0,12]](https://tex.z-dn.net/?f=%5B0%2C12%5D)
consult the attached figure
but bear in mind that
The width of the base must be
meters shorter than the height of the prism
thus
the solution for x is confined to the interval ------> ![(9,12]](https://tex.z-dn.net/?f=%289%2C12%5D)
The maximum height of the prism equals 
Answer:
600 books
Step-by-step explanation:
The dimensions of the bin are
5 by 2 by 3
The volume of the bin is found by multiplying these three dimensions.
Volume of Bin = 5 * 2 * 3 = 30 cubic feet
To find the volume of each book, we use the same method. The dimensions of one book are:
1 by 0.5 by 0.1
Volume of 1 book = 1 * 0.5 * 0.1 = 0.05 cubic feet
The total number of books fitting into the bin is calculated by:
30/0.05 = 600 books
A 40-degree angle may be applicable for this question