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1 answer:
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Answer:
Option 1 - 19, because the number of books is 95 over 4 divided by 5 over 4
Step-by-step explanation:
Given : Samantha has a shelf that is 95 over 4 inches wide.
To find : How many books can Samantha arrange on the shelf if each book is 5 over 4 inches thick?
Solution :
The thickness of shelf = inches
Each book thickness = inches
Let the total number of books that could be arranged in the shelf be 'n'.
Substitute the values,
Therefore, option 1 is correct.
19, because the number of books is 95 over 4 divided by 5 over 4
Check the picture below.
as you can see, the graph of the volume function comes from below goes up up up, reaches a U-turn then goes down down, U-turns again then back up to infinity.
the maximum is reached at the close up you see in the picture on the right-side.
Why we don't use a higher value from the graph since it's going to infinity?
well, "x" is constrained by the lengths of the box, specifically by the length of the smaller side, namely 5 - 2x, so whatever "x" is, it can't never zero out the smaller side, and that'd happen when x = 2.5, how so? well 5 - 2(2.5) = 0, so "x" whatever value is may be, must be less than 2.5, but more than 0, and within those constraints the maximum you see in the picture is obtained.
