How did the Germanic tribes contribute to the decline of the Western Roman Empire? Write your answer in a paragraph of 125 words
1 answer:
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Answer:
See proof below
Step-by-step explanation:
We will use properties of inequalities during the proof.
Let . then we have that
. Hence, it makes sense to define the positive number delta as
(the inequality guarantees that these numbers are positive).
Intuitively, delta is the shortest distance from y to the endpoints of the interval. Now, we claim that , and if we prove this, we are done. To prove it, let
, then
. First,
then
hence
On the other hand, then
hence
. Combining the inequalities, we have that
, therefore
as required.
If you notice the picture below, the amount of fencing, or perimeter, that will be used will be 3w + 2l
now
solve for "w", to see what critical points you get, and then run a first-derivative test on them, for the minimum
notice the
so. you can pretty much skip that one, though is a valid critical point, the width can't clearly be 0
so.. check the critical points on the other
now
solve for "w", to see what critical points you get, and then run a first-derivative test on them, for the minimum
notice the
so.. check the critical points on the other
