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antcobra
21.07.2019 •
Mathematics
Acampground owner plans to enclose a rectangular field adjacent to a river. the owner wants the field to contain 180,000 square meters. no fencing is required along the river. what dimensions will use the least amount of fencing?
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Ответ:
The area is the product between the two sizes:
While the perimeter is twice the sum of the two sizes:
From (1) we can write
and we can substitute it into (2):
To find the minimum value of the perimeter, we have to calculate its derivative and put it equal to zero:
The derivative of the perimeter is
If we require p'(x)=0, we find
And the other side is
This means that the dimensions that require the minimum amoutn of fencing are (424.26 m, 424.26 m), so it corresponds to a square field.
Ответ:
It should be 57.6 minutes.
Step-by-step explanation:
Because if you divide 24 by 15 you get 1.6 and 1.6 times 36 is 57.6