linag969p9xeno
30.10.2019 •
Mathematics
Afarmer is building a rectangular pen with three parallel partitions, shown in the diagram. he has 500 feet of
fencing available. what is the maximum area he can enclose?
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Ответ:
10,416.67 ft²
Step-by-step explanation:
If the length of the three parallel partitions is h, and the width of the two parallel walls is w, then the perimeter is:
500 = 3h + 2w
The area is:
A = hw
Solve for w in the first equation:
2w = 500 − 3h
w = 250 − 1.5h
Substitute into the second equation:
A = h (250 − 1.5h)
A = 250h − 1.5h²
We can find the maximum using vertex of a parabola:
h = -b / (2a)
h = -250 / (2 × -1.5)
h = 83.33
Or using calculus:
dA/dh = 250 − 3h
0 = 250 − 3h
h = 83.33
Therefore, the maximum area is:
A = 250h − 1.5h²
A = 10,416.67
Ответ:
x = -96/23
Step-by-step explanation
- = 4
multiply each side of equation by 24 to eliminate denominators
(24) - = 4 (24)
3(3x) - 8(4x) = 96
9x - 32x = 96
-23x = 96
x = -96/23