Answer:
The required width of the field that would maximize the area is = 1250 feet
Step-by-step explanation:
Given that:
The total fencing length = 5000 ft
Let consider w to be the width and L to be the length.
Then; the perimeter of the rectangular field by assuming a parallel direction is:
P = 3L + 2w
⇒ 3L + 2w = 5000
3L = 5000 - 2w
![L = \dfrac{5000}{3} - \dfrac{2w}{3}](https://tex.z-dn.net/?f=L%20%3D%20%5Cdfrac%7B5000%7D%7B3%7D%20-%20%5Cdfrac%7B2w%7D%7B3%7D)
Recall that:
The area of the rectangle = L×w
![A(w) = ( \dfrac{5000}{3}-\dfrac{2}{3} ) w](https://tex.z-dn.net/?f=A%28w%29%20%3D%20%28%20%5Cdfrac%7B5000%7D%7B3%7D-%5Cdfrac%7B2%7D%7B3%7D%20%29%20w)
![A(w) = \dfrac{5000}{3}w-\dfrac{2}{3} w^2](https://tex.z-dn.net/?f=A%28w%29%20%3D%20%20%5Cdfrac%7B5000%7D%7B3%7Dw-%5Cdfrac%7B2%7D%7B3%7D%20%20w%5E2)
Taking the differentiation of both sides with respect to t; we have:
![A' (w) = \dfrac{5000}{3} - \dfrac{2}{3} ( 2 w)](https://tex.z-dn.net/?f=A%27%20%28w%29%20%3D%20%5Cdfrac%7B5000%7D%7B3%7D%20-%20%5Cdfrac%7B2%7D%7B3%7D%20%28%202%20w%29)
![A' (w) = \dfrac{5000}{3} - \dfrac{4w}{3}](https://tex.z-dn.net/?f=A%27%20%28w%29%20%3D%20%5Cdfrac%7B5000%7D%7B3%7D%20-%20%5Cdfrac%7B4w%7D%7B3%7D)
Then; we set A'(w) to be equal to zero;
So; ![\dfrac{5000}{3} - \dfrac{4w}{3}=0](https://tex.z-dn.net/?f=%5Cdfrac%7B5000%7D%7B3%7D%20-%20%5Cdfrac%7B4w%7D%7B3%7D%3D0)
5000 = 4w
w = 5000/4
w = 1250
Thus; the required width of the field that would maximize the area is = 1250 feet
Also, the length
can now be :
![L = \dfrac{5000}{3} - \dfrac{2(1250)}{3}](https://tex.z-dn.net/?f=L%20%3D%20%5Cdfrac%7B5000%7D%7B3%7D%20-%20%5Cdfrac%7B2%281250%29%7D%7B3%7D)
L = (5000 -2500)/3
L = 2500/3 feet
Suppose, the farmer divides the plot parallel to the width; Then 2500/3 feet = 833.33 feet and the length L = 1250 feet.
Answer:
C D E
Step-by-step explanation:
They are the options that are clear enough
Answer: x is 5
Step-by-step explanation: 9 x 5 = 5 x 5 + 20
Answer:
the volume is 60 cm cubed
Step-by-step explanation:
(5 x 8) / 2 x 3
5 x 8 = 40
40 / 2 = 20
20 x 3 = 60
C=2pier
C= 2 • 3.14 • 1.5 (radius if 1/2 of diameter)
C= 9.42
Hope that helps!