Answer:
Dimensions :
x (the longer side, only one side with fence ) = 90 ft
y ( the shorter side two sides with fence ) = 45 ft
Total fence used 45 * 2 + 90 = 180 ft
A(max) =
Step-by-step explanation: If a farmer has 180 ft of fencing to encloses a rectangular area with fence in three sides and the river on one side, the farmer surely wants to have a maximum enclosed area.
Lets call "x" one the longer side ( only one of the longer side of the rectangle will have fence, the other will be along the river and won´t need fence. "y" will be the shorter side
Then we have:
P = perimeter = 180 = 2y + x ⇒ y = ( 180 - x ) / 2 (1)
And A (r) = x * y
A(x) = x * ( 180 - x ) /2 ⇒ A(x) = (180/2) *x - x² / 2
Taking derivatives on both sides of the equation :
A´(x) = 90 - x
Then if A´(x) = 0 ⇒ 90 - x = 0 ⇒ x = 90 ft
and from : y = ( 180 - x ) / 2 ⇒ y = 90/2
y = 45 ft
And
A(max) = 90 * 45 = 4050 ft²
= 39.84
:
100^2=251
10000=251
ℎ
251 ℎ
10000/251=251/251
39.84=1
39.84=
Answer:
Yes О.31243576 is a rational number
Length - l
Width - w
Given,
Perimeter = 60
2(l +w) = 60
l + w = 30
l = 30 - w
Given,
l = 3w
30 - w = 3w
4w = 30
--- w = 7.5
--- l = 3w = 3 * 7.5 = 29.5
Hence, the length of the rectangle is 29.5 and the width is 7.5
A) the middle of the range is 39.5%
b) the difference between the middle and the ends of the range is ±1.5%
c) less than a majority favor change. Change seems unlikely.
