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
A) yes
B) yes
C) no
For each of these, substitute the value of x in the ordered pair into x in the function.
For A, x = -5; -5<2, so the piece of the function we want is f(x) = 3. In our ordered pair, y=f(x)=3, so yes, it is a solution.
For B, x = 2; 2≤2<6, so the piece of the function we want is f(x) = -x+1. In our ordered pair, y=f(x)=-1; -2+1=-1, so yes, it is a solution.
For C, x = 8; 8≥6, so the piece of the function we want is f(x) = x. In our ordered pair, y=f(x)=-7; -7≠8, so no, it is not a solution.
This problem has been solved! See the answer Determine Um (mode ), average U, and Urms for a group of ten automobiles clocked by radar at speeds 38,44,48,50,55,55,57,58 and 60mi/h respectively
A. The sculptor will have to sculpt away 1M on each side.
Explanation: 3 • 1_1/2 • 1_1/2
To get to 2 • 1/2 • 1/2, subtract 1 meter from each side of the rectangular prism and you’ll get that! :)
