Answer:
11.27
Step-by-step explanation:
The potential solutions of 
are 2 and -8.
<h3>Properties of Logarithms</h3>
From the properties of logarithms, you can rewrite logarithmic expressions.
The main properties are:
- Product Rule for Logarithms -
- Quotient Rule for Logarithms -
- Power Rule for Logarithms -
The exercise asks the potential solutions for . In this expression you can apply the Product Rule for Logarithms.
Now you should solve the quadratic equation.
Δ=
. Thus, x will be 
. Then:
The potential solutions are 2 and -8.
Read more about the properties of logarithms here:
brainly.com/question/14868849
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
