Answer:1
Step-by-step explanation:
The line is intercepted with the number one
Answer:
a) A(x) = 90*x/2 - x²/2
b) A(max) = 1012.5 m²
Step-by-step explanation:
L = 90 meters of fencing
Rectangular area is
A(r) = x*y . where x and y are the sides of the rectangle
the perimeter is ( we are going to fence only 3 sides, then)
x + 2*y = 90 or . y = ( 90 - x ) /2
Area as a function of x is:
A(x) = x * ( 90 - x)/2
A(x) = 90*x/2 - x²/2
Tacking derivatives on both sides of the equation:
A´(x) =45 - 2*x/2 A´(x) =45 - x
A´(x) = 0 . 45 - x = 0 . x = 45 . meters
and . y = ( 90 - x ) 2
y = ( 90- 45 )/2
y = 22.5 meters
A(max) = 45*22.5 m²
A(max) = 1012.5 m²
If we get the second derivative of A(x) . A"(x) = - 1 A"(x) < 0
Then A(x) has a maximum for x = 45
