Answer:
A(max) = (9/2)*L² ft²
Dimensions:
x = 3*L feet
y = (3/2)*L ft
Step-by-step explanation:
Let call "x" and " y " sides of the rectangle. The side x is parallel to the wall of the house then
Area of the rectangle is
A(r) = x*y
And total length of fence available is 6*L f , and we will use the wall as one x side then, perimeter of the rectangle which is 2x + 2y becomes x + 2*y
Then
6*L = x + 2* y ⇒ y = ( 6*L - x ) /2
And the area as function of x is
A(x) = x* ( 6*L - x )/2
A(x) = ( 6*L*x - x² ) /2
Taking derivatives on both sides of the equation we get:
A´(x) = 1/2 ( 6*L - 2*x )
A´(x) = 0 ⇒ 1/2( 6*L - 2*x ) = 0
6*L - 2*x = 0
-2*x = - 6*L
x = 3*L feet
And
y = ( 6*L - x ) /2 ⇒ y = ( 6*L - 3*L )/ 2
y = ( 3/2)*L feet
And area maximum is:
A(max) = 3*L * 3/2*L
A(max) = (9/2)*L² f²
Answer:
94
Step-by-step explanation:
(x+5)+(x-13) = 180
2x -8 = 180
2x = 188
x= 94
Answer:
side c is 25
Step-by-step explanation:
Answer:
756.36 meters
Step-by-step explanation:
Draw a diagram. Let's call the horizontal distance from the top of the mountain to the closest point x.
Using tangent = opposite / adjacent, we can write two equations:
tan 35.3° = h / x
tan 25.76° = h / (x + 500)
Solve for x in the first equation and substitute into the second.
x = h / tan 35.3°
tan 25.76° = h / ((h / tan 35.3°) + 500)
Solve for h.
tan 25.76° (h / tan 35.3°) + 500 tan 25.76° = h
500 tan 25.76° = h (1 − (tan 25.76° / tan 35.3°))
500 tan 25.76° tan 35.3° = h (tan 35.3° − tan 25.76°)
h = 500 tan 25.76° tan 35.3° / (tan 35.3° − tan 25.76°)
h ≈ 756.36 meters