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
This is exponential growth...
F=ar^t
F=25(1.15^t) so in six weeks...
F=25(1.15^6)
F≈57.82
F≈58 words per minute (to nearest whole word per minute)
375/4 = 93.75 per g
750/9 = about 83.30 per g
Answer: 750g cereal for $9
2x-2(-2+1)=4
Distribute the -2 to the numbers in parantheses.
2x+4-2=4
Combine all numbers
2x+2=4
Subtract 2 from both sides
2x=2
Then divide by two
x=1