Answer:
x = 8,49 ft
y = 4,24 ft
Step-by-step explanation:
Let x be the longer side of rectangle and y the shorter
Area of rectangle = 36 ft² 36 = x* y ⇒ y =36/x
Perimeter of rectangle:
P = 2x + 2y for convinience we will write it as P = ( 2x + y ) + y
C(x,y) = 1 * ( 2x + y ) + 3* y
The cost equation as function of x is:
C(x) = 2x + 36/x + 108/x
C(x) = 2x + 144/x
Taking derivatives on both sides of the equation
C´(x) = 2 - 144/x²
C´(x) = 0 2 - 144/x² = 0 ⇒ 2x² -144 = 0 ⇒ x² = 72
x = 8,49 ft y = 36/8.49 y = 4,24 ft
How can we be sure that value will give us a minimun
We get second derivative
C´(x) = 2 - 144/x² ⇒C´´(x) = 2x (144)/ x⁴
so C´´(x) > 0
condition for a minimum
X=5 y=1 this what i got when i worked it out on my paper. hope that helps.
1. Given
2. Addition property
3. Division property
The GCF of 27 and 18 would be 9. It is the largest or greatest common factor that can be evenly divided by in both the numbers 27 and 18.
