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
Answer: 7
Step-by-step explanation:
Step 1: Subtract 3 from both sides.
6a+3−3=45−3
6a=42
Step 2: Divide both sides by 6.
6a
/6
=
42
/6
Answer:
432 pages.
Step-by-step explanation:
We know Madison reads 24pgs/ per day. She reads for nine days, so she reads 24*9 pages, or 216.
We know also that this is halfway through her book, so 2*216= the whole book, so the book has 432 pages
10 would be the answer I believe.
A reclined chair or maybe a laptop
