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:
Step-by-step explanation:
Givens
C = 12 * pi
C = 2*pi * r
Solution
2*pi * r = 12*pi Divide both sides by 2pi
2*pi * r/ 2*pi = 12*pi/2pi
r = 6
Answer: the diameter = 2 * r
the diameter = 12
Answer:
i dont know
Step-by-step explanation:
Answer:
2/5 or .4
Step-by-step explanation:
basically look at the points where the line meets the graph. two points would be 0,20 and 50,40. then count the amount that it changes vertically and then horizontally. +20vertical +50 horizonal giving the slope 20/50. this can then be simplified to 2/5 or the equivalent number .4
