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
Step-by-step explanation:
Answer: 3x-7
Explanation: x times 3
(3x)
subtracted by 7
(3x-7)
Is this what you are looking for?
Answer:
C = D all real Numbers ; R y>= -2
Step-by-step explanation:
for discover the domain we have to look the x axis and check for what x the graph exist. If we look this graph we can see that there are two solid lines.
the two arrows indicate that the graph continues both to left and to the right
so the domain is all real numbers
for the range we have to check the y axis. If we look at the graph we can see that under -2 there is nothing, while up -2 the graph continues to raise,
so the range is y>= -2
so the final answer is C
Plug the values (x,y)=(0,0) into the inequalities:
0 isn't greater than 0, no (0,0) is not a solution to either of these inequalities.
The answer is D.
Depending on the length of the two sides of the triangle the length could be smaller than 1.
The answer that is not true is :
B. It is always greater than 1
