Given Information:
Area of rectangle = 16 square feet
Required Information:
Least amount of material = ?
Answer:
x = 4 ft and y = 4 ft
Step-by-step explanation:
We know that a rectangle has area = xy and perimeter = 2x + 2y
We want to use least amount of material to design the sandbox which means we want to minimize the perimeter which can be done by taking the derivative of perimeter and then setting it equal to 0.
So we have
xy = 16
y = 16/x
p = 2x + 2y
put the value of y into the equation of perimeter
p = 2x + 2(16/x)
p = 2x + 32/x
Take derivative with respect to x
d/dt (2x + 32/x)
2 - 32/x²
set the derivative equal to zero to minimize the perimeter
2 - 32/x² = 0
32/x² = 2
x² = 32/2
x² = 16
x = 
ft
put the value of x into equation xy = 16
(4)y = 16
y = 16/4
y = 4 ft
So the dimensions are x = 4 ft and y = 4 ft in order to use least amount of material.
Verification:
xy = 16
4*4 = 16
16 = 16 (satisfied)
Answer:
¿cual es la influencia que tiene la revolución cubana en el surgimiento de grupos armados en Colombia?
Step-by-step explanation:
Answer:
; line D in the options.
Step-by-step explanation:
The set of equations has no solutions if the two lines are parallel. A quick way to create a parallel line is to solve for y, put it in slope-intercept form. Else, as long as the cofficient of x and y are in the same ratio (in this case 1:1), the two lines are parallel, you just have to be careful not to pick the same line again!
The condition 
makes sure you are still getting lines (else you would get rid of both x and y); the condition 
makes sure you're not picking line A again, just written in a different form.
Now that we have the options:
A and C have a different ratio for the coefficient of x and y (2:1 and 1:2) so are not good.
Choice B is just a more complicated way to write the same line, you can see by dividing both sides by 2 and get back x+y=2.
Line D is correct.
The space between each board is 15.56 144/9.25=15.56
