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)
To test for a triangle, the two smallest sides added together have to be greater than the third side.
3.95 + 4.56 > 8.65
8.51 > 8.65
this is false
4.56 + 8.65 > 10.31
13.21 > 10.31
could be it
4.56 + 8.65 > 13.21
13.21 > 13.21
no, this would mean they're equal
4.56 + 8.65 > 20.25
13.21 > 20.25
this is also false
<span>B. 10.31 cm
</span>
Answer:320
Step-by-step explanation: 8 bats equals 40 grams of insect. 8 x 5= 40. 64 bats equals 320. 64 x 5 =320.
Answer: 2x is the slope
Y= 2x-2
When finding slope think “rise over run” implying that when writing it as a fraction the rise would go over the run, this answer for example would be 2/1x because the line rises 2 for every 1 unit it passes. I don’t think you need this large of a explanation but I thought it would help
Answer: 13 13/15
Step-by-step explanation: