<span>The area of the base is x^2> The height is h. Each side of the box has area xh. There are 4 sides of the box so the total surface area of the box is x^2+4xh and that is equal to 1000. Solve that equation for h:
x^2+4xh = 1000 h = (1000-x^2)/4x so the Volume = x^2[(1000-x^2)/4x]
Simplify and get V = 250x-x^3/4
The volume will be a maximum when its first derivative is 0.
V' = 250-3/4x^2
Set to 0 and solve. x=18.26
Now plug into the volume function to find the maximum volume:
V=250(18.26)-(18.26)^3/4
V= 4564.35 - 1522.10 =3042.25</span>
The distance d is 9 ft and the height is 12ft.
<h3>
How to find the distance and the height?</h3>
Here we can model the situation with a right triangle, where the length of the wire is the hypotenuse.
The height is one cathetus and the distance is the other catheti.
Let's define:
- h = height
- d = distance.
- hypotenuse = 15ft
We know that the height of the tower is 3 ft larger than the distance, then:
h = d + 3ft
Now we can use the Pythagorean theorem, it says that the sum of the squares of the cathetus is equal to the square of the hypotenuse.
Then:
Now we can solve this equation for d:
Then the solutions are:
We only take the positive solution:
d = (-3ft + 21ft)/2 = 9ft
And the height is 3 ft more than that, so:
h = 9ft + 3ft = 12ft
The distance d is 9 ft and the height is 12ft.
If you want to learn more about right triangles:
brainly.com/question/2217700
#SPJ1
Hello there, and thank you for posting your question here on brainly.
To find mean absolute deviation, (MAD) you have to add all the numbers together, and then divide by how much numbers are in the set.
So we have to do 10 + 11 + 15 + 16 + 18, and then divide by 5.
10 + 11 + 15 + 16 + 18 ===> 70
Now, divide by 5.
70 / 5 ===> 14
The mean absolute deviation is 14.
Hope this helped! ☺♥
Answer:
R = 6
Step-by-step explanation:
Remember... Circle area is:
A = pi×R^2
Where R is the circle radius.
Then,
Pi×R^2=36×Pi
R = square root of 36
R = 6
2/10, just simplify the fraction by dividing both numbers by ten.
