Given the data, as shown in the image below, determine if the distribution is uniformly distributed, symmetrically distributed,

A Norman window is a window with a semi-circle on top of regular rectangular window. (See the picture.) What should be the dimen

Vikki [24]

Answer:

bottom side (a) = 3.36 ft

lateral side (b) = 4.68 ft

Step-by-step explanation:

We have to maximize the area of the window, subject to a constraint in the perimeter of the window.

If we defined a as the bottom side, and b as the lateral side, we have the area defined as:

$A=A_r+A_c/2=a\cdot b+\dfrac{\pi r^2}{2}=ab+\dfrac{\pi}{2}\left (\dfrac{a}{2}\right)^2=ab+\dfrac{\pi a^2}{8}$

The restriction is that the perimeter have to be 12 ft at most:

$P=(a+2b)+\dfrac{\pi a}{2}=2b+a+(\dfrac{\pi}{2}) a=2b+(1+\dfrac{\pi}{2})a=12$

We can express b in function of a as:

$2b+(1+\dfrac{\pi}{2})a=12\\\\\\2b=12-(1+\dfrac{\pi}{2})a\\\\\\b=6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a$

Then, the area become:

$A=ab+\dfrac{\pi a^2}{8}=a(6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a)+\dfrac{\pi a^2}{8}\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a^2+\dfrac{\pi a^2}{8}\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{4}-\dfrac{\pi}{8}\right)a^2\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{8}\right)a^2$

To maximize the area, we derive and equal to zero:

$\dfrac{dA}{da}=6-2\left(\dfrac{1}{2}+\dfrac{\pi}{8}\right )a=0\\\\\\6-(1-\pi/4)a=0\\\\a=\dfrac{6}{(1+\pi/4)}\approx6/1.78\approx 3.36$

Then, b is:

$b=6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a\\\\\\b=6-0.393*3.36=6-1.32\\\\b=4.68$

3 0

3 years ago

The volume of a cone is 200.96 cubic yards. What is the radius of the cone if the height is 12 yd? Use pi =3.14 and round your a

Naddika [18.5K]

Answer:

If I'm doing the problem correctly, the radius should be 4 yards.

Step-by-step explanation:

You work the problem backwards. Multiply 200.96 by 3, since it's a cone, so you're working with the volume of what a cylinder would be with the same dimensions. Then divide by the height (12 yd), then divide by pi. You should end up with 16, and 4 squared equals 16. Work the problem forwards from there to check.

4 squared is 16. 16 times 3.14 is 50.24. 50.24 times 12 is 602.88. 602.88 divided by 3 is 200.96.

8 0

2 years ago

Read 2 more answers

Please help me out on this !!!

lawyer [7]

Answer:

Tu is your answer hope it helps you

8 0

2 years ago

Cole bought 7 bricks. All together, the bricks weighed 95.26 pounds. To the nearest thousandth of a pound, how much did each bri

Agata [3.3K]

Answer:

13.608

Step-by-step explanation:

hope I can help man. good luck.

8 0

2 years ago

Please help me with this question look at the image. I will mark the brainiest.

kirill [66]

Answer:

5 ft

Step-by-step explanation:

trapezoid area = ((base + base) / 2) height

25.5 = ((3.2+7)/2) height

25.5= 10.2/2height

25.5/5.1

height = 5

8 0

2 years ago