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Mathematics

1 answer:

pshichka [43]3 years ago

3 0

Answer:

£30

Step-by-step explanation:

Krutika should get £30 of it

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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

Analyze the diagram below and answer the question that follows. 2004-02-03-05-00_files/i0500000.jpg Which of the following is no

meriva

I think the answer is d.8

6 0

3 years ago

Every dimension of a triangular pyramid is multiplied by 10 to produce a new figure that is geometrically similar. What effect d

ICE Princess25 [194]

Answer:

Step-by-step explanation:

Since the question is asking for surface area and the dimensions are multiplied by 10, the surface area is multiplied by 10^2, or 100. (For area it would be 10^3, or 1000)

8 0

3 years ago

A librarian surveyed her reading club. Of those surveyed, 7 favored mysteries, 4 favored fantasy, 3 favored science fiction, and

blsea [12.9K]

answer:

338 out of 520

step by step:

13 out of 20 dont favor mystery

13:20

? :520

520÷20=26

13×26= 338

338 students out of 520 do not favor mysteries

7 0

4 years ago

2(17 - 1) A.32 B.33 C.34 D.216

barxatty [35]

A is the answer for the question

5 0

3 years ago