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eimsori [14]
3 years ago
7

[WILL MARK BRAINLIEST]

Mathematics
1 answer:
Firlakuza [10]3 years ago
5 0

Answer:

A≈94.25in²

Step-by-step explanation:

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A norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular. Find the dimensions of a norman
Yanka [14]

Answer:

W\approx 8.72 and L\approx 15.57.

Step-by-step explanation:

Please find the attachment.

We have been given that a norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular. The total perimeter is 38 feet.

The perimeter of the window will be equal to three sides of rectangle plus half the perimeter of circle. We can represent our given information in an equation as:

2L+W+\frac{1}{2}(2\pi r)=38

We can see that diameter of semicircle is W. We know that diameter is twice the radius, so we will get:

2L+W+\frac{1}{2}(2r\pi)=38

2L+W+\frac{\pi}{2}W=38

Let us find area of window equation as:

\text{Area}=W\cdot L+\frac{1}{2}(\pi r^2)

\text{Area}=W\cdot L+\frac{1}{2}(\pi (\frac{W}{2})^2)

\text{Area}=W\cdot L+\frac{\pi}{2}(\frac{W}{2})^2)

\text{Area}=W\cdot L+\frac{\pi}{2}(\frac{W^2}{4})

\text{Area}=W\cdot L+\frac{\pi}{8}W^2

Now, we will solve for L is terms W from perimeter equation as:

L=38-(W+\frac{\pi }{2}W)

Substitute this value in area equation:

A=W\cdot (38-W-\frac{\pi }{2}W)+\frac{\pi}{8}W^2

Since we need the area of window to maximize, so we need to optimize area equation.

A=W\cdot (38-W-\frac{\pi }{2}W)+\frac{\pi}{8}W^2  

A=38W-W^2-\frac{\pi }{2}W^2+\frac{\pi}{8}W^2  

Let us find derivative of area equation as:

A'=38-2W-\frac{2\pi }{2}W+\frac{2\pi}{8}W  

A'=38-2W-\pi W+\frac{\pi}{4}W    

A'=38-2W-\frac{4\pi W}{4}+\frac{\pi}{4}W

A'=38-2W-\frac{3\pi W}{4}

To find maxima, we will equate first derivative equal to 0 as:

38-2W-\frac{3\pi W}{4}=0

-2W-\frac{3\pi W}{4}=-38

\frac{-8W-3\pi W}{4}=-38

\frac{-8W-3\pi W}{4}*4=-38*4

-8W-3\pi W=-152

8W+3\pi W=152

W(8+3\pi)=152

W=\frac{152}{8+3\pi}

W=8.723210

W\approx 8.72

Upon substituting W=8.723210 in equation L=38-(W+\frac{\pi }{2}W), we will get:

L=38-(8.723210+\frac{\pi }{2}8.723210)

L=38-(8.723210+\frac{8.723210\pi }{2})

L=38-(8.723210+\frac{27.40477245}{2})

L=38-(8.723210+13.70238622)

L=38-(22.42559622)

L=15.57440378

L\approx 15.57

Therefore, the dimensions of the window that will maximize the area would be W\approx 8.72 and L\approx 15.57.

8 0
3 years ago
Please someone should help me out​
ki77a [65]

Answer:

6cm is the missing length

Step-by-step explanation:

See the 10cm and the 4cm?

If you look at in a way if you added 6 more centimeters to the 4cm it would be 10, leaving 6cm as the missing length.

8 0
3 years ago
Whats The Answer Marking Brainliest, Please explain your answer:D..............................Please HELP!!!!!!!!!!!!!!!!!!!!!!
GREYUIT [131]

Answer: D.

Step-by-step explanation: Every min is 60 sec. Multiply that by 4, and then add that by 30. That equals 270 and that is lower than Wyatt's time.

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What is the value of the product of -20/48 times 6 in simplified form
KATRIN_1 [288]
-20/48 x 6 =   \frac{-20}{48}    x  \frac{6}{1}

I would cancel out the 6 in the numerator and the 48 in the denominator 
Now I have <u />\frac{-20}{8}  or <u />\frac{-5}{2} reduced.

-5 ÷ 2  = -2 1/2 and that is the answer in simplest form
8 0
3 years ago
Which of the following would you expect to find on a monthly account statement?
timama [110]
The answer is D
here's your answer
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3 years ago
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