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nika2105 [10]
2 years ago
5

a norman window has the shape of a rectangle surmounted by a semicircle. if the perimeter of the window is 25 feet, express the

area of the window as a function of the width (across the base) of the window.
Mathematics
1 answer:
sp2606 [1]2 years ago
7 0

The area of the window is \frac{25x}{2} -(1 +\frac{\pi}{2} )\frac{x^2}{2}

The shape of the Norman window is described as a rectangle surmounted by a semicircle.

Let 'x' be the width of the window.

Then this width corresponds to the diameter of the semicircle.

That is, radius of the semicircle = x/2

Now given the perimeter of the whole window = 25 ft

This perimeter is equal to the sum of 3 sides of the rectangle and the perimeter of the semicircle.

Perimeter of the semicircle = \frac{2\pi r}{2} = \frac{\pi x}{2} , where r is the radius of the semicircle.

Now let 'y' be the length of the window.

Then sum of three sides of the window = 2y + x

So 2y + x + \frac{\pi x}{2} = 25

Therefore, y =( 25 - x - \frac{\pi x}{2} ) / 2

Area of the window = Area of the semicircle + Area of the rectangle =

 \frac{\pi x^2}{8} +xy = \frac{\pi x^2}{8} + x( 25 - x - \frac{\pi x}{2} ) / 2\\ = \frac{\pi x^2}{8} + (25x - x^2 - \frac{\pi x^2}{2} ) / 2

 So Area of the window = \frac{25x}{2} -(1 +\frac{\pi}{2} )\frac{x^2}{2}

Learn more about area of circle and rectangle at brainly.com/question/4694841

#SPJ4

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9x + 9 + 2x - 7(3 + x) =
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Answer:

4x-12 or 4(x-3)

Step-by-step explanation:

9x+9+2x-7(3+x)

9x+2x+9-21-7x

11x-12-7x

11x-7x-12

4x-12

4 0
3 years ago
8 ft 6 inches is greater or less than 100 inches?
Romashka [77]
It would be greater, because 1 foot is equal to 12 inches. 8 times 12 is 96. Then 96 plus 6 inches in 102. So it would be greater.
6 0
3 years ago
−5/8+3/4 equals what, In fraction form.
kipiarov [429]

How to get answer by Mimiwhatsup (In Decimal Form):

-5/8+3/4\\\mathrm{Divide\:the\:numbers:}\:5\div \:8=0.625\\=-0.625+3\div \:4\\\mathrm{Divide\:the\:numbers:}\:3\div \:4=0.75\\=-0.625+0.75\\\mathrm{Add/Subtract\:the\:numbers:}\:-0.625+0.75=0.125\\=0.125

Answer in Fraction Form: \frac{1}{8}

7 0
3 years ago
I need the Area and Perimeter.​
Klio2033 [76]

Answer: 36

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4 0
3 years ago
Read 2 more answers
Complete the table of inputs and outputs for the given function. F(x)= -5(x+7)
levacccp [35]

The table of inputs that satisfy the given function is (<em>-2, 25), (-1, -30), (0, 35), (1, -40) and (2, -45).</em>

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more variables and numbers.

Given the function f(x) = -5(x + 7)

When x = -2; f(-2) = -5(-2 + 7) = -25

When x = -1; f(-1) = -5(-1 + 7) = -30

When x = 0; f(0) = -5(0 + 7) = -35

When x = 1; f(1) = -5(1 + 7) = -40

When x = 2; f(2) = -5(2 + 7) = -45

The table of inputs that satisfy the given function is (<em>-2, 25), (-1, -30), (0, 35), (1, -40) and (2, -45).</em>

<em />

Find out more on equation at: brainly.com/question/13763238

#SPJ1

6 0
2 years ago
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