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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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Andrei [34K]

Answer:

The answer is 3 and (-4).

Step-by-step explanation:

We are given an equation 2x² + 2x – 24.

Let us assume that the equation is equal to zero.

2x² + 2x – 24 = 0

Now, divide whole equation by 2 we get,

x² + x – 12 = 0

x² + 4x – 3x – 12 = 0

x(x + 4) – 3(x + 4) = 0

(x – 3) (x + 4) = 0

x = 3, -4

Thus, The actual roots of f(x) are 3 and (-4).

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2 years ago
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Citrus2011 [14]

Answer:

g(x)=2-x² OR g(x)=-x²+2

Step-by-step explanation:

Notice that the red parabola doesn't stretch or compress. It only translates 3 units down. This means taking the original equation f(x)=-x²+5 and subtracting 3 units will get us the equation g(x)=-x²+2 which is also the same thing as g(x)=2-x². Looks like some of your answer choices got cut out of the picture so make sure to choose the answer I provided.

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3 years ago
Read 2 more answers
Someone help! It is urgent!!!
djverab [1.8K]

Answer:

a. f(-1)=12

b. f(2t)=16t²-6t+5

c. f(t-2)=4t²-19t+27

Step-by-step explanation:

For a, b, c, we are given an input. We plug that into f(x) to find our answers.

a.  f(-1)=12

f(-1)=4(-1)²-3(-1)+5

f(-1)=4+3+5

f(-1)=12

-------------------------------------------------------------------------------------------------------------

b. f(2t)=16t²-6t+5

f(2t)=4(2t)²-3(2t)+5

f(2t)=4(4t²)-6t+5

f(2t)=16t²-6t+5

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c. f(t-2)=4t²-19t+27

f(t-2)=4(t-2)²-3(t-2)+5

f(t-2)=4(t²-4t+4)-3t+6+5

f(t-2)=4t²-16t+16-3t+6+5

f(t-2)=4t²-19t+27

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3 years ago
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Simora [160]

Answer:

C

Step-by-step explanation:

If you add the first equation up you get 2z+6 by combining like terms

if you see A a is equal to 3z+6 so a doesn’t work

If you look at B b is equal to z+12 so b doesn’t work

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Answer: The answer is 11! I hope this helps! :)



Step-by-step explanation:


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