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pantera1 [17]
3 years ago
13

A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of t

he rectangle. What is the area of the largest possible Norman window with a perimeter of 41 feet?
Mathematics
1 answer:
Makovka662 [10]3 years ago
3 0

Answer:

132.233 ft2

Step-by-step explanation:

Let's call the width of the rectangle 'w' and the length 'x'. So the area of the semicircle is:

A_1 = \pi*radius^2/2

A_1 = \pi*(w/2)^2/2

A_1 = \pi/8*w^2

And the area of the rectangle is:

A_2 = w*x

If the perimeter of the window is 41 feet, we have:

Perimeter = length + 2*width + \pi*radius

41 = x + 2*w + \pi*w/2

x = 41 - w(2 + \pi/2)

Now, the equation for the total area of the window is:

A = A_1 + A_2 = \pi/8*w^2 + w*x

A = \pi/8*w^2 + w*(41 - w(2 + \pi/2))

A = (\pi/8-2 - \pi/2)*w^2 + 41w = -3.1781w^2 + 41w

To find the maximum area, we can find the x-coordinate of the vertex of the quadratic equation:

x\_vertex = -b / 2a = -41 / (-3.1781*2) = 6.45

So the width that gives us the maximum area of the window is 6.45 feet, and the area will be:

A = -3.1781w^2 + 41w = -3.1781*(6.45)^2 + 41*6.45 = 132.233\ ft^2

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The sides are 2x, 3x-5 and 4x+2
perimiter is the sum of the sides

a.
2x+3x-5+4x+2=63 is an equation

b.
solve
group like terms
2x+3x+4x-5+2=65
add like terms
9x-3=65
add 3 to both sides
9x=68
divide both sides by 9
x=68/9


2x=2(68/9)=136/9 in
3x-5=3(68/9)-5=(68/3)-5=(68/3)-(15/3)=53/3
4x+2=4(68/9)+2=272/9+2=272/9+18/2=290/9

the side lengths are 136/9in, 53/3in, and 290/9in
3 0
2 years ago
The price of a pair of shoes is $45.90. The sales-tax rate is 5 percent. How much sales tax do you need to pay?
Airida [17]
45.90*0.05=2.295. The answer is $2.30 when you round it off.
5 0
3 years ago
Choose the correct answer choice.
Dafna1 [17]

Answer:

The T shirt choice

Step-by-step explanation:

Both values increase at the same rate therefore is proportional.

7 0
3 years ago
In the diagram below, TUVW is a rectangle. Prove triangle TZW is congruent to triangle UZV.
otez555 [7]

Answer:

By S.S.S. congruence property;  ΔTZW ≅ ΔVZU

Step-by-step explanation:

Given:

TUVW is a rectangle.

To Prove : TZW ≅ UZV

Proof:

Since TUVW is a rectangle, and we know that opposite side of a rectangle is equal.

So,

TW = UV \ \ .\ .\ .\ .\ 1

And also TV and WU are the diagonals of the rectangle.

And the diagonals of rectangle bisects each other.

Therefore;

TZ=ZV.........\ 2\\\\WZ=ZU..........\ 3

Now In ΔTZW and ΔVZU

TW = UV (from 1)

TZ = ZV (from 2)

WZ = ZU (from 3)

So, by S.S.S. congruence property;

ΔTZW ≅ ΔVZU

Hence proved.

8 0
3 years ago
What is 36÷2/3×9×1/2
krok68 [10]

Answer:

1/3

Step-by-step explanation:

Simplify the following:

((36/2)/(3×9))/2

((36/2)/(3×9))/2 = 36/(3×9×2×2):

36/(3×9×2×2)

36/9 = (9×4)/9 = 4:

4/(3×2×2)

4/2 = (2×2)/2 = 2:

2/(3×2)

2/(3×2) = 2/2×1/3 = 1/3:

Answer: 1/3

6 0
3 years ago
Read 2 more answers
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