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algol [13]
2 years ago
12

I will mark brainliest IF CORRECT

Mathematics
1 answer:
umka2103 [35]2 years ago
3 0

Answer:

1 - (π/6) - (√3/4)

Step-by-step explanation:

First, calculate the area of ABCD. That's just 1*1 = 1 un^{2}

Then, we are told that arcs BD and AC are circular, meaning they are portions of a circle. Therefore, let's redraw this image a little. Look below for the image.

Essentially, what I've done is created an equilateral triangle and two sectors. You may be wondering why the triangle is equilateral. Well, we firstly know it's isosceles because the two original arcs are circular and congruent. Their overlap creates two congruent lines that can be extend from point M to the vertices A and D. These two lines also happen to be radii of the quarter circles because the two sectors have AM AND AD as radii. AM and AD = 1, so AMD is an equilateral triangle.

Draw altitude OD. This is a right angle. Since equilateral triangles are also isosceles triangles, and isosceles triangles have the property of sharing the median to base and altitude to base, we can say that OD = \frac{1}{2} AD = \frac{1}{2}. MD = 1, so this triangle is a 30-60-90 triangle. Why? This is because of the 30º angle converse theorem. The shorter leg is half of the hypotenuse MD, so <OMD is a 30º angle, making <ODM a 60º angle and inevitably <MDC a 30º angle (because <D is a right angle) and <ABM as well because the two sectors are congruent.

Because m<ABM = m<MDC = 30º, these two sectors are 30/360 of the individual circles or 1/12 of the original circles, which have areas of π (because 1^2*π = π). Each is 1/12π, combined they are 1/6π.

The area of the equilateral triangle is √3/8. This is because MO can be calculated, using the 30-60-90 ratios, to be √3/2. (1 * √3/2)/2 = (√3/2)/2 = √3/4; this uses the area of a triangle. Now, time to calculate the shaded area.

The area of the square is 1, the area of the sectors π/6, and the equilateral triangle √3/4. Subtract the equilateral triangle and sectors' areas from the area of the square to be left with the remaining shaded part. 1-(π/6)-(√3/4) is your final answer. To put that a little more cleanly below in the image.

Hope this helps, have a great day.

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Which is greater? 0.04 or 0.39
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Answer:

0.39

Step-by-step explanation:

think about it this way, if you take away the decimal it would be 39 and 04. 04 is another way to write 4 and  4 is less than 39. so 0.04 is less than 0.39

6 0
2 years ago
Read 2 more answers
Y= -3x-9 and y=1/3 x -39
iren2701 [21]
(9,-36)
X=9 Y= -36
-3x-9=1/3x-39
Solve it
The answer is x=9
Y=-3x-9
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8 0
2 years ago
the first term of a geometric progression is 12 and the second term is -6. Find the (i) the tenth term of the progression (ii) t
lesantik [10]

Step-by-step explanation:

a1=ar⁰=12 A2=ar¹=-6

a=12 ar=-6

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6 0
3 years ago
find the smaller number of two consecutive odd numbers such that the sum of the larger numbers and twice the smaller number is 2
Contact [7]

Answer: 29

Step-by-step explanation:

Let the smaller number be x

Let the bigger number be x+2

The information given in the question can be represented in a equation as:

x + 2 + 2x = 4x - 27

3x + 2 = 4x - 27

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x = 29

The smaller number is 29

6 0
3 years ago
Help me please thank you
algol13

Answer:

8

Step-by-step explanation:

7 0
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