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Answer:
1 - (π/6) - (√3/4)
Step-by-step explanation:
First, calculate the area of ABCD. That's just
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 = AD =
. 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.
Answer: Write the expression as:
" 70
+
2
* 2
− 18a " ;
______________________________________________________
or; write as:
______________________________________________________
" 70.32 + (2.1) * (2.7) − 18a " ;
______________________________________________________
To simplify:
______________________________________________________
Using "PEDMAS" (the "order of operations") ;
the "multiplication" comes first;
So: → "(2.1) * (2.7) = 5.67 " .
And rewrite:
______________________________________________________
" 70.32 + 5.67 − 18a " .
Now: " 70.32 + 5.67 = 75.99 " ;
So, we can the final simplified expression as:
______________________________________________________
" 75.99 − 18a " ;
or; write as: " 75
− 18a " .
______________________________________________________
" 70
2
______________________________________________________
or; write as:
______________________________________________________
" 70.32 + (2.1) * (2.7) − 18a " ;
______________________________________________________
To simplify:
______________________________________________________
Using "PEDMAS" (the "order of operations") ;
the "multiplication" comes first;
So: → "(2.1) * (2.7) = 5.67 " .
And rewrite:
______________________________________________________
" 70.32 + 5.67 − 18a " .
Now: " 70.32 + 5.67 = 75.99 " ;
So, we can the final simplified expression as:
______________________________________________________
" 75.99 − 18a " ;
or; write as: " 75
______________________________________________________
4. Supplementary angles together make a straight line (two right angles). So BOE is supplementary to BOC
Answer: ∠BOE
5. Distance and midpoint between (4,-2), (6,8)
midpoint
Answer: distance 2√26, midpoint (5, 3)
6.That's a rectangle oriented parallel to the axes, width parallel to the x axis of 7 - -3 = 10 and length along y of 1 - - 4 = 5, so an area of 10(5)=50
Answer: 50