Casey for 50 pounds of dirt she was 10 pounds pounds to fill a hole in the yard then she filled pots with 5 pounds of soil in ea
1 answer:
Answer:
8 pots.
Step-by-step explanation:
Given:
Casey for 50 pounds of dirt, she used 10 pounds to fill a hole in the yard.
From remaining dirt, she filled pots with 5 pounds of soil in each pot.
Question asked:
How many pots could Casey fill ?
Solution:
Total quantity of dirt, Casey has = 50 pounds
She used quantity of dirt to fill a hole in the yard = 10 pounds
Remaining quantity of dirt = 50 pounds - 10 pounds = 40 pounds
Now, as given that from remaining dirt, she filled pots with 5 pounds of soil in each pot and we have to find number of pot filled, <u>we will simply divide remaining dirt by quantity of dirt filled in each pot</u>
40 5 = 8 pots
Thus, Casey can fill 8 pots having 5 pounds in each pot.
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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.
