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s2008m [1.1K]
2 years ago
5

Which civilization was known to use geometry to construct canals for the transportation of water?

Mathematics
2 answers:
Alina [70]2 years ago
6 0
The correct answer should be D. Babylonians.
tresset_1 [31]2 years ago
5 0
The correct answer I believe is D
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Which is greater 20.903 or 2.209
goldenfox [79]

Answer:

20.903

Step-by-step explanation:

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$5,000 is invested at 3% interest.
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5000*0.03+0.05x=275
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The answer is b
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Answer to -13.62-(27.9)
PolarNik [594]

Answer:

−  1049

Step-by-step explanation:

-13.62-(27.9)

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8 0
3 years ago
The table shows data from a survey about the number of times families eat at restaurants during a week. The families are either
kifflom [539]

Hey there,

To solve this problem, let us first define what is mean and median. Mean is the average of all the numbers in the data set while the median is the number in the middle of the data set in ascending order. If we create a box plot for the data of Rome and New York, we can see that there is an outlier in the data for New York. Since New York has an outlier, so the mean is not a good representation on the central tendency of the data. The mean is skewed (distorted) by the outlier. So in this case it is better to use the median. While the Rome data is nice and symmetrical, it does not seem to have an outlier,  so we can use the mean for this data set.

Therefore the answer is:

The Rome data center is best described by the mean. The New York data center is best described by the median

Hoped I Helped

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3 years ago
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What is the area of the shaded region in the figure below ? Leave answer in terms of pi and in simplest radical form
ser-zykov [4K]

Answer:

Step-by-step explanation:

That shaded area is called a segment. To find the area of a segment within a circle, you first have to find the area of the pizza-shaped portion (called the sector), then subtract from it the area of the triangle (the sector without the shaded area forms a triangle as you can see). This difference will be the area of the segment.

The formula for the area of a sector of a circle is:

A_s=\frac{\theta}{360}*\pi r^2 where our theta is the central angle of the circle (60 degrees) and r is the radius (the square root of 3).

Filling in:

A_s=\frac{60}{360}*\pi (\sqrt{3})^2 which simplifies a bit to

A_s=\frac{1}{6}*\pi(3) which simplifies a bit further to

A_s=\frac{1}{2}\pi which of course is the same as

A_s=\frac{\pi}{2}

Now for tricky part...the area of the triangle.

We see that the central angle is 60 degrees. We also know, by the definition of a radius of a circle, that 2 of the sides of the triangle (formed by 2 radii of the circle) measure √3. If we pull that triangle out and set it to the side to work on it with the central angle at the top, we have an equilateral triangle. This is because of the Isosceles Triangle Theorem that says that if 2 sides of a triangle are congruent then the angles opposite those sides are also congruent. If the vertex angle (the angle at the top) is 60, then by the Triangle Angle-Sum theorem,

180 - 60 = 120, AND since the 2 other angles in the triangle are congruent by the Isosceles Triangle Theorem, they have to split that 120 evenly in order to be congruent. 120 / 2 = 60. This is a 60-60-60 triangle.

If we take that extracted equilateral triangle and split it straight down the middle from the vertex angle, we get a right triangle with the vertex angle half of what it was. It was 60, now it's 30. The base angles are now 90 and 60. The hypotenuse of this right triangle is the same as the radius of the circle, and the base of this right triangle is \frac{\sqrt{3} }{2}. Remember that when we split that 60-60-60 triangle down the center we split the vertex angle in half but we also split the base in half.

Using Pythagorean's Theorem we can find the height of the triangle to fill in the area formula for a triangle which is

A=\frac{1}{2}bh. There are other triangle area formulas but this is the only one that gives us the correct notation of the area so it matches one of your choices.

Finding the height value using Pythagorean's Theorem:

(\sqrt{3})^2=h^2+(\frac{\sqrt{3} }{2})^2 which simplifies to

3=h^2+\frac{3}{4} and

3-\frac{3}{4}=h^2 and

\frac{12}{4} -\frac{3}{4} =h^2 and

\frac{9}{4} =h^2

Taking the square root of both the 9 and the 4 (which are both perfect squares, thankfully!), we get that the height is 3/2. Now we can finally fill in the area formula for the triangle!

A=\frac{1}{2}(\sqrt{3})(\frac{3}{2}) which simplifies to

A=\frac{3\sqrt{3} }{4}

Therefore, the area in terms of pi for that little segment is

A_{seg}=\frac{\pi}{2}-\frac{3\sqrt{3} }{4}, choice A.

8 0
3 years ago
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