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question:Is the number 28721 a prime number?

answer:To determine if 28721 is a prime number, we perform a primality test: 1. Since sqrt{28721} approx 169.4, we only need to check divisibility by primes less than or equal to 169. 2. 28721 is odd, so it is not divisible by 2. 3. The sum of the digits (2 + 8 + 7 + 2 + 1) equals 20, which is not divisible by 3, so 28721 is not divisible by 3. 4. The last digit of 28721 is not 5 or 0, so it is not divisible by 5. 5. When we divide 7 into 28721, it divides exactly: 28721 div 7 = 4103 Since 28721 is divisible by 7, it is not a prime number. Therefore, 28721 is composite.

question:What theory emerged from archaeological evidence that the Harappan civilization was not destroyed by external invasion?

answer:The Aryan migration theory

question:A side-angle-side triangle has sides of length 7.17 and 7.78 units and an angle of measure frac{4 pi }{5} radians. Determine the coordinates of the points that define the lines for the triangle's altitude, cevian, median, and symmedian lines.

answer:To find the coordinates of the points that define the lines for the triangle's altitude, cevian, median, and symmedian lines, we can use the following formulas: Median: The median of a triangle is a line segment that connects a vertex to the midpoint of the opposite side. The coordinates of the midpoint of the side with length 7.78 are left(frac{7.17}{2}, 0right). Therefore, the coordinates of the points that define the line for the median are left(7.11, 0right) and left(3.72, 1.15right). Symmedian: The symmedian of a triangle is a line segment that connects a vertex to the centroid of the triangle. The centroid of a triangle is the point of intersection of the medians. Therefore, the coordinates of the centroid are left(frac{7.11+3.72}{3}, frac{0+1.15}{3}right) = left(3.61, 0.38right). Therefore, the coordinates of the points that define the line for the symmedian are left(7.11, 0right) and left(5.92, 1.84right). Cevian: A cevian is a line segment that connects a vertex to any point on the opposite side. Since the cevian is not specified, we can choose any point on the opposite side. Let's choose the point left(0, 0right). Therefore, the coordinates of the points that define the line for the cevian are left(7.11, 0right) and left(3.72, 1.15right). Altitude: The altitude of a triangle is a line segment that is perpendicular to a side and passes through the opposite vertex. The altitude of the triangle with sides of length 7.17 and 7.78 and an angle of measure frac{4 pi }{5} radians has length frac{7.17 cdot 7.78 sin frac{4 pi }{5}}{7.78} = 6.49. Therefore, the coordinates of the points that define the line for the altitude are left(7.11, 0right) and left(12.97, 4.03right). Median: left( begin{array}{cc} 7.11 & 0 3.72 & 1.15 end{array} right) Symmedian: left( begin{array}{cc} 7.11 & 0 5.92 & 1.84 end{array} right) Cevian: left( begin{array}{cc} 7.11 & 0 3.72 & 1.15 end{array} right) Altitude: left( begin{array}{cc} 7.11 & 0 12.97 & 4.03 end{array} right)

question:What was the difference between the motivations for creating Black-only infantries in the Union and Confederate armies?

answer:The Union's 54th Infantry was formed to fight for the abolition of slavery, while the Confederate army created Black-only infantries to maintain the institution of slavery and force enslaved people to fight for their own oppression.

Released under the MIT License.

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