Extended Problem #1
Search for numbers having exactly 7 factors.
Numbers having exactly 7 factors are numbers that are perfect squares; perfect squares are the squares of whole numbers that have an odd number of factors. Furthermore, the square of a number is that number times itself. Perfect squares: 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169… Although the number 7 is a squared number, it also has 6 other factors. The number that’s being squared will have 3 factors on each side. Therefore by taking prime numbers into consideration, the perfect squares of a prime number will have 3 factors because prime numbers only have factors of 1 and themselves. So, the prime number will be raised to a certain power. When raising the squared
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For the 7 factors we can include the number 8 along with the numbers 1, 2, and 4. By using this method of multiplying the factors to get others, we get the perfect square 16 because we multiply out the factors 8 and 2. If we continue to use this method we find that the numbers are similar and result as perfect squares. By multiplying the factors we have, we are then able to find the numbers being squared. If we use the middle number which is 8 and multiply it by the factor 4 we get 32 which is also a number of the 7 factors, along with the numbers 1, 2, 4, 8, and 16. As we continue to find the other factors, we can determine that the middle number (which is 8) is a square; therefore 8 squared is 64 and 64 has 7 …show more content…
Using this method, we then looked at the prime number 3; the perfect square of 3 is 9.
Factors of 9: 1, 3, and 9.
However, since we are looking to find 7 factors we must determine the 4 other factors of the mystery number along with 1, 3, and 9. To find this number, we began by multiplying the factors together (1x3x9) which gave us 27; after finding 27, we came to the realization that 27 would be the middle number. We then multiplied the factors again (1x3x9x27), which is initially 27 multiplied by itself— yielding a perfect square (27x27).
As we continued to analyze these numbers further, we came to recognize that the numbers tripled. To explain further, the factors were increasing by 3; this allowed us to determine our next factor by multiplying our last factor, 27, by 3 which gives us 81.
1x3= 9, 9x3=27, 27x3= 81, 81x3= 243, 243x3= 729
Factors: 1, 3, 9, 27, 81, 243,
17. Beach sandals are on sale for $2 a pair. Josey wants to buy a pair for all of her friends. She can spend at most $45. How many pairs of sandals can Josey buy? Write an inequality to best fits the problem. Then solve the inequality to find the number of pairs of sandals.
During the course ofthe conversation, the Monarch called the Square and his ideas "uneducated," "irrational," and "audacious" (P. 51). The Monarch thinks if A. Square "had a particle of sense, [he] would listen to reason" (P. 51). Upon listening to the opinion that Flatland is lacking so much as compared to Lineland, A. Square strikes back, saying, "you think yourself the perfection of existence, while you are in reality the most imperfect and imbecile" (P. 5I). A. Square continues, claiming, "I am the completion of your incomplete self" (P. 51). Neither the Monarch nor A. Square could be swayed to the other one's way of thinking.
This is the perfect opportunity to take that expression or equation that was built in the first half and start the process of finding x. Combining terms and subtracting numbers from both sides will aid in the process of the ultimate goal of finding the unknown number. Many times teachers us a balance with chess pieces and students have a hard time visualizing why 2 paws have to be taken from both sides. The Napping House (1984) clearly depicts how subtraction needs to occur on both sides of the equation. Ultimately, just like balancing equations, the story ends beautifully with everyone and everything
We know this because as a child he claims the “Good life said to exist in those far Northern places”. This belief was brought up upon cultural differences in these different areas. What's ironic about this story is that the narrator is introduced to square
"Sphere", bestows upon A. Square the greatest gift he could hope for, knowledge. It is only after the Sphere forcibly takes A. Square out of his dimension, however, that he is able to shrug off his ignorance and accept the fact that what cannot be, can, and much of what he believed before is wrong. When he sees first hand that a square can have depth simply by lining up a parallel square above it and connecting the vertices with lines he is awestruck by its beauty. A cube now exists, seemingly made out of squares. Where there was but one square before now there are six connected. To A. Square's mindset, this thing of beauty is something he could become if only he could lift up. It gives him hope, for in his world you are ranked without say according to your shape. From the lowest convict shapes to the - not - quite - perfectly - round - but - practically - there priests. When A. Square asks the sphere deity what comes next, what about the fourth dimension, Sphere becomes vexed and sends A. Square plummeting back to his original world without the necessary knowledge to be effective in spreading the gospel of the third dimension. This is, of course, what leads to the end for A. Square; being locked up in an insane asylum for speaking of what simply cannot be. Adding to the irony is that no matter how hard A. Square tries, it is quite impossible for hi...
“In art class, though, he was great. Just give him a pencil or paints and he would make pictures that were so full of life that even the teacher was amazed.” K’s art is the biggest symbolic object in the book. Some may argue that the wave is the biggest symbol but others may disagree, the wave represents The Sevenths Man's fears but the artwork represents his reconciliation and the object that gave him the chance to start his life over again. K, also was an important symbol, he represented a brother, a best friend and a responsibility the Seventh Man took upon himself to protect and love:. “And because he was so frail, I always played his protector, whether at school or at home. But the main reason I enjoyed spending time with K. was that he was such a sweet, pure-hearted
The square is a shape that not only represents the plays character’s view of Othello but outlines his true inner character. First of al, the geometrical properties of a square support its representing character. The square, having straight rigid edges, appears to be a very strong shape. It’s sides and angle,
“Class,” I announced, “today I will teach you a simpler method to find the greatest common factor and the least common multiple of a set of numbers.” In fifth grade, my teacher asked if anyone had any other methods to find the greatest common factor of two numbers. I volunteered, and soon the entire class, and teacher, was using my method to solve problems. Teaching my class as a fifth grader inspired me to teach others how important math and science is. These days, I enjoy helping my friends with their math homework, knowing that I am helping them understand the concept and improve their grades.
every number. Then move your ruler down to the bottom. No, put it across the bottom. Now
I am going to begin by investigating a square with a side length of 10
Text Box: In the square grids I shall call the sides N. I have colour coded which numbers should be multiplied by which. To work out the answer the calculation is: (2 x 3) – (1 x 4) = Answer Then if I simplify this: 6 - 4 = 2 Therefore: Answer = 2
If p is a prime, is 2p - 1 always square free? i.e. not divisible by the square of a prime.
“Class,” I announced, “today I will teach you a simpler method to find the greatest common factor and the least common multiple of a set of numbers.” In fifth grade, my teacher asked if anyone had any other methods to find the greatest common factor of two numbers. I volunteered, and soon the entire class, and teacher, was using my method to solve problems. Teaching my class as a fifth grader inspired me to teach others how important math and science is. These days, I enjoy helping my friends with their math homework, knowing that I am helping them understand the concept and improve their grades.
The concept of perfect market allocation of resources was in W. Baumol's (1988,631), view largly theroretical. Baumol believed that economic models relied upon the concept of the invisible hand first discussed by Adam Smith. In these models, the perfectly competetive economy was able to allocate resources efficiently, without the need for market intervention by outside agents, including governments. However, there were significant weaknesses in these models particuarly in the area of ensuring equity of acess, social objectives and in the provision of public goods.
Then in Euclid II, 7, it goes farther to explain that “if a straight line be cut at random, the square on the whole and that on one of the segments both together, are equal to twice the rectangle contained by the whole and said segm...