unit_1_mathIIB_assignment
... The astronomy club plans to wash cars to raise money for a new telescope. With tax, the telescope costs $327.19. Estimate how many cars will have to be washed to cover the entire cost of the telescope if the club charges $5.00 per car ...
... The astronomy club plans to wash cars to raise money for a new telescope. With tax, the telescope costs $327.19. Estimate how many cars will have to be washed to cover the entire cost of the telescope if the club charges $5.00 per car ...
Decimal expansions of fractions
... Corollary. If k is the smallest positive number with N k = 1 modulo p, then k|p − 1. Corollary. If p is a prime number, then the repeat length of the fraction 1/p in base B expression divides p − 1. Lets’ look at an example. Let p = 1/13. The decimal expression for 1/13 is 0.0769230769123 . . .. It ...
... Corollary. If k is the smallest positive number with N k = 1 modulo p, then k|p − 1. Corollary. If p is a prime number, then the repeat length of the fraction 1/p in base B expression divides p − 1. Lets’ look at an example. Let p = 1/13. The decimal expression for 1/13 is 0.0769230769123 . . .. It ...
Fractions and Mixed Numbers Fractions are a way of representing
... The number on the bottom is called the denominator, and indicates how many pieces the whole has been divided into. The number on top is the numerator, and shows how many pieces of the whole we have. Example: What fraction of the large box is shaded? The box is divided into 10 pieces, of which 6 are ...
... The number on the bottom is called the denominator, and indicates how many pieces the whole has been divided into. The number on top is the numerator, and shows how many pieces of the whole we have. Example: What fraction of the large box is shaded? The box is divided into 10 pieces, of which 6 are ...
// DOES RANDOM MEAN PURE CHANCE? It is hard to know if
... random? In a mathematical sense, there’s a choice being made here — specifically whom to shoot. Apparently, the victims do not know their killer, but the killer clearly chooses his victim — the killer is using a high-power rifle and is taking aim. So, how does the killer choose his victims? Possibly ...
... random? In a mathematical sense, there’s a choice being made here — specifically whom to shoot. Apparently, the victims do not know their killer, but the killer clearly chooses his victim — the killer is using a high-power rifle and is taking aim. So, how does the killer choose his victims? Possibly ...
Primes, Polygons, and Polynomials
... Gauss did not actually show the construction of the 17-gon. This was done a few years later. In 1832, a description of the construction of a 257-gon was published; the description took over 200 pages! It would have to be a big 257-gon, or it would look like a circle, and I can’t imagine how much acc ...
... Gauss did not actually show the construction of the 17-gon. This was done a few years later. In 1832, a description of the construction of a 257-gon was published; the description took over 200 pages! It would have to be a big 257-gon, or it would look like a circle, and I can’t imagine how much acc ...
Document
... Terms are separated by addition signs. If there are subtraction signs, we can find an equivalent expression that uses addition signs. ...
... Terms are separated by addition signs. If there are subtraction signs, we can find an equivalent expression that uses addition signs. ...
Geodesics, volumes and Lehmer`s conjecture Mikhail Belolipetsky
... setting, the volume would have to grow much faster. It is unknown if for n ≥ 4 there exist hyperbolic n-manifolds M with Syst1 (M ) → 0 and Vol(M ) growing slower than a polynomial in 1/Syst1 (M ). Let us also remark that an alternative proof of part (A) of Theorem 1 can be given using the original ...
... setting, the volume would have to grow much faster. It is unknown if for n ≥ 4 there exist hyperbolic n-manifolds M with Syst1 (M ) → 0 and Vol(M ) growing slower than a polynomial in 1/Syst1 (M ). Let us also remark that an alternative proof of part (A) of Theorem 1 can be given using the original ...
Addition
Addition (often signified by the plus symbol ""+"") is one of the four elementary, mathematical operations of arithmetic, with the others being subtraction, multiplication and division.The addition of two whole numbers is the total amount of those quantities combined. For example, in the picture on the right, there is a combination of three apples and two apples together; making a total of 5 apples. This observation is equivalent to the mathematical expression ""3 + 2 = 5"" i.e., ""3 add 2 is equal to 5"".Besides counting fruits, addition can also represent combining other physical objects. Using systematic generalizations, addition can also be defined on more abstract quantities, such as integers, rational numbers, real numbers and complex numbers and other abstract objects such as vectors and matrices.In arithmetic, rules for addition involving fractions and negative numbers have been devised amongst others. In algebra, addition is studied more abstractly.Addition has several important properties. It is commutative, meaning that order does not matter, and it is associative, meaning that when one adds more than two numbers, the order in which addition is performed does not matter (see Summation). Repeated addition of 1 is the same as counting; addition of 0 does not change a number. Addition also obeys predictable rules concerning related operations such as subtraction and multiplication.Performing addition is one of the simplest numerical tasks. Addition of very small numbers is accessible to toddlers; the most basic task, 1 + 1, can be performed by infants as young as five months and even some non-human animals. In primary education, students are taught to add numbers in the decimal system, starting with single digits and progressively tackling more difficult problems. Mechanical aids range from the ancient abacus to the modern computer, where research on the most efficient implementations of addition continues to this day.