37(2)
... Also, it is clear that G is bijective and x < G(x) for all x > 0. Thus, G~l exists and is also strictly increasing with G~l(x) < x. Let u = G_1(x). Then G(u) = x and u = 3x + v8x 2 +1. Since u < x, we have u = 3x - V8x2 4-1. Also, since 8(G_1(x))2 +1 = (8x - 3V8x2 +1) 2 is a perfect square, it follo ...
... Also, it is clear that G is bijective and x < G(x) for all x > 0. Thus, G~l exists and is also strictly increasing with G~l(x) < x. Let u = G_1(x). Then G(u) = x and u = 3x + v8x 2 +1. Since u < x, we have u = 3x - V8x2 4-1. Also, since 8(G_1(x))2 +1 = (8x - 3V8x2 +1) 2 is a perfect square, it follo ...
X - University of California, Santa Barbara
... Source http://www.math.psu.edu/dna/455.f96/disasters.html Unmanned Ariane 5 rocket of the European Space Agency veered off its flight path, broke up, and exploded only 30 s after lift-off (altitude of 3700 m) The $500 million rocket (with cargo) was on its first voyage after a decade of development ...
... Source http://www.math.psu.edu/dna/455.f96/disasters.html Unmanned Ariane 5 rocket of the European Space Agency veered off its flight path, broke up, and exploded only 30 s after lift-off (altitude of 3700 m) The $500 million rocket (with cargo) was on its first voyage after a decade of development ...
Hexadecimal Worksheet Solution
... What happens if we add 11+1? We get 100. Do you see the pattern? Try it for yourself below, by continually adding one to get the decimal number on the left: ...
... What happens if we add 11+1? We get 100. Do you see the pattern? Try it for yourself below, by continually adding one to get the decimal number on the left: ...
Scientific Notation
... size of an atom is about 0.00000003 centimeters across. The length of these numbers in standard notation makes them awkward to work with. Scientific notation is a shorthand way of writing such numbers. ...
... size of an atom is about 0.00000003 centimeters across. The length of these numbers in standard notation makes them awkward to work with. Scientific notation is a shorthand way of writing such numbers. ...
On the least prime in certain arithmetic
... The weaker conjecture that P (q)= (q) log q ! 1 is still unsolved though, by (5), it can be seen to hold for almost all q. (This conjecture seems to be most dicult to prove when q is the product of the rst k primes). Prachar [9] and Schinzel [11] have shown that there is some absolute constant > ...
... The weaker conjecture that P (q)= (q) log q ! 1 is still unsolved though, by (5), it can be seen to hold for almost all q. (This conjecture seems to be most dicult to prove when q is the product of the rst k primes). Prachar [9] and Schinzel [11] have shown that there is some absolute constant > ...
Permutations and combinations
... bomb in your city, and it is your job to disable it by cutting wires to the trigger device. There are 10 wires to the device. If you cut exactly the right three wires, in exactly the right order, you will disable the bomb, otherwise it will explode! If the wires all look the same, what are your chan ...
... bomb in your city, and it is your job to disable it by cutting wires to the trigger device. There are 10 wires to the device. If you cut exactly the right three wires, in exactly the right order, you will disable the bomb, otherwise it will explode! If the wires all look the same, what are your chan ...
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.