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Hi bobbym and Relentless,

The Answer #2299 is correct! Excellent, Relentless!

#2301. What does the noun *biathlon* mean?

#2302. What does the noun *bewilderment* mean?

Hi Relentless and bobbym,

The six solutions in #2718 are correct! Marvelous!

#2719. Find the whole number which when decreased by 20 is equal to 69 times the reciprocal of the number.

Hi bobbym,

The Answer #2298 is correct! Good work!

#2299. What does the noun *bête noire* mean?

#2300. What does the noun *bevel* mean?

Hi Relentless and bobbym,

The solution #2717 is correct! Excellent!

#2718. A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is

(i) the seven of clubs

(ii) jack

(iii) the ace of spades

(iv) a queen

(v) a heart

(vi) a red card

Hi Relentless and bobbym,

The solution #2716 is correct! Excellent!

#2717. If

, find the value of .61. The Wright brothers, Orville (August 19, 1871 – January 30, 1948) and Wilbur (April 16, 1867 – May 30, 1912), were two American brothers, inventors, and aviation pioneers who are credited with inventing and building the world's first successful airplane and making the first controlled, powered and sustained heavier-than-air human flight, on December 17, 1903 four miles south of Kitty Hawk, North Carolina. In 1904-1905 the brothers developed their flying machine into the first practical fixed-wing aircraft. Although not the first to build and fly experimental aircraft, the Wright brothers were the first to invent aircraft controls that made fixed-wing powered flight possible.

The brothers' fundamental breakthrough was their invention of three-axis control, which enabled the pilot to steer the aircraft effectively and to maintain its equilibrium. This method became and remains standard on fixed-wing aircraft of all kinds. From the beginning of their aeronautical work, the Wright brothers focused on developing a reliable method of pilot control as the key to solving "the flying problem". This approach differed significantly from other experimenters of the time who put more emphasis on developing powerful engines. Using a small homebuilt wind tunnel, the Wrights also collected more accurate data than any before, enabling them to design and build wings and propellers that were more efficient than any before. Their first U.S. patent, 821,393, did not claim invention of a flying machine, but rather, the invention of a system of aerodynamic control that manipulated a flying machine's surfaces.

They gained the mechanical skills essential for their success by working for years in their shop with printing presses, bicycles, motors, and other machinery. Their work with bicycles in particular influenced their belief that an unstable vehicle like a flying machine could be controlled and balanced with practice. From 1900 until their first powered flights in late 1903, they conducted extensive glider tests that also developed their skills as pilots. Their bicycle shop employee Charlie Taylor became an important part of the team, building their first airplane engine in close collaboration with the brothers.

The Wright brothers' status as inventors of the airplane has been subject to counter-claims by various parties. Much controversy persists over the many competing claims of early aviators. Historian Edward Roach argues that they were excellent self-taught engineers with a knack for tinkering more than for systematic research, but they proved to be poor businessmen.

Hi bobbym,

The Answer #2296 is correct! Excellent!

#2297. What does the verb (used with object) *bestrew* mean?

#2298. What does the verb (used with object) *bestride* mean?

Hi bobbym,

The solution #2715 is correct! Excellent!

#2716. If

, find the value of .Hi bobbym,

The Answer #2293 is correct! Neat work!

#2295. What does the noun *bestiary* mean?

#2296. What does the verb (used with object) *bestir* mean?

Hi bobbym,

The solution #2714 is correct! Brilliant!

#2715. If

, find the value of .Hi bobbym,

The Answer #2291 is correct! Good work!

#2293. What does the verb (used with object) *besmirch* mean?

#2294. What does the adjective *besotted* mean?

Hi bobbym,

#2714. If

, find the .Hi bobbym,

The Answer #2289 is correct! Good work!

#2291. What does the verb (used with object) *besiege* mean?

#2292. What does the adjective *besmeared* mean?

Hi Relentless and bobbym,

The solution #2712 is perfect! Excellent, Relentless and bobbym!

#2713. If

, where 4A is an acute angle, find the value of A.Hi philaretus,

**Welcome to the forum!**

Hi bobbym,

The solution #2711 is correct! Brilliant!

#2712. A train travels a distance of 300 km at constant speed. If the speed of the train is increased by 5 km an hour, the journey would have taken 2 hours less. Find the original speed of the train.

Hi bobbym,

The solution (both parts) is correct! Good work!

#2711. Solve for x:

60. Euclid, sometimes called Euclid of Alexandria to distinguish him from Euclid of Megara, was a Greek mathematician, often referred to as the "Father of Geometry". He was active in Alexandria during the reign of Ptolemy I (323–283 BC). His 'Elements' is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics (especially geometry) from the time of its publication until the late 19th or early 20th century. In the 'Elements', Euclid deduced the principles of what is now called Euclidean geometry from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory and rigor.

Although many of the results in 'Elements' originated with earlier mathematicians, one of Euclid's accomplishments was to present them in a single, logically coherent framework, making it easy to use and easy to reference, including a system of rigorous mathematical proofs that remains the basis of mathematics 23 centuries later.

There is no mention of Euclid in the earliest remaining copies of the Elements, and most of the copies say they are "from the edition of Theon" or the "lectures of Theon", while the text considered to be primary, held by the Vatican, mentions no author. The only reference that historians rely on of Euclid having written the' Elements' was from Proclus, who briefly in his Commentary on the 'Elements' ascribes Euclid as its author.

Although best known for its geometric results, the Elements also includes number theory. It considers the connection between perfect numbers and Mersenne primes (known as the Euclid-Euler theorem), the infinitude of prime numbers, Euclid's lemma on factorization (which leads to the fundamental theorem of arithmetic on uniqueness of prime factorizations), and the Euclidean algorithm for finding the greatest common divisor of two numbers.

The geometrical system described in the Elements was long known simply as geometry, and was considered to be the only geometry possible. Today, however, that system is often referred to as Euclidean geometry to distinguish it from other so-called non-Euclidean geometries that mathematicians discovered in the 19th century.

Hi bobbym,

Revised: #2710. If one root of the quadratic equation

is 2, find the value of k. Also, find the other root.Hi bobbym,

The solution #2709 (four parts) are correct! Wonderful!

#2710. If one root of the quadratic equation

, find the value of k. Also, find the other root.Hi bobbym and math9maniac,

The solution #2708 is correct, bobbym and math9maniac! Excellent!

The problem #2707 may be treated as 'Null and Void'!

#2709. A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is

(i) other than an ace

(ii) a ten

(iii) a spade

(iv) a black card

Hi bobbym,

#2708. Given that 16cotA = 12, find the value of

.59. Aristotle (384-322 BC) was a Greek philosopher and scientist born in the city of Stagira, Chalkidice, on the northern periphery of Classical Greece. His father, Nicomachus, died when Aristotle was a child, whereafter Proxenus of Atarneus became his guardian. At eighteen, he joined Plato's Academy in Athens and remained there until the age of thirty-seven (c. 347 BC). His writings cover many subjects – including physics, biology, zoology, metaphysics, logic, ethics, aesthetics, poetry, theater, music, rhetoric, linguistics, politics and government – and constitute the first comprehensive system of Western philosophy. Shortly after Plato died, Aristotle left Athens and, at the request of Philip of Macedon, tutored Alexander the Great starting from 343 BC. According to the Encyclopædia Britannica, "Aristotle was the first genuine scientist in history ... [and] every scientist is in his debt."

Teaching Alexander the Great gave Aristotle many opportunities and an abundance of supplies. He established a library in the Lyceum which aided in the production of many of his hundreds of books. The fact that Aristotle was a pupil of Plato contributed to his former views of Platonism, but, following Plato's death, Aristotle immersed himself in empirical studies and shifted from Platonism to empiricism. He believed all peoples' concepts and all of their knowledge was ultimately based on perception. Aristotle's views on natural sciences represent the groundwork underlying many of his works.

Aristotle's views on physical science profoundly shaped medieval scholarship. Their influence extended into the Renaissance and were not replaced systematically until the Enlightenment and theories such as classical mechanics. Some of Aristotle's zoological observations, such as on the hectocotyl (reproductive) arm of the octopus, were not confirmed or refuted until the 19th century. His works contain the earliest known formal study of logic, which was incorporated in the late 19th century into modern formal logic.

In metaphysics, Aristotelianism profoundly influenced Judeo-Islamic philosophical and theological thought during the Middle Ages and continues to influence Christian theology, especially the scholastic tradition of the Catholic Church. Aristotle was well known among medieval Muslim intellectuals and revered as "The First Teacher".

His ethics, though always influential, gained renewed interest with the modern advent of virtue ethics. All aspects of Aristotle's philosophy continue to be the object of active academic study today. Though Aristotle wrote many elegant treatises and dialogues – Cicero described his literary style as "a river of gold" – it is thought that only around a third of his original output has survived.

58. Captain James Cook (7 November 1728 – 14 February 1779) was a British explorer, navigator, cartographer, and captain in the Royal Navy. Cook made detailed maps of Newfoundland prior to making three voyages to the Pacific Ocean, during which he achieved the first recorded European contact with the eastern coastline of Australia and the Hawaiian Islands, and the first recorded circumnavigation of New Zealand.

Cook joined the British merchant navy as a teenager and joined the Royal Navy in 1755. He saw action in the Seven Years' War, and subsequently surveyed and mapped much of the entrance to the Saint Lawrence River during the siege of Quebec. This helped bring Cook to the attention of the Admiralty and Royal Society. This notice came at a crucial moment in both Cook's career and the direction of British overseas exploration, and led to his commission in 1766 as commander of HM Bark Endeavour for the first of three Pacific voyages.

In three voyages Cook sailed thousands of miles across largely uncharted areas of the globe. He mapped lands from New Zealand to Hawaii in the Pacific Ocean in greater detail and on a scale not previously achieved. As he progressed on his voyages of discovery he surveyed and named features, and recorded islands and coastlines on European maps for the first time. He displayed a combination of seamanship, superior surveying and cartographic skills, physical courage and an ability to lead men in adverse conditions.

Cook was killed in Hawaii in a fight with Hawaiians during his third exploratory voyage in the Pacific in 1779. He left a legacy of scientific and geographical knowledge which was to influence his successors well into the 20th century and numerous memorials worldwide have been dedicated to him.

Hi bobbym,

The solution #2706 is correct! Neat work!

#2707. Points A and B km apart from each other on a highway. A car starts from 'A' and another from 'B' at the same time. If they go in the same direction they meet in 9 hours and if they go in opposite directions they meet in 9/7 hours. Find their speeds.