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A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.
Gottfried Wilhelm Leibniz (or Leibnitz; [a] 1 July 1646 [O.S. 21 June] – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat who is credited, alongside Sir Isaac Newton, with the creation of calculus in addition to many other branches of mathematics, such as binary arithmetic and statistics.
Long-term net migration (the number of people immigrating minus the number emigrating) reached a record of 764,000 in 2022, with immigration at 1.26 million and emigration at 493,000. [408] In 2023, net migration was 685,000; 10% of the total who came to the UK in that year were EU Nationals. [403] More EU Nationals left the UK than arrived. [403]
Archimedes challenges them to count the numbers of cattle in the Herd of the Sun by solving a number of simultaneous Diophantine equations. There is a more difficult version of the problem in which some of the answers are required to be square numbers .
The 2020 election held in July saw the PAP drop to 61% of the vote, while the Workers' Party took 10 of the 93 seats, the highest number ever won by another party. [122] On 15 May 2024, Lawrence Wong became Singapore's fourth Prime Minister; he is the first prime minister born after independence. [123]
Approximately 4.8% or 36,845.6 square kilometres (3,684,560 ha) of Pakistan was forested in 2021. [202] [j] Markhor is the national animal of Pakistan. [203] Pakistan's fauna mirrors its diverse climate. The country boasts around 668 bird species, [204] including crows, sparrows, mynas, hawks, falcons, and eagles.
Each side of the bridge contains an anchorage for the main cables. The anchorages are trapezoidal limestone structures located slightly inland of the shore, measuring 129 by 119 feet (39 by 36 m) at the base and 117 by 104 feet (36 by 32 m) at the top. [5] [6] Each anchorage weighs 60,000 short tons (54,000 long tons; 54,000 t). [5]