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number of ways = (7 x 6 x 5) x (9 x 8 x 7) = 105840

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Q: A music festival gives 1st 2nd and 3rd prize in each category If there are 7 violin and 9 piano contestants in how many ways can the six awards be given?
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Where did the expression?

The "World's Smallest Violin" expression was first used when a T. Rex first played it for the rest of the dinosaurs when they were facing extinction. Of course, the T. Rex, being the king of all Dinosaurs, thought this would not effect him so he (archeologists assume male due to enlarged sarcasm gland perfectly fossilized) proceeded to play, what to him was the world's smallest violin. By today's standards this violin was a full size 4/4 violin but to a T. Rex this was tiny. While scale played a huge importance here and continues to do so when modern humans play the smallest violin for their purposes, this was the first instance of: "This is the world's smallest violin I am playing for you."


10 pitched and 10 unpitched instruments?

PITCHED: flute,keyboard,violin,trumpet,double bass, cello, clarinet,piccolo,bassoon,harp. (any instrument that you can play different notes on) UNPITCHED:drums,tamtam,cymbals,triangles,tambourine,maracas,cowbell,timpani,timbales,marching drum.(any instrument that you cant play different notes on)


Which type of graph would best show the number of fifth graders and the number of sixth graders who play the violin piano or flute?

A stacked bar chart with a mid-section that shows people who play both.


What is the history of fourier series?

It is quite complicated, and starts before Fourier. Trigonometric series arose in problems connected with astronomy in the 1750s, and were tackled by Euler and others. In a different context, they arose in connection with a vibrating string (e.g. a violin string) and solutions of the wave equation.Still in the 1750s, a controversy broke out as to what curves could be represented by trigonometric series and whether every solution to the wave equation could be represented as the sum of a trigonometric series; Daniel Bernoulli claimed that every solution could be so represented and Euler claimed that arbitrary curves could not necessarily be represented. The argument rumbled on for 20 years and dragged in other people, including Laplace. At that time the concepts were not available to settle the problem.Fourier worked on the heat equation (controlling the diffusion of heat in solid bodies, for example the Earth) in the early part of the 19th century, including a major paper in 1811 and a book in 1822. Fourier had a broader notion of function than the 18th-century people, and also had more convincing examples.Fourier's work was criticised at the time, and his insistence that discontinuous functions could be represented by trigonometric series contradicted a theorem in a textbook by the leading mathematician of the time, Cauchy.Nonetheless Fourier was right; Cauchy (and Fourier, and everyone else at that time) was missing the idea of uniform convergence of a series of functions. Fourier's work was widely taken up, and also the outstanding problems (just which functions can be represented by Fourier series?; how different can two functions be if they have the same Fourier series?) were slowly solved.Source: Morris Kline, Mathematical Thought from Ancient to Modern Times, Oxford University Press, 1972, pages 478-481, 502-514, 671-678,and 964.