Mathematics and art have a long historical relationship. The ancient Egyptians and ancient Greeks knew about the golden ratio‚ regarded as an aesthetically pleasing ratio‚ and incorporated it into the design of monuments including the Great Pyramid‚[1] theParthenon‚ the Colosseum. There are many examples of artists who have been inspired by mathematics and studied mathematics as a means of complementing their works. The Greek sculptor Polykleitos prescribed a series of mathematical proportions for
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1. The use of knowledge and understanding of mathematics in engineering context. Mathematics is science of pattern that engineers seek out whether found in numbers‚ space‚ science‚ computers‚ imaginary abstractions‚ or elsewhere. Knowledge and use of basic mathematics have always been an inherent and integral part of engineering. In our previous semester‚ basic mathematics was applied in almost every module. From stress analysis of simple machine components to numerical description of various
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John has $20‚000 to invest. He invests part of his money at an annual interest rate of 6%‚ the rest at 9% annual rate. The return on these two investments over one year is $1‚440. How much does he invest at each rate? Solution Paul made two investments totaling $15‚000. The percentage return on the first investment was 7% annually‚ while the the percentage return on the second one was 10% annually. If the total return on the two investments over one year was $1‚350‚ how much was invested
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below shows some of the formulae entered to generate the spreadsheet above. Extrapolation in terms of a diagram and geometric progressions T8 T16 “T32”“ T64” X According to the theory derived earlier 32 16 16 8 1 ( - 4 T T≈ + T T ) This gives us the so called “extrapolated” value 32 16 16 8 1 " " ( -). 4 T T TT = + Note‚ this is exactly how “T32” was calculated on the previous page. And then 2 2 64 32 16 8 16 16 8 16 8 1 11
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MDM 4U Chapter 5 Test K ( ) T ( / ) A( / ) C( / ) Short Answer 1. For a calculus quiz‚ the teacher will choose 11 questions from the 15 in a set of review exercises. How many different sets of questions could the teacher choose? K-6 2. All 16 people at a function shake hands with everyone else at the function. Use combinations to find the total number of handshakes. T- 6 3. How many different sums of money can you make with three pennies‚ a nickel
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SPM(U) 2006 : http://mathsmozac.blogspot.com Section A [52 marks] Answer all questions in this section. 1 The Venn diagram in the answer space shows sets P‚ Q and R such that the universal set‚ ξ = P ∪ Q ∪ R . On the diagram in the answer space‚ shade (a) the set P ∪ R ‚ (b) the set (P ∩ R ) ∪ Q ’ . [3 marks] Answer: (a) P Q R (b) P R Q 2 Diagram 1 shows a solid cuboid. A cone is removed from this solid. 12 cm 10 cm 15 cm DIAGRAM 1 The diameter of the base of the cone is 7 cm
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University of Rizal System Morong‚ Rizal Submitted to: Dr. Juliet Beringuel Submitted by: Germaine L. Acapulco Title of the Study: Groups of Piecewise Linear Homeomorphisms Author: Melanie Stein Date Conducted: August 1991 Place Conducted: Abstract: In this paper we study a class of groups which may be described as groups of piecewise linear bijections of a circle or of compact intervals of the real line. We use the action of these groups on simplicial complexes to obtain homological
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5C Problems involving triangles cQ1. The diagram shows a sector AOB of a circle of radius 15 cm and centre O. The angle at the centre of the circle is 115. Calculate (a) the area of the sector AOB. (b) the area of the shaded region. (226 ‚ 124 nQ2. Consider a triangle and two arcs of circles. The triangle ABC is a right-angled isosceles triangle‚ with AB = AC = 2. The point P is the midpoint of [BC]. The arc BDC is part of a circle with centre A
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COURSE: Pre IBDP Algebra 2 Trigonometry Assessment Model: 80-20 2013-2014 YEAR AT A GLANCE Sept. 2 (2 = 1st day; 4 days) Class expectations Review Algebra – ch 1 & 2 Nov 4 (5=workday; 4 days) 10-7 Non-Linear Systems of Equations Jan 27 (27 = workday; 4 days) STATISTICS INVESTIGATION UNIT 13 – Statistics 11-1 permutations & combinations measures of central tendency Mar 31 (31=workday; 4 days) 13-4 inverses of trigonometric functions
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Mr. Keshav Singh Kansana 1. The product of 2 numbers is 60 and their arithmetic mean in 8‚ find the numbers. 2. The monthly salary of a persona was Rs. 320 for each of the first three years. He next got annul increment of Rs. 40 per month for each of the following successive 12 years. His salary remained stationary till retirement when he found that his average monthly salary during the service period was Rs. 698. Find the period of his service. 3. Divide 36 into 6 parts in A.P such that the sum
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