Geometric Sequence
... The number you multiply by each time to get the next term is the ratio between the terms. The ratio can also be determined by writing the ratio of each term to its previous term. ...
... The number you multiply by each time to get the next term is the ratio between the terms. The ratio can also be determined by writing the ratio of each term to its previous term. ...
Sample Individual Questions
... integers. The average of the fourth and eighth terms in the sequence is 2720. Determine the value c. 8. The symbol bxc denotes the greatest integer less than or equal to x. For example, b3c = 3, b5.7c = 5. If n is an integer less than 64 and ...
... integers. The average of the fourth and eighth terms in the sequence is 2720. Determine the value c. 8. The symbol bxc denotes the greatest integer less than or equal to x. For example, b3c = 3, b5.7c = 5. If n is an integer less than 64 and ...
Algebra 1 - Cobb Learning
... Use the digits 1 to 5 with each number representing a basketball card. Use the random number generator on your graphing calculator. Keep generating values until all five numbers appear. Record your result. Divide a spinner into five equal parts and label A to E. Spin the spinner and record the numbe ...
... Use the digits 1 to 5 with each number representing a basketball card. Use the random number generator on your graphing calculator. Keep generating values until all five numbers appear. Record your result. Divide a spinner into five equal parts and label A to E. Spin the spinner and record the numbe ...
Candidate Name Centre Number Candidate Number 0
... spaces at the top of this page. Answer all the questions in the spaces provided in this booklet. Take π as 3∙14. INFORMATION FOR CANDIDATES You should give details of your method of solution when appropriate. Unless stated, diagrams are not drawn to scale. Scale drawing solutions will not be accepta ...
... spaces at the top of this page. Answer all the questions in the spaces provided in this booklet. Take π as 3∙14. INFORMATION FOR CANDIDATES You should give details of your method of solution when appropriate. Unless stated, diagrams are not drawn to scale. Scale drawing solutions will not be accepta ...
The Uniform Continuity of Functions on Normed Linear Spaces
... 1. The Uniform Continuity of Functions on Normed Linear Spaces For simplicity, we follow the rules: X, X1 are sets, s, r, p are real numbers, S, T are real normed spaces, f , f1 , f2 are partial functions from S to T , x1 , x2 are points of S, and Y is a subset of S. Let us consider X, S, T and let ...
... 1. The Uniform Continuity of Functions on Normed Linear Spaces For simplicity, we follow the rules: X, X1 are sets, s, r, p are real numbers, S, T are real normed spaces, f , f1 , f2 are partial functions from S to T , x1 , x2 are points of S, and Y is a subset of S. Let us consider X, S, T and let ...
MATH 31 CLASS NOTES XII – Section 5
... Relating a geometric sequence to the geometric mean. a1 , a2 , a3 , ..., an is a geometric sequence if and only if the ratio of any 2 consecutive terms is constant. This is equivalent to saying: The 2nd of any 3 consecutive terms in a geometric sequence is the geometric mean between the first and th ...
... Relating a geometric sequence to the geometric mean. a1 , a2 , a3 , ..., an is a geometric sequence if and only if the ratio of any 2 consecutive terms is constant. This is equivalent to saying: The 2nd of any 3 consecutive terms in a geometric sequence is the geometric mean between the first and th ...
Axioms and Theorems
... it must be even, this means that p2 is an even number. If a square is an even number, the original number (p) itself must be even. Therefore p can be written as p= 2m where m is a whole number. ...
... it must be even, this means that p2 is an even number. If a square is an even number, the original number (p) itself must be even. Therefore p can be written as p= 2m where m is a whole number. ...
Louisiana Grade Level Expectations
... (1) Within a well-balanced mathematics curriculum, the primary focal points at Grade 6 are using ratios to describe proportional relationships involving number, geometry, measurement, and probability and adding and subtracting decimals and fractions. (2) Throughout mathematics in Grades 6-8, student ...
... (1) Within a well-balanced mathematics curriculum, the primary focal points at Grade 6 are using ratios to describe proportional relationships involving number, geometry, measurement, and probability and adding and subtracting decimals and fractions. (2) Throughout mathematics in Grades 6-8, student ...
Mathematical Practices - Anderson School District 5
... b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent ...
... b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent ...
Candidate Name Centre Number Candidate Number 0 GCSE
... spaces at the top of this page. Answer all the questions in the spaces provided in this booklet. Take π as 3∙14. INFORMATION FOR CANDIDATES You should give details of your method of solution when appropriate. Unless stated, diagrams are not drawn to scale. Scale drawing solutions will not be accepta ...
... spaces at the top of this page. Answer all the questions in the spaces provided in this booklet. Take π as 3∙14. INFORMATION FOR CANDIDATES You should give details of your method of solution when appropriate. Unless stated, diagrams are not drawn to scale. Scale drawing solutions will not be accepta ...
7.1 Ratio and Proportion
... Also, a ratio has no units attached to it. We can use ratio to find the measure of angles. ...
... Also, a ratio has no units attached to it. We can use ratio to find the measure of angles. ...
I.2.2.Operations on sets
... Rough-Set Theory Rough-set theory postulates that all things have something in common with at least one other thing. The difficulty in quantifying these sets gives rise to the name "rough sets." These sets provide a way of comparing and drawing conclusions regarding operational elements that may not ...
... Rough-Set Theory Rough-set theory postulates that all things have something in common with at least one other thing. The difficulty in quantifying these sets gives rise to the name "rough sets." These sets provide a way of comparing and drawing conclusions regarding operational elements that may not ...
Ratio and Proportion for Health Science 43
... cats. In the fraction form, the first number (dogs) is written on top, or as the numerator and the second number (cats) is written below, or as the denominator. *Like fractions, ratios can be reduced to their lowest terms. 12 reduces to 4 ...
... cats. In the fraction form, the first number (dogs) is written on top, or as the numerator and the second number (cats) is written below, or as the denominator. *Like fractions, ratios can be reduced to their lowest terms. 12 reduces to 4 ...
MATHEMATICAL DIVERSIONS 2011
... Archimedes (287-212 BCE) was one of the greatest mathematicians/physicists of all times. By a process similar to Calculus (2000 years before it was invented) he found that the volume of a sphere of radius r is given by V =(4/3)π r3 . Knowing this, which of the following could be a formula for a sphe ...
... Archimedes (287-212 BCE) was one of the greatest mathematicians/physicists of all times. By a process similar to Calculus (2000 years before it was invented) he found that the volume of a sphere of radius r is given by V =(4/3)π r3 . Knowing this, which of the following could be a formula for a sphe ...
majlis peperiksaan malaysia
... Mathematics is a diverse and growing field of study. The study of mathematics can contribute towards clear, logical, quantitative and relational thinking, and also facilitates the implementation of programmes which require mathematical modeling, statistical analysis, and computer technology. Mathema ...
... Mathematics is a diverse and growing field of study. The study of mathematics can contribute towards clear, logical, quantitative and relational thinking, and also facilitates the implementation of programmes which require mathematical modeling, statistical analysis, and computer technology. Mathema ...
950 matematik - Portal Rasmi Majlis Peperiksaan Malaysia
... Mathematics is a diverse and growing field of study. The study of mathematics can contribute towards clear, logical, quantitative and relational thinking, and also facilitates the implementation of programmes which require mathematical modeling, statistical analysis, and computer technology. Mathema ...
... Mathematics is a diverse and growing field of study. The study of mathematics can contribute towards clear, logical, quantitative and relational thinking, and also facilitates the implementation of programmes which require mathematical modeling, statistical analysis, and computer technology. Mathema ...
7.1 Ratios and Proportions - Cardinal O'Hara High School
... pots of daffodils to sell at their fundraiser. They plan to buy 120 pots of flowers. The ratio number of tulip pots : number of daffodil pots will be 2 : 3. How many pots of each type of flower should they buy? • Let 2x = number of tulip pots • Let 3x = number of daffodil pots 2x + 3x = 120 5x =120 ...
... pots of daffodils to sell at their fundraiser. They plan to buy 120 pots of flowers. The ratio number of tulip pots : number of daffodil pots will be 2 : 3. How many pots of each type of flower should they buy? • Let 2x = number of tulip pots • Let 3x = number of daffodil pots 2x + 3x = 120 5x =120 ...
Fibonacci Sequence http://www.youtube.com/watch?v
... "Fibonacci" was his nickname, which roughly means "Son of Bonacci". As well as being famous for the Fibonacci Sequence, he helped spread through Europe the use of Hindu-Arabic Numerals (like our present number system 0,1,2,3,4,5,6,7,8,9) to replace Roman Numerals (I, II, III, IV, V, etc). That has s ...
... "Fibonacci" was his nickname, which roughly means "Son of Bonacci". As well as being famous for the Fibonacci Sequence, he helped spread through Europe the use of Hindu-Arabic Numerals (like our present number system 0,1,2,3,4,5,6,7,8,9) to replace Roman Numerals (I, II, III, IV, V, etc). That has s ...
Chapter 1
... 7.2.4.2. Second property of proportions: Reciprocal property of proportions: For nonzero integers a, b, c, and d, ba cd if and only if ba cd 7.2.5. Solving proportional problems 7.2.5.1. can be solved in a variety of ways 7.2.5.2. methods are related but require different procedures ...
... 7.2.4.2. Second property of proportions: Reciprocal property of proportions: For nonzero integers a, b, c, and d, ba cd if and only if ba cd 7.2.5. Solving proportional problems 7.2.5.1. can be solved in a variety of ways 7.2.5.2. methods are related but require different procedures ...
Algebra is a Language - The Language of Mathematics
... blocks or marbles. Your concept of five became a noun–a mental object in its own right. It was abstracted from many instances where five was an adjective. You can touch five blocks, but you can not touch five. It is a new reality at a higher conceptual level. Five retains its important role as an ad ...
... blocks or marbles. Your concept of five became a noun–a mental object in its own right. It was abstracted from many instances where five was an adjective. You can touch five blocks, but you can not touch five. It is a new reality at a higher conceptual level. Five retains its important role as an ad ...
Mathematics and art
Mathematics and art are related in a variety of ways. Mathematics has itself been described as an art motivated by beauty. Mathematics can be discerned in arts such as music, dance, painting, architecture, sculpture, and textiles. This article focuses, however, on mathematics in the visual arts.Mathematics and art have a long historical relationship. Artists have used mathematics since the 5th century BC when the Greek sculptor Polykleitos wrote his Canon, prescribing proportions based on the ratio 1:√2 for the ideal male nude. Persistent popular claims have been made for the use of the golden ratio in ancient times, without reliable evidence. In the Italian Renaissance, Luca Pacioli wrote the influential treatise De Divina Proportione (1509), illustrated with woodcuts by Leonardo da Vinci, on the use of proportion in art. Another Italian painter, Piero della Francesca, developed Euclid's ideas on perspective in treatises such as De Prospectiva Pingendi, and in his paintings. The engraver Albrecht Dürer made many references to mathematics in his work Melencolia I. In modern times, the graphic artist M. C. Escher made intensive use of tessellation and hyperbolic geometry, with the help of the mathematician H. S. M. Coxeter, while the De Stijl movement led by Theo van Doesberg and Piet Mondrian explicitly embraced geometrical forms. Mathematics has inspired textile arts such as quilting, knitting, cross-stitch, crochet, embroidery, weaving, Turkish and other carpet-making, as well as kilim.Mathematics has directly influenced art with conceptual tools such as linear perspective, the analysis of symmetry and mathematical objects such as polyhedra and the Möbius strip. The construction of models of mathematical objects for research or teaching has led repeatedly to artwork, sometimes by mathematicians such as Magnus Wenninger who creates colourful stellated polyhedra. Mathematical concepts such as recursion and logical paradox can be seen in paintings by Rene Magritte, in engravings by M. C. Escher, and in computer art which often makes use of fractals, cellular automata and the Mandelbrot set. Controversially, the artist David Hockney has argued that artists from the Renaissance onwards made use of the camera lucida to draw precise representations of scenes; the architect Philip Steadman similarly argued that Vermeer used the camera obscura in his distinctively observed paintings.Other relationships include the algorithimic analysis of artworks by X-ray fluorescence spectroscopy; the stimulus to mathematics research by Filippo Brunelleschi's theory of perspective which eventually led to Girard Desargues's projective geometry; and the persistent view, based ultimately on the Pythagorean notion of harmony in music and the view that everything was arranged by Number, that God is the geometer of the world, and that the world's geometry is therefore sacred. This is seen in artworks such as William Blake's The Ancient of Days.