...density of the Earth. Where does the value fit among those listed in Tables 1.5 and 14.1? Look up the density of a typical surface rock like granite in another source and compare also to it. 3. The standard kilogram is a platinum-iridium cylinder 39.0 mm in height and 39.0 mm in diameter. What is the density of the material? 4. A major motor company displays a die-cast model of its first automobile, made from 9.35 kg of iron. To celebrate its hundredth year in business, a worker will recast the model in gold from the original dies. What mass of gold is needed to make the new model? 5. What mass of a material with density [pic] is required to make a hollow spherical shell having inner radius r1 and outer radius r2? 6. Two spheres are cut from a certain uniform rock. One has radius 4.50 cm. The mass of the other is five times...
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...thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat.[1] It is the two-dimensional analog of the length of a curve (a one-dimensional concept) or the volume of a solid (a three-dimensional concept). The area of a shape can be measured by comparing the shape to squares of a fixed size.[2] In the International System of Units (SI), the standard unit of area is the square metre (written as m2), which is the area of a square whose sides are one metre long.[3] A shape with an area of three square metres would have the same area as three such squares. In mathematics, the unit square is defined to have area one, and the area of any other shape or surface is a dimensionless real number. There are several well-known formulas for the areas of simple shapes such as triangles, rectangles, and circles. Using these formulas, the area of any polygon can be found by dividing the polygon into triangles.[4] For shapes with curved boundary, calculus is usually required to compute the area. Indeed, the problem of determining the area of plane figures was a major motivation for the historical development of calculus.[5] For a solid shape such as a sphere, cone, or cylinder, the area of its boundary surface is called the surface area.[1][6] Formulas for the surface areas of simple shapes were computed by the ancient Greeks, but computing the surface area of a more complicated shape usually requires multivariable...
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...each page or on blank pages. l Do all rough work in this book. Information l The marks for questions are shown in brackets. l The maximum mark for this paper is 70. l The quality of your written communication is specifically assessed in Questions 9 and 13. These questions are indicated with an asterisk (*). l You may ask for more answer paper, tracing paper and graph paper. These must be tagged securely to this answer book. Advice l In all calculations, show clearly how you work out your answer. (JAN1343651H01) WMP/Jan13/43651H 43651H 2 Formulae Sheet: Higher Tier a 1 Area of trapezium = – (a + b)h 2 h b Volume of prism = area of cross-section × length crosssection h lengt 4 Volume of sphere = – π r 3 3 r Surface area of sphere = 4 π r 2 1 Volume of cone = – π r 2 h 3 l r h Curved surface area of cone = π rl In any triangle ABC Area of triangle = 2 ab sin C Sine rule 1 C b c sin C a c B a sin A = b sin B = A Cosine rule a 2 = b 2 + c 2 – 2bc cos A The Quadratic Equation The solutions of ax 2 + bx + c = 0, where a ≠ 0, are given by x= – b ± √ (b2 – 4ac) 2a (02)...
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...question are shown in brackets – use this as a guide as to how much time to spend on each question. Questions labelled with an asterisk (*) are ones where the quality of your written communication will be assessed. Advice Read each question carefully before you start to answer it. Keep an eye on the time. Try to answer every question. Check your answers if you have time at the end. mathsgenie.co.uk GCSE Mathematics 1MA0 Formulae: Higher Tier You must not write on this formulae page. Anything you write on this formulae page will gain NO credit. Volume of prism = area of cross section × length Area of trapezium = 1 (a + b)h 2 a cross section h b h lengt Volume of sphere = 4 3 Volume of cone = 3 Surface area of sphere = 4 1 3 h 2 Curved surface area of cone = 2 r l h r The Quadratic Equation The solutions of ax2 + bx + c = 0 where 0, are given by In any triangle ABC C b A Sine Rule a c x= B a b c = = sin A sin B sin C...
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...origin and a moving point on the graph of [pic] if [pic]cm/sec. [pic] [pic] [pic] 2. Find the rate of change of the distance between the origin and a moving point on the graph of [pic] if [pic]cm/sec. [pic] [pic] [pic] 3. The radius (r) of a circle is increasing at a rate of 4 centimeters per minute. Find the rates of change of the area when. [pic] [pic] a. r = 8 centimeters b. r = 32 centimeters [pic] [pic] 4. The included angle of two sides of constant equal length s of an isosceles triangle is [pic]. If [pic] is increasing at a rate of ½ radian per minute, find the rates of change of the area when: [pic] [pic] [pic] a [pic] b. [pic] [pic] [pic] 5. The radius r of a sphere is increasing at a rate of 3 inches per minute. Find the rates of change of the volume when: [pic] [pic] a. r = 9 inches b. r = 36 inches [pic] [pic] 6. A spherical balloon is inflated with gas at a rate of 800 cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is: [pic] [pic] a. 30 cm b. 60 cm [pic] [pic] 7. All edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the volume changing when each edge is: [pic] [pic] a. 2 cm b. 10 cm [pic] [pic] 8. All edges of a cube are expanding at a rate of 6 centimeters per second. Determine how fast the surface area is changing when each...
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...Lab #3 Measurements & Density Experiment 3A I Purpose: To determine the area of a sheet of typing paper and express the answer in mm2, cm2, and in2. II Equipment/Reagents: A sheet of regular typing paper and ruled provided in lab kit. III Procedure: Measure the length and width of the sheet of typing paper and express this measurement in millimeters rounded to the nearest tenth of a millimeter. Calculate the area of the sheet using the formula: Area= (length)(width) Round your answers to the correct number of significant digits and write the answers in the correct units. Convert your answer to cm2 and in2. IV Data or Observations: Length | Width | Area | 279 mm | 215 mm | 6.00x104 mm2 | 27.9 cm | 21.5 cm | 6.00x102 cm2 | 11.0 in | 8.46 in | 93.1 in2 | V Calculations: (279 mm)(215 mm)= 6.00x104 mm2 (27.9 cm)(21.5 cm)= 6.00x102 cm2 (11.0 in)(8.46 in)= 93.1 in2 VI Results/Summary: The area of the typing paper was found to be 6.00x10^4 mm^2, 6.00x 10^2 cm^2, and 93.1 in^2. Sierra Sisco Lab #3 Measurements & Density Experiment 3B I Purpose: To determine the volume of a rectangular solid and express the answer in mm3, cm3, and in3. II Equipment/Reagents: Rectangular block in lab kit and vernier caliper. III Procedure: Measure the length width and height of of the rectangular solid and express measurements in millimeters rounded to the nearest tenth of a millimeter. Record your answers and calculate the volume...
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...philosophers and cultures throughout history. For thousands of years man has observed and studied the Earth. Through observations, spiritual beliefs and empirical findings, many theories developed regarding the shape of the Earth. How has our understanding of the shape of the Earth changed over time? • Most ancient cultures, such as the Sumerians, Babylonians, even Greece , until the 5th or 6th century B.C., believed that the Earth was flat. (Garwood, 2007, p. 16) • The Egyptians believed the universe was rectangular-shaped with four pillars that supported a flat ceiling. Egypt was in the center of a flat Earth which was surrounded by water. (Moore, 1968, p. 16) • Greek philosopher Pythagoras, populated the idea that the Earth must be a sphere back in the 6th century B.C. • Around 330 B.C. Aristotle accepted the spherical shape of the Earth, observing that the Earth casts a round shadow on the moon. • Sir Isaac Newton observed the shape of the Earth to be oblate spheroidal or oval shaped, not prolate spheroidal or spherical. (According to Choi, 2007) • Giovanni Cassini, who discovered four moons of Saturn and estimated the distance between the Earth and Sun to be 87 million miles, maintained that the Earth was flat at the equator. His theory stirred controversy, contradicting Newton’s and others who maintained that the Earth was flattened at the poles. (Burns, 2001, p. 55) What are some discoveries and examples that brought us new knowledge to our understanding of the...
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... I have had a good chance to observe Mr. Mirzaev’s in both academic and professional development over the past 5 years. He was one of my distinguished students in Tashkent State University of Economy who performed himself as an initiative person and showed diligence as well as hardworking ability among all students of his batch. After his graduation, I invited him to work for the department of Foreign Investment of Chamber of commerce and industry of Uzbekistan which I managed in that period. As a specialist Mr. Mirzaev could show himself a very talented individual, promising young leader with strong analytical skills and leadership potential. Especially, working in the sphere of business development, export promotion and investment attraction has enabled him to become a good specialist in these spheres. In the process of his job I regularly read the analytical reports prepared by him and I should mention that no matter what he prepared (reports, statements, feedbacks, etc.) he always completed assignments with great responsibility and they appeared to be logically arranged, coherent and easy to follow. The same concerns were with his public speaking skills where he impressed people with his assertiveness and resourcefulness. To sum up, once again I would like to reiterate my strong support for Mr. Shakhzod Mirzaev’s candidacy and urge you to support it. Should you have any questions, please contact. Yours sincerely, Farhod Kurbonov (Mr.) Program Officer ...
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...A. Les quatre parties du monde soutenant la sphère (English name: The Four Parts of the World Holding the Celestial Sphere) is a sculpture by Jean-Baptiste Chapeaux. The plaster model was made in 1872. It’s dimensions are w1770 x h2800 x d1450 cm. The sculpture shows an African, Chinese, European, and Native American women joining together to hold the sphere. The ethnicity of the women can be seen through the features of the sculpture. For example, the Native American woman is wearing a headdress. B. Even though the obvious difference can be offensive. I think that the sculpture is about the different parts (Asia, Africa, Europe, and America) coming together to hold the world. In the sculpture the sphere represents the global, which...
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...Box Portfolio The purpose of this portfolio was to use my knowledge of understanding how to solve a problem using dimensions to find the maximum volume of a box. The problem I had to solve was to take a 11x17 ½ piece of paper and turn it into a box. In order to do this, a square needs to be cut out of each corner. I had to figure out how big of a square needed to be cut out in order to create a box with the maximum volume possible. I did this by narrowing down the possibilities of the dimensions to the nearest ten thousands. (See tables attached) In order to find the maximum volume possible, I made tables using the graphing calculator. In the first column of the first table (L1), I put the size of the square that would be cut out from each corner. In L1, I started with a 1 inch square and went up to a 5.5 inch square. In the second column of the first table (L2), I put the width of the piece of paper subtracting 2 (1 for each corner) and multiplied it by L1 (11-2*L1). In the third column of the first table (L3), I did the same thing as I did in L2 using the length of the paper instead (17.5-2*L1). I used the last column (L4) of the first table to find the volumes (L1*L2*L3). (refer to the tables for widths, lengths and volumes) Using the first table, I was able to narrow down the size of the square to 2 in. Using what I found in table one, I then took the 2 in. square, went down .1 five times and up .1 five times and put that into L1 to try and narrow the size...
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...a UNIVERSITI TUNKU ABDUL RAHMAN |Centre |: |Centre for Foundation Studies (CFS) | |Unit Code |: |FHSP 1014 | |Course |: |Foundation in Science | |Unit Title |: |Physics I | |Year/ Trimester |: |Year 1 / Trimester 1 | |Lecturer |: |Ms.Nurfadzilah | |Session | | | | | |Mr Chin Kong Yew | | |: |2014/05 | | | | | Tutorial 1: Introduction 1. How many significant figures do each of the following numbers have: (a) 214, (b) 81.60, (c) 7.03, (d) 0.03, (e) 0.0086, (f) 3236, and (g) 8700? 2. Write the following into scientific notation (a) 165 000 000 (b) 0.0446 (c) 0.0005 (d) 11 000 3. (a) The diameter of the earth is about 1.27 x 107 m. Find its diameter in (i) Millimeters, (ii) Mega-meters [Answer: 1.27(1010 mm; 12.7 Mm] (b) Express the following sum to the correct number of significant figures/decimal places: 1.80 m + 142.5 cm + 5.34 × 105 (m [Answer: 3...
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...Global Warming If the global climate were to warm significantly as a result of the greenhouse effect or other climatic change, the Arctic ice cap would start to melt. This ice cap contains the equivalent of some 680,000 cubic miles of water. More than 200 million people live on land that is less than 3 feet above sea level. In the United States several large cities have low average elevations. Three examples are Boston (14 feet), New Orleans (4 feet), and San Diego (13 feet). In this exercise you are to estimate the rise in sea level if the Arctic ice cap were to melt and to determine whether this event would have a significant impact on people living in coastal areas. (a) The surface area of a sphere is given by the formula where r is its radius. Although the shape of Earth is not exactly spherical, it has an average radius of 3960 miles. Estimate the surface area of Earth. The surface area of a sphere is found by using the following formula: s = 4r2, where s represents surface area and r represents radius. To find the approximate surface area of the Earth, the equation would be set up as follows: S = 439602 = 197060797.4 This calculation shows that the approximate surface area of the Earth 197060797.4 square miles. (b) Oceans cover approximately 71% of the total surface area of Earth. How many square miles of Earth’s surface are covered by oceans? To calculate how many square miles of Earth’s surface are covered by oceans one must multiply...
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...My first reaction viewing Sara’s portable planetarium was a mess of objects which didn’t quite make sense in their placement, but after a few seconds you can see how Sara placed each object strategically to capture the viewers attention and how each object has meaning. The installation art piece is most definitely a full round sculpture with a combination of linear elements. The planetarium doesn’t seem to have a beginning or end, there’s no focal point. It’s three-dimensional nature seems to give it an air of a “huge jumble” and it gives you the impression of “I don’t know where to look first”. The linear elements are the mobiles at the end, which seem to hang from wires and strings. The planetarium was made using the method of construction. Sara used all kinds of materials to create her work of art such as lamps, ladders, pebbles, plastic bottles, buckets, papers, and even a projector. There is a contrast of both negative space and closed space, the open spaces seems to continually bring you back to the closed space. Even though the sculpture seems “crazy” there sees to be an element of proportion. The linear objects share a relationship with the spherical objects. But there are also components of dissonance since the sculpture seems to be moving. The name of Portable Planetarium is a complete contradiction since it seems like all the objects are stable in their positions, and looks like they cannot be moved without the whole thing coming down. I believe the artist’s...
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...Metrobank – MTAP – DepEd Math Challenge 2013 Regional Team Orals – Grade 6 15-Second Questions 1. Two numbers are in the ratio 5:8. If their difference is 60, what is the smaller number? [ 100 ] 2. The edge of a cube is double that of another cube. How many times as big is the volume of the bigger than the smaller cube? [ 8 times bigger ] 3. Alyssa is as old in months as Bernadette in years. The sum of their ages is 13 years. How old is Alyssa? [ 1 year old ] 4. Which has a greater volume? A] two boxes of the same dimensions or [B] B] one box with twice the dimensions of each box? 5. If 3 is added to the numerator and the denominator of 9/13, give the simplest form of of the resulting fraction? [ 3/4 ] 6. Write the product of 5 000 and 8 000 in scientific notation. [ 4 x 107 ] 7. The area of a square is 49 cm2. If its side is trebled, what is the area of the new square? [ 441 cm2 ] 8. The product of two numbers is 1. One number is 1 2/5. What is the other number? [ 5/7 ] 9. The sum of two whole numbers is 100. One number is divisible by 7 and the other by 11. Find the number divisible by 7. [ 56 ] 10. The sum of the edges of a cube is 240 cm. Find the total surface area. [ 2400 cm2 ] 11. Which fraction is the smallest among the fractions in the set {11/12, 13/16, 17/20,19/20}? [ 13/16 ] 30-Second Questions 1. If 4/5 of a number is 3/10, what is 2/3 of the number? [ 1/4 ] 2. A residential compound has parallel frontage and back side whose measures...
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...technology such as Business Sufficiency, Business Spheres, and Decision Cockpits allows employees at all levels to view and make real-time decisions in the company. Executives use the Business Sufficiency software to make 6-12 month predictions about P&G's performance statistics. The goal of this software is to make leaders within the company aware of what is going on and help them to determine what actions are required to solve any issues. The software provides real-time data on issues and allows leaders to focus on these issues rather than on gathering data. P&G has seven business sufficiency models that provide information on a specific problem set. These sets identify specific variables about the problem and are key to determining how to correct the problem. Business Sufficiency is extremely effective. The most important item required in making a decision is data. If managers spend too much time searching for data they may miss the opportunity to correct an issue. Business Sufficiency ensure that executives have access to data immediately and that everyone is using the same data. Business Spheres (figure 1) are specially designed meeting rooms that have visual information displays in a spherical shape around the room. P&G has 50 areas that are equipped with Business Spheres. These rooms provide executives with real-time visual data when meeting to analyze information and make business decisions. Business Spheres are effective at providing data to executives during...
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