...Problem Set A. Mensuration on Triangles 1. Find the area of the oblique triangle with sides 3m, 4m, 5m. 2. A tree is broken 3m above the level ground. The top strikes the ground 4m from the foot, while the other end of the broken part remains attached to the stump. How high is the tree if it not broken? 3. A right triangle has legs 4 cm. and 3 cm. How far from the vertex must this triangle be cut by a line parallel to the longer diagonal so that (a) The area of the small right triangle will be equal to the area of the trapezoid formed? (b) The perimeter of the small triangle is equal to the perimeter of the trapezoid? 4. A sail has spread of canvas as shown. Find the surface area of the sail. All measures are in meter. 9 10 3 4 5. The points C and D lie on the level ground in the same vertical plane with the tip B of the tower. If the tower AB is 300 ft. high and measurements give A1B1= 5 ft., CA1= 12 ft., A2B2= 6 ft., and A2D = 8 ft.. Find the distance CD. B B1 B2 C A1 ...
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...BATANGAS FACTORS AFFECTING THE ACADEMIC PERFORMANCE OF ENGINEERING STUDENTS In partial Fulfillment for the Requirements for Methods of Reasearch by Carandang, Castillo, Gonda, Santos, I. Introduction Engineers nowadays are in demand to lots of companies here and abroad. In fact, thousands of engineering graduates and board passers work mostly in other countries. This is the reason why lots of students took engineering courses. Engineering has always been considered as a very difficult course by most of the students. It’s almost always the last thing that will come to the minds of the students when it comes to choosing their course or program. Engineering, as a program has a lot of difficulties within its name. There are lots of math and science subjects and instructional activities that students will really find it difficult to pass. It requires a great responsibility in achieving the title “Engineer”. Some students who are already taking up engineering doesn’t know the hardships that they are still about to face, that’s why a large number of students tend to have a low academic performances. The field of engineering has become so diverse in recent years that a definition is not easy to come by. Engineers still build skyscrapers, design machinery, and oversee public works. They also address society's needs and problems on a number of other scales with a unique blend of technology and science. At the macro level, environmental engineers are quantifying...
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...Mensuration of Triangles Formulas: Right Triangle altitude base hypotenuse – it is always the longest side of a right tringle. Side Pythagorean Theorem If the length of both a and b are known, then c can be calculated as follows. c=√(a^2+b^2 ) If the length of hypotenuse c and one leg (a or b) are known, then the length of the other leg can be calculated with the following equations: a=√(a^2+b^2 ) or b=√(a^2+b^2 ) Perimeter Formula: P=a+b+c Area Formula: A= ½ bh or ½ ab or The Heron’s Formula which is A= √p/2 (p/2-s1) (p/2-s2) (p/2-s3) Example: a= 4 b= 3 c= ? c=√42+√32 c=√16+9 c=√25 c=5 Perimeter Formula: P=a+b+c P=4+3+5 P=12 Area Formula: A=1/2 bh or ½ ab or The Heron’s Formula which is A= √p/2 (p/2-s1) (p/2-s2) (p/2-s3) A=1/2 (3)(4) =12/2 = 6cm2 Isosceles Triangle P=s1+s2+s3 A=b√4a 2+√b2 / 4 or The Heron’s Formula which is A= √p/2 (p/2-s1) (p/2-s2) (p/2-s3) Line AB =5in Line AC=5in Line BC= ? BC=? AB=AC>BC 5+5>BC 10>BC The base should be lesser then the sum of the legs so let the length BC = 9. P=5+5+9 =19inches A= b√4a 2+√b2 / 4 =9√4(9)2 – 52 / 4 =9√324-25 / 4 =9√299 / 4 Equilateral/ Equiangular Triangle P=3s or a + b + c A=s2√3 / 4 or The Heron’s Formula which is A= √p/2 (p/2-s1) (p/2-s2) (p/2-s3) 2 2 2 P=s1+s2+s3 =6cm A=√3(1)(1)(1) A=s2√3 / 4 =√3 cm2 =22√3 /4 =4√3 / 4 =√3 cm2 Scalene Triangle P=s1+s2+s3 A=Hero’s...
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...Elementary Mathematics Syllabus Arithmetic Number System-Natural numbers, Integers, Rational and Real numbers. Fundamental operations addition, subtraction, multiplication, division, Square roots, Decimal fractions. Unitary method-time and distance, time and work, percentages, applications to simple and compound interest, profit and loss, ratio and proportion, variation. Elementary Number Theory- Division algorithm. Prime and composite numbers. Tests of divisibility by 2,3,4,5,9 and 11. Multiples and factors. Factorisation Theorem. H.C.F. and L.C.M. Euclidean algorithm, Logarithms to base 10, laws of logarithms, use of logarithmic tables. Algebra Basic Operations, simple factors, Remainder Theorem, H.C.F., L.C.M. Theory of polynomials, solutions of quadratic equations, relation between its roots and coefficients (Only real roots to be considered). Simultaneous linear equations in two unknowns-analytical and graphical solutions. Simultaneous linear equations in two variables and their solutions. Practical problems leading to two simultaneous linear equations or inequations in two variables or quadratic equations in one variable & their solutions. Set language and set notation, Rational expressions and conditional identities, Laws of indices. Trigonometry Sine x, cosine x, Tangent x when 0 deg < x < 90 deg Values of sin x, cos x and tan x, for x = 0 deg, 30 deg, 45 deg, 60 deg and 90 deg Simple trigonometric identities. Use of trigonometric tables. simple cases of heights...
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...The Overall Goal of K to 12 TLE Curriculum The holistic development of every Filipino learner with 21st century skills who is: * Adequately prepared for work * Entrepreneurship * Middle level skills development * Higher education TLE is geared towards the development of technological proficiency and is anchored on knowledge and information, entrepreneurial concepts, process and delivery, work values and life skills. K to 12 TLE is... a. One that is built on adequate mastery b. One that equip students with skills for lifelong learning and c. One that is founded on cognitive, behavioral or psychomotor and affective dimensions of human development. Conceptual Framework HIGHER EDUCATION MIDDLE LEVEL MANPOWER ENTREPRENEURSHIP EMPLOYMENT AFA ICT A S S E S S M E N T A S S E S S M E N T TECHNOLOGICAL PROFICIENCY HE IA KNOWLEDGE and INFORMATION ENTREPRENEURIAL CONCEPTS PROCESS and DELIVERY WORK VALUES and LIFE SKILLS Figure 1. TLE Framework The diagram shows that Technology and Livelihood Education encompasses the field of Home Economics, Industrial Arts, Agri-Fishery Arts and ICT. The 24 TLE courses can be categorized under any of these fields. The diagram likewise shows that entrepreneurial concepts also form part of the foundation of quality TLE. It is expected that your TLE students, after learning the different areas of TLE, imbibe the entrepreneurial spirit and consequently...
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...Statement and Assumptions/Conclusions English Language Total No of Questions: 40 Maximum Marks: 40 The topics to be covered in this section are Reading comprehension including Synonyms and Antonyms Sentence rearrangement or Para jumbles Sentence Correction/ Error Finding Spell Checks Fillers Cloze Test Quantitative Aptitude Total No of Questions: 50 Maximum Marks: 50 The topics to be covered in this section are http://www.affairscloud.com/uiiclao2016patternsyllabus/ 2/5 6/10/2016 UIICL AO 2016 Pattern and Syllabus Simplification Number Series Data Sufficiency Data Interpretation [ Bar Graph, Pie Chart, Table, Line Graph, Radar Chart, Mixed Graph] Quadratic Equations Time and Work Partnership Profit and Loss Mensuration Time, Distance and Speed – Trains, Boats n Streams Simple and Compound interest Mixture and Alligation Ratio and Proportion, Percentages, Averages General Awareness (with special reference to Financial Sector) Total No of Questions: 40 Maximum Marks: 40 The syllabus for this section is...
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...Gretchel M. Quinones HUMA 101 WORK SHOP 4 Essay Ricardo Serano Greek science and math the influence: Development of Science Long time ago, people lacked knowledge on why certain things happened. Without scientific answers, like we have today, the Ancient Greeks created their own answers about the world and an individual’s place in it. By doing the research for this essay I had learn a lot of the Greeks contribution in science and math methods. Science in Ancient Greece was based on logical thinking and mathematics. It was also based on technology and everyday life. The arts in Ancient Greece were sculptors and painters. The Greeks wanted to know more about the world, the heavens and themselves. People studied about the sky, sun, moon, and the planets. The Greeks found that the earth was round. Many important people contributed to Greek scientific thought and discoveries. Biology, a very vast and interesting topic, was studied by Hippocrates, Aristotle, Theophrastus, Dioscorides, Pliny, and Galen. These men were among the main researchers of Greek biology who contributed many ideas, theories, and discoveries to science. Some of their discoveries were observations, descriptions, and classifications of the various forms of plants and animal life. Other discussions in biology were natural selection and zoology. All living things were the basic concern of biology. Greek biologists were interested in how living things began, how they developed, how they functioned, and...
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...Alternatives to Euclidean Geometry and Its Applications Negations to Euclid’s fifth postulate, known as the parallel postulate, give rise to the emergence of other types of geometries. Its existence stands in the respective models which their originators have imagined and designed them to be. The development of these geometries and its eventual recognition give humans some mathematical systems as alternative to Euclidean geometry. The controversial Euclid’s fifth postulate is phrased in this manner, to wit: “If a straight line crossing two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if extended indefinitely, meet on that side on which is the angles less than the two right angles.” which has been rephrased, and what is known as the parallel postulate as follows: “Given a line L and an external point P not on L, there exists a unique line m passing through P and parallel to L.” With the sphere as its model, is spherical (also called reimannian or elliptic) geometry being advanced by German mathematician, Bernhard Riemann who proposes the absence of a parallel line with Euclid’s fifth postulate as reference. His proposition is as follows: “ If L is any line and P is any point not on L, then there are no lines through P that are parallel to L” It contradicts Euclid’s fifth postulate mainly because no matter how careful one in constructing a line with a straightedge- as straight as it is- that line...
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...PURE MATHEMATICS Mensuration Surface area of sphere = 4πr 2 Area of curved surface of cone = πr × slant height Arithmetic series S n a l n[ a n d] u a n d n n ( ) 2 ( 1) = ( 1) 2 1 2 = 1 + = + − + − Geometric series 1 for 1 1 (1 ) 1 = − < − = − = ∞ − r r S a r S a r u ar n n n n Summations ( )1 2 1 1 + = Σ= r n n n r ( 1)(2 1) 6 1 1 2 + + = Σ= r n n n n r 2 2 4 1 1 3 ) 1 ( + = Σ= r n n n r Trigonometry – the Cosine rule a2 = b2 + c2 − 2bc cos A Binomial Series ∈ + + ⎟ ⎟⎠ ⎞ ⎜ ⎜⎝ ⎛ + + ⎟ ⎟⎠ ⎞ ⎜ ⎜⎝ ⎛ + ⎟ ⎟⎠ ⎞ ⎜ ⎜⎝ ⎛ + = + − − a − b b n r n a b n a b n a b n an n n n r r n ( 2 1 ( ) 1 2 2 … … ) where !( )! C ! r n r n r n r n − = = ⎟ ⎟⎠ ⎞ ⎜ ⎜⎝ ⎛ + = + + − + + − − + x + x < n∈ r x n nx n n x n n n r r ( 1, 1.2 ( 1) ( 1) 1.2 (1 ) 1 ( 1) 2 … … … … ) Logarithms and exponentials ax = exln a Complex numbers {r(cosθ + i sinθ )}n = r n (cos nθ + i sin nθ ) eiθ = cosθ + i sinθ The roots of z n = 1 are given by n k z 2π i = e , for k = 0, 1, 2, … , n −1 N R klj 5 Maclaurin’s series f( ) f(0) f (0) 2! f (0) … ! f ( ) (0) … 2 = + ′ + ′′ + + r + r r x x x x r x x x x x x r e exp( ) 1 2! ! for all 2 = = + + +…+ +… r x x x x x x r + = − + − + (−1)r+ + (−1 < ln(1 ) 2 3 2 3 1 … … 1) x r x x x x x r r for all (2 1)! ( 1) 3! 5! sin 3 5 2 1 … +… + = − + − + − + x r x x x x r r for all (2 )! ( 1) 2! 4! cos 1 2 4 2 = − + −…+ − +… Hyperbolic...
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...Egyptian Math This is a math course and I am from Egypt so what better to talk about than the practice of mathematics during the ancient Egyptian era. The use of organized mathematics in Egypt has been dated back to the third millennium BC. Egyptian mathematics was dominated by arithmetic, with an emphasis on measurement and calculation in geometry. With their vast knowledge of geometry, they were able to correctly calculate the areas of triangles, rectangles, and trapezoids and the volumes of figures such as bricks, cylinders, and pyramids. They were also able to build the Great Pyramid with extreme accuracy. Early surveyors found that the maximum error in fixing the length of the sides was only 0.63 of an inch, or less than 1/14000 of the total length. They also found that the error of the angles at the corners to be only 12", or about 1/27000 of a right angle (Smith 43). Three theories from mathematics were found to have been used in building the Great Pyramid. The first theory states that four equilateral triangles were placed together to build the pyramidal surface. The second theory states that the ratio of one of the sides to half of the height is the approximate value of P, or that the ratio of the perimeter to the height is 2P. It has been discovered that early pyramid builders may have conceived the idea that P equaled about 3.14. The third theory states that the angle of elevation of the passage leading to the principal chamber determines the latitude of...
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...similar to another major composer of the time, Du Fay, but were different in four major ways. First, there were four voices in independent lines with a contrapuntal texture. Second, the bass part would go lower; and third, this would leave the music sounding fuller and darker. And lastly, Ockeghem tried to vary his music by leaving independent sections of duet or trio. Ockeghem’s masses are distinct in sound because of the fuller and darker texture, and he began an expansion of the range in masses. Johannes Ockeghem had two major masses that were important: Missa Cuiusvis Toni and Missa Prolationum. The former was famous because it can be sung in any mode for example 1, 3, 5, or 7. The latter is important because each movement is a double mensuration canon. Missa Prolationum is a musical composition that, “has been prized for over five hundred years for addressing two audiences simultaneously [...] well: the singers and other musical connoisseurs [...], and listeners.” These notable missal compositions represent the free feeling of the Renaissance compared to earlier music in the church, even though it still followed a strict form. Many compositions during the Renaissance period were adapted and played in many different manners, making the music have a more universal feel as well. Prior to the Renaissance, sacred music tended to be compliant to a certain form, or formes fixes. However, the Renaissance brought about a change in that imitative counterpoint became commonly used. Imitative...
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...Service Road, South Superhighway, Taguig City, Metro Manila | TABLE OF CONTENTS Page A. COURSE DESIGN 1-5 B. MODULES OF INSTRUCTION 6-73 • Basic Competencies 6 o Participating in workplace communication ………………… 7-10 o Working in a team environment ……………….... 11-13 o Practicing career professionalism .……………. 14-17 o Practicing occupational health and safety procedures 18-22 • Common Competencies 23 o Applying quality standards …………………………………… 24-27 o Performing computer operations 28-34 o Performing mensuration and calculation 35-38 o Preparing and interpreting...
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...Service Road, South Superhighway, Taguig City, Metro Manila | TABLE OF CONTENTS Page A. COURSE DESIGN 1-5 B. MODULES OF INSTRUCTION 6-73 • Basic Competencies 6 o Participating in workplace communication ………………… 7-10 o Working in a team environment ……………….... 11-13 o Practicing career professionalism .……………. 14-17 o Practicing occupational health and safety procedures 18-22 • Common Competencies 23 o Applying quality standards …………………………………… 24-27 o Performing computer operations 28-34 o Performing mensuration and calculation 35-38 o Preparing and interpreting technical drawing 39-42 o Using hand tools 43-47 o Terminating and connecting electrical...
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...forestry as forest areas need to be adequately managed. As Young (1982) stated a long time ago, management of the forest for multiple land use is now common. This is due to the encroachment of forest areas and illegal felling in the protected forest areas. This brings about the determination of the use of the forest, forest land and forest products to ensure that the benefits derived today are similarly obtained in the future. Adekunle et al (2013), indicated that since the knowledge of tree growth parameters plus yield is very essential for effective forest management; data for the growth/ yield parameters can be obtained through field inventory by recording diameters and height along the stem or bole of a tree (Tonolli et al, 2011) Forest mensuration forms the basis for Sustainable Forest Management as it is the assessment of both quality and quantity of available forest resources needed for management. This can be done through Volume equations, Volume models, Volume estimation, Diameter-height relationship etc. They are needed to obtain reliable and up-to-date estimates of the forest stock. Adekunle (2005) noted that it is the best and reliable procedure for volume estimation of trees and is based on the relationship between volume and other variables such as diameter (diameter at the top, diameter at the middle, diameter at the base & diameter at breast height) and height (total & merchantable height) Hence, this paper is discussing adequately the roles of different volume models...
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...wherein they use factual sources, studies, statistics, Quran verses, Hadith, or other kinds of evidential proof. Give the references or citations provided for this proof (do not just mention it- give the actual statistics and data with the source citations). Finish by stating your own opinion regarding the reading. There is no answer key for this assignment. Note: Roded 7 doesn’t really go into the topic in depth, but has a detailed view on the topic of purity on the whole. Include the entire topic in your summary of that chapter below. 1. Roded Chapter 7 a. Position defended: Pro b. Time period: traditional c. Rationale/details: Purity is very important. Many of the older women were considered to be unclean. During mensuration a woman was to wrap a cloth tight around her waist. Men could touch her above the cloth as they saw fit. Specific rituals were done for washings. Water was splashed over head’s three times. Roots of hair were washed. In 2.26 a man is permitted to have sexual relations with his wife during menstruation if he chooses to do so. If water was not available to clean oneself not considered impure. Women were not allowed to pray...
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