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This document is a lesson on proportions that includes examples of setting up and solving proportions. It begins with a definition of a proportion as an equality of two ratios. It then works through examples of solving single-variable proportions by cross multiplying. Later examples ask students to determine if two ratios form a proportion and solve a word problem involving converting between nautical and statute miles using a proportion. The homework assignment is to complete problems 5 through 20 on page 292.
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This document discusses dividing polynomials by monomials. It provides examples of dividing terms with variables by monomials, including factoring out negatives. The homework assignments are to complete odd problems from pages 297 and 303 of the textbook, with no additional problems from an online system.
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1) Square numbers are numbers that can be expressed as the product of a number multiplied by itself.
2) Between two consecutive square numbers n2 and (n+1)2, there are 2n non-square numbers.
3) The sum of the first n odd natural numbers is n2, meaning square numbers must be the sum of consecutive odd numbers starting from 1.
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2) Between two consecutive square numbers n2 and (n+1)2, there are 2n non-square numbers.
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This document provides an agenda and notes for a math lesson on ordering fractions. The lesson includes comparing fractions with different denominators using a common denominator, using a number line to graph and compare fractions, and ordering fractions from least to greatest. The homework assigned is problems 6 through 42 on page 229, which involve finding multiples of 3.
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This document discusses dividing polynomials by monomials. It provides examples of dividing terms with variables by monomials, including factoring out negatives. The homework assignments are to complete odd problems from pages 297 and 303 of the textbook, with no additional problems from an online system.
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1) Square numbers are numbers that can be expressed as the product of a number multiplied by itself.
2) Between two consecutive square numbers n2 and (n+1)2, there are 2n non-square numbers.
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1) Square numbers are numbers that can be expressed as the product of a number multiplied by itself.
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This document provides an agenda and notes for a math lesson on ordering fractions. The lesson includes comparing fractions with different denominators using a common denominator, using a number line to graph and compare fractions, and ordering fractions from least to greatest. The homework assigned is problems 6 through 42 on page 229, which involve finding multiples of 3.
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The document discusses reflections of functions across the x-axis and y-axis. Reflecting across the y-axis causes the x-values to become opposite, resulting in the function y=f(-x). Reflecting across the x-axis causes the y-values to become opposite, resulting in the function y=-f(x). The document provides examples of determining the reflected point for a given point on a function, and instructs the reader to sketch both the original and reflected graphs.
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Exponent1
1. Exponents indicate how many times a base is multiplied by itself. The laws of exponents describe how to manipulate exponents in algebraic expressions.
2. When multiplying or dividing expressions with the same base, exponents are added or subtracted. When raising a power to another exponent, the exponents are multiplied.
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This document contains notes from a math lesson on multiplying and dividing integers:
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The document discusses dilations in geometry. It notes that a dilation with a scale factor between 0 and 1 results in a reduction, while a scale factor greater than 1 results in an enlargement. It also mentions that dilations can be represented using matrices by multiplying the scale factor by the polygon matrix. Several homework problems are assigned from page 629 involving dilation.
7.3 notes
The document discusses solving multi-step equations with fractions and decimals. It provides examples of equations to solve, such as 2n + 53 = 47 and -3a + 15 = 13. The objective is to solve these types of equations. Students are assigned homework problems on page 356 numbers 6 through 39 involving multiples of 3.
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This document appears to be notes from a math lesson on exponents. It includes examples of exponent expressions and their values, as well as homework assignments involving simplifying expressions with exponents and evaluating expressions for given values of variables. The document provides instruction and practice with the concepts and skills of exponents.
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This document contains notes on finding the surface area of pyramids and cones. It provides the formulas for calculating surface area of regular pyramids as one-half of the perimeter of the base times the sum of the slant height and apothem. For cones, the surface area formula is given as the area of the base plus the radius times pi times the slant height. The document includes examples of applying these formulas to find the surface area of various pyramids and cones.
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Students were instructed to make two solids by naming them on their bases, coloring the faces, folding the faces, gluing the edges, and displaying the finished solids. They then classified solids as prisms or pyramids based on the shape of each solid's base. The document appears to be notes from a math class lesson on identifying and constructing different types of three-dimensional solids.
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The document is notes from a geometry class that include:
1) A bellwork assignment with geometry problems to solve.
2) Instructions for students to fill in properties of special quadrilaterals like rectangles, rhombus, squares, kites and trapezoids from their textbook.
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The document discusses properties of parallelograms. It states that a parallelogram is a quadrilateral with both pairs of opposite sides parallel. It presents several theorems: if a quadrilateral is a parallelogram, then its opposite sides are congruent; if a quadrilateral is a parallelogram, then its opposite angles are congruent; if a quadrilateral is a parallelogram, then the sum of its consecutive angles is 180 degrees; if a quadrilateral is a parallelogram, then its diagonals bisect each other. The document assigns homework problems from page 518, numbers 3 through 31 odds.
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5.2 notes
The document provides instruction on converting between fractions and decimals. It explains that to write a fraction as a decimal, one divides the numerator by the denominator. Terminating decimals have a repeating pattern of zeros at the end, while repeating decimals have a non-zero digit that repeats. Examples are shown of writing fractions as decimals and decimals as fractions by moving the decimal point and reducing. Students are assigned homework problems practicing converting fractions and decimals.
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The document appears to be notes from a math class on equations of circles. It includes the standard equation for a circle (x - h)2 + (y - k)2 = r2 where (h, k) is the center and r is the radius. It also gives a homework problem asking to write the equation of a circle with center (-6, 4) and a point on the circle being (2, -2).
8.1 notes
This document is from a math class and covers relations and functions. It includes examples of relations that are and aren't functions, as it discusses the key characteristics of relations being sets of ordered pairs and functions having each domain paired with exactly one range. The homework assigned is to complete problems 1-5 and 11-22 on page 403.
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This document appears to be notes from a math class on classifying polygons and angles. It includes examples of classifying various angles as acute, right, or obtuse. It also defines and provides examples of different types of triangles, quadrilaterals, and regular polygons. There are practice problems asking students to name properties of different quadrilaterals and calculate the perimeter of a regular octagonal gazebo.
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This document contains notes from a math lesson on multiplying and dividing integers:
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9.7 notes
The document discusses dilations in geometry. It notes that a dilation with a scale factor between 0 and 1 results in a reduction, while a scale factor greater than 1 results in an enlargement. It also mentions that dilations can be represented using matrices by multiplying the scale factor by the polygon matrix. Several homework problems are assigned from page 629 involving dilation.
7.3 notes
The document discusses solving multi-step equations with fractions and decimals. It provides examples of equations to solve, such as 2n + 53 = 47 and -3a + 15 = 13. The objective is to solve these types of equations. Students are assigned homework problems on page 356 numbers 6 through 39 involving multiples of 3.
4.2 notes
This document appears to be notes from a math lesson on exponents. It includes examples of exponent expressions and their values, as well as homework assignments involving simplifying expressions with exponents and evaluating expressions for given values of variables. The document provides instruction and practice with the concepts and skills of exponents.
12.3 notes
This document contains notes on finding the surface area of pyramids and cones. It provides the formulas for calculating surface area of regular pyramids as one-half of the perimeter of the base times the sum of the slant height and apothem. For cones, the surface area formula is given as the area of the base plus the radius times pi times the slant height. The document includes examples of applying these formulas to find the surface area of various pyramids and cones.
8.5 notes
The document defines trapezoids and kites. It states that a trapezoid is a quadrilateral with one pair of parallel sides called bases and two non-parallel sides called legs. An isosceles trapezoid has two legs of equal length. The midsegment of a trapezoid is parallel to the bases and half the sum of the bases in length. A kite is a quadrilateral with two consecutive pairs of equal sides but not opposite sides. The diagonals of a kite are equal in length and one pair of opposite sides are equal. The document instructs the reader to complete homework problems on trapezoids and kites.
12.1 notes
Students were instructed to make two solids by naming them on their bases, coloring the faces, folding the faces, gluing the edges, and displaying the finished solids. They then classified solids as prisms or pyramids based on the shape of each solid's base. The document appears to be notes from a math class lesson on identifying and constructing different types of three-dimensional solids.
12.4 notes
This document provides instruction on calculating the volume of prisms and cylinders. It defines volume as the amount of space inside an object. To find the volume of a prism or cylinder, students are told to find the area of the base and multiply it by the height of the object. Formulas for calculating the volume of prisms and cylinders are provided, with the key being to identify the base shape and insert its area formula. Examples of prism and cylinder volume problems are given for students to work through.
8.6 notes
The document is notes from a geometry class that include:
1) A bellwork assignment with geometry problems to solve.
2) Instructions for students to fill in properties of special quadrilaterals like rectangles, rhombus, squares, kites and trapezoids from their textbook.
3) The date and homework assigned which is to complete problems 13-16 and 18-22 on page 554 of their textbook.
8.2 notes
The document discusses properties of parallelograms. It states that a parallelogram is a quadrilateral with both pairs of opposite sides parallel. It presents several theorems: if a quadrilateral is a parallelogram, then its opposite sides are congruent; if a quadrilateral is a parallelogram, then its opposite angles are congruent; if a quadrilateral is a parallelogram, then the sum of its consecutive angles is 180 degrees; if a quadrilateral is a parallelogram, then its diagonals bisect each other. The document assigns homework problems from page 518, numbers 3 through 31 odds.
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5.2 notes
The document provides instruction on converting between fractions and decimals. It explains that to write a fraction as a decimal, one divides the numerator by the denominator. Terminating decimals have a repeating pattern of zeros at the end, while repeating decimals have a non-zero digit that repeats. Examples are shown of writing fractions as decimals and decimals as fractions by moving the decimal point and reducing. Students are assigned homework problems practicing converting fractions and decimals.
10.7 notes
The document appears to be notes from a math class on equations of circles. It includes the standard equation for a circle (x - h)2 + (y - k)2 = r2 where (h, k) is the center and r is the radius. It also gives a homework problem asking to write the equation of a circle with center (-6, 4) and a point on the circle being (2, -2).
8.1 notes
This document is from a math class and covers relations and functions. It includes examples of relations that are and aren't functions, as it discusses the key characteristics of relations being sets of ordered pairs and functions having each domain paired with exactly one range. The homework assigned is to complete problems 1-5 and 11-22 on page 403.
9.3 notes
This document appears to be notes from a math class on classifying polygons and angles. It includes examples of classifying various angles as acute, right, or obtuse. It also defines and provides examples of different types of triangles, quadrilaterals, and regular polygons. There are practice problems asking students to name properties of different quadrilaterals and calculate the perimeter of a regular octagonal gazebo.
5.5-5.6 notes
The document discusses triangle inequalities and theorems. It states that the sum of any two side lengths of a triangle must be greater than the third side length. It also presents the hinge theorem, which says that if two triangles have two equal sides and the included angle of one is larger, then the third side of that triangle is longer. The converse of the hinge theorem is also described as having the third side be longer if the included angle is smaller. Examples are given to illustrate the triangle inequality theorem.
6.5 notes
The document appears to be notes from a math class on the topic of proportions and percents. It includes examples of percent problems worked out step-by-step, such as finding 65% of 245 and 43% of 230. It also provides word problems involving percentages, such as calculating what percent 52 is of 60. Additional practice problems are assigned from the textbook.
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This document discusses ratios, proportions, and geometric mean. It defines a ratio as a comparison of two quantities using division (a/b or a:b). It explains that equivalent ratios are in the same simplified form. It also defines proportions as two ratios that are equal, and shows how to use cross multiplication to solve proportions. Finally, it defines the geometric mean as the square root of the product of two numbers.
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This document contains class notes on geometric probability from April 2nd, 2014. It discusses the definition of geometric probability as the ratio of geometric measures of two spaces. Examples are given for calculating the probability of a driver speeding in front of a school based on road length ratios, and the probability of a fly landing on a beach ball compared to the total area of a blanket. The student is assigned homework problems from page 774 involving geometric probability calculations.
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12.7 notes
This document contains notes from a math class on similar solids. It defines similar solids as two solids of the same type that have equal ratios, known as a scale factor. It then states the Similar Solids Theorem: if two similar solids have a scale factor of a:b, their corresponding areas have a ratio of a2:b2 and their corresponding volumes have a ratio of a3:b3. Examples of homework problems involving similar solids are listed.
12.6 notes
The document discusses surface area and volume formulas for spheres. It provides examples of calculating the surface area of spheres with given diameters, as well as the volume of spheres and other objects like snow cones that can be modeled as spheres. Students are assigned homework problems applying these formulas to calculate surface areas and volumes.
12.5 notes
The document is notes from a math class lesson on finding the volumes of cones and pyramids. It includes the objectives of learning the formulas for these volumes. The formulas given are that the volume of a cone is 1/3πr^2h and the volume of a pyramid is 1/3Bh, where B is the area of the base and h is the height. There are examples provided of applying these formulas to find volumes.
12.4 notes
This document contains notes from a math lesson on finding the volumes of prisms and cylinders. It defines volume as the amount of space inside an object. It explains that to find the volume of a prism or cylinder, you calculate the area of the base and multiply it by the height. For a prism, the base can be any shape and its area formula is used. For a cylinder, the base is a circle so the volume formula is πr^2h, with r as the radius and h as the height. Examples of volume problems are shown and homework problems are assigned from the textbook.
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12.3 notes
This document contains notes and examples for calculating the surface area of pyramids and cones. It provides the formulas for finding the surface area of regular pyramids and cones. For pyramids, the surface area equals one-half the perimeter of the base times the sum of the slant height and apothem. For cones, the surface area equals pi times the radius squared plus pi times the radius times the slant height. The document includes practice problems applying these formulas to find the surface area of various pyramids and cones.
12.2 notes
The document discusses surface area formulas for prisms and cylinders. It defines surface area as the sum of the areas of all surfaces that enclose a solid. For prisms, surface area is calculated as the perimeter of the base multiplied by the height, plus twice the area of the base. For cylinders, surface area is the circumference of the base multiplied by the height, plus twice the area of the circular base. The document provides examples of applying these formulas to prisms and cylinders.
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This document contains notes from a math class where students were working on homework problems involving trigonometry (SOHCAHTOA) and multiples of 3. The notes are dated April 08, 2015 and reference homework page 648 problems 12 through 36 dealing with multiples of 3.
11.7 notes
This document contains notes from an 11th grade math class on the topic of geometric probability. It includes examples of calculating the probability of events based on ratios of lengths and areas, such as the probability of a driver speeding in front of a school based on the length of road in front of the school over the total road length. The homework problems assigned were problems 4-10 of the even numbers, 20-23, and 30-33 on page 774 of the textbook.
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This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
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Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
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6.2 notes
- 3. 6.2 proportions November 26, 2013 Solve x = 4 . 9 6 Jan 302:55 PM HW pg. 292 #520 3
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