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Monday, July 5, 2021
Monday, March 27, 2017
TOP SCORERS FOR FINALS GIVEN ON MARCH 22 - 25, 2017
CONGRATULATIONS
Top Scorers for FINALS
Given on March
22 – 24, 2017
PHYSICS E
22 – Modern Physics
Name Score
1.
Geisler Cabayao 96
2. Korina
T. Dayot 94
3.
Nathalie Gay C. Patricio 93
4.
Carmel Therese Triumfante 92
5.
Amerah Ampatuan 91
6.
Kenneth Gallano 90
7.
Aushe Mae Montebon 86
8.
Cristy Juliet Reyes 82
PHYS 21 Fundamentals of Physics
Name Score
1. Farouk Gumaan 96
2. Russel Ann Completano 95
3. Bai Astrafiah Cassandra Abas 92
Krizza Joy Buckles 92
4. Baialmanisan Dimasangkay 88
MATH 23/
MATH 201 Plane Trigonometry
Name Score
1. Melanie Talusan 98
2. Angelo Florague 84
3. Mhil Rose Zhine Taytay 82
4. Benjie Ibot 80
MATH
25 Analytic Geometry
Name Score
1. Melanie Talusan 100
2. Benjie Ibot 92
3. Ivy Valenzuela 90
Johwena Cuevas 90
4. Angelo Florague 80
MATH 11
College Algebra
Name
Score
1. Kevin Guiang 88
Wahida Manial 88
2. Winona Dojinog 85
3. Kathleen Faye Dacanay 83
MATH 22C
Automata & Language Theory
Name Score
1. Ritche Sal grande 98
2. Jay Harley Gadingan 94
Cristy Joy Ybanez 94
3. Charlotte Evangelio 92
4. Joevin Niel Poquita 91
5. Jeanifer Aban 86
6. Kenneth Jude Carrera 83
7. Vicio Untal III 81
LANG 32
– Foreign Language 2
Name Score
1. Jane Mae
Tampus 100
Al Suod Mascud 100
Mohamad Mustapha 100
Kimberly
Olmoguez 100
Wahida Manial 100
Kapia Sabpa 100
2.
Benny Chua 98
Samraida Mamay 98
Alchelou Balogo 98
3.
Adrian Camatac 96
Ervin Ibot
96
Bainisan
Balad 96
4. Sheena Rose Eduarte 84
Efren F. Cadungog, Sr., MIM
Class adviser
Wednesday, November 26, 2014
POLAR
COORDINATES
Polar
points are plotted using the polar coordinate plane with the line OX as initial
line or polar axis, point 0 as the pole or origin and the distance of the point
from O as the radius vector.
The position of any point P in the
plane is determined if the length of the line OP together with the angle that
this line makes with OX are known, both the length and the angle being measured
in a definite sense.
From the figure :
r = radius vector, + if measured along the terminal side of
Ө,
–
if measured in the opposite direction along the terminal
side of Ө
Ө =
polar angle
OX
= initial line or polar axis
O =
pole or origin
Polar Coordinate paper – it is where
the polar points are plotted.
-
to be illustrated on the board during lecture
Plot the following points :
1.
(
2, 30º ) 6. ( 3,
60º )
2.
(
4, 225º )
7. ( 4,
– 315º )
3.
(
– 6, –120º )
8. ( – 3, –240º )
4.
(
– 4, 330º ) 9. ( 4, – 330º )
5.
(
6, – 150º ) 10. (– 6, 150º )
Distance between two points in Polar
Coordinates : by Cosine law
Conversion
- Polar
to rectangular coordinates
1) x = r cos Ө
2) y = r sin Ө
- Rectangular
to Polar coordinates
1) r = sqrt( x2 + y2 )
2) Ө = Arctan ( y/x )
Exercises
1.
The
point ( r , Ө ) is equidistant from ( 2 , 90º ) and (– 2 , 150º ). Express the
statement into an algebraic expression.
2.
Show
that the given points ( 2 , 45º ), ( sqrt( 2 ), 90º ) and ( – 2 , 135º ) are
vertices of a right triangle and find its area.
3.
Convert
to rectangular coordinate.
a)
(
3 , 240º )
b)
(
4 , 150º )
c)
(–
5 , 150º )
4.
Convert
to polar coordinate
a)
(
2 , –2 )
b)
(
– 1 , – sqrt ( 3 ) )
c)
(
– 3 , 3 )
5.
Find
the distance between the following points.
a)
(
3 , 240º ) and (– 5 , 150º )
b)
(
4 , 150º ) and ( 2 , 45º )
c)
(
2 , 90º ) and ( – 2 , 135º )
Friday, June 28, 2013
Analytic Geometry : Introduction
Analytic Geometry
Analytic geometry is a branch of mathematics which uses algebraic equations to describe the size and position of geometric figures on a coordinate system. Developed during the seventeenth century, it is also known as Cartesian geometry or coordinate geometry. The use of a coordinate system to relate geometric points to real numbers is the central idea of analytic geometry. By defining each point with a unique set of real numbers, geometric figures such as lines, circles, and conics can be described with algebraic equations. Analytic geometry has found important applications in science and industry alike. During the seventeenth century, finding the solution to problems involving curves became important to industry and science. In astronomy, the slow acceptance of the heliocentric theory of planetary motion required mathematical formulas which would predict elliptical orbits. Other areas such as optics, navigation and the military required formulas for things such as determining the curvature of a lens, the shortest route to a destination, and the trajectory of a cannon ball. Although the Greeks had developed hundreds of theorems related to curves, these did not provide quantitative values so they were not useful for practical applications. Consequently, many seventeenth-century mathematicians devoted their attention to the quantitative evaluation of curves. Two French mathematicians, Rene Descartes (1596-1650) and Pierre de Fermat (1601-1665) independently developed the foundations for analytic geometry. Descartes was first to publish his methods in an appendix titled La geometrie of his book Discours de la methode (1637). The link between algebra and geometry was made possible by the development of a coordinate system which allowed geometric ideas, such as point and line, to be described in algebraic terms like real numbers and equations. In the system developed by Descartes, called the rectangular Cartesian coordinate system, points on a geometric plane are associated with an ordered pair of real numbers known as coordinates. Each coordinate describes the location of a single point relative to a fixed point, the origin, which is created by the intersection of a horizontal and a vertical line known as the x-axis and y-axis respectively. The relationship between a point and its coordinates is called one-to-one since each point corresponds to only one set of coordinates. The x and y axes divide the plane into four quadrants. The sign of the coordinates is either positive or negative depending in which quadrant the point is located. Starting in the upper right quadrant and working clockwise, a point in the first quadrant would have a positive value for the abscissa and the ordinate. A point in the fourth quadrant (lower right hand corner) would have negative values for each coordinate. The notation P (x,y) describes a point P which has coordinates x and y. The x value, called the abscissa, represents the horizontal distance of a point away from the origin. The y value, known as the ordinate, represents the vertical distance of a point away from the origin.
DEPRECIATION, DEPLETION and VALUATION of Properties
DEPRECIATION, DEPLETION and VALUATION of Properties
1.
Depreciation is the decrease or the reduction of the value of a property, an equipment such as machinery, building or other structure due to passage of time. It is that portion of the cost of the equipment which is charged off periodically as an expense in operating the business enterprise.
Depreciation is the decrease or the reduction of the value of a property, an equipment such as machinery, building or other structure due to passage of time. It is that portion of the cost of the equipment which is charged off periodically as an expense in operating the business enterprise.
Excluded from this definition are properties whose values increase with time, such as antiques, paintings of the masters, rare stamps, rare coins, and in most cases land.
Depreciation must always be included in the cost of production of any product or the rendering of any service where equipment is used for the following reasons ;
a) To provide for the replacement of the equipment either at the end of its physical or economic life or at the time when its operation no longer result in a satisfactory profit.
b) To provide for the maintenance of capital to replace the decrease in the value of equipment caused by physical or functional causes.
2. A natural resource such as mine, quarries, an oil or gas well, or a piece of timber land wastes or depletes away due to the gradual extraction of the contents of such properties and are being sold. The corresponding reduction in the value of the resource is called depletion. To provide for the recovery of capital invested in such assets, a depletion fund is provided. The annual charge set aside in the fund is called depletion cost rather than depreciation cost.
3. Valuation is the process of determining the value of certain property for a definite reason.
Types of depreciation :
Decrease in the value of property with the passage of time are due mainly to the following:
1. Physical depreciation caused by the following:
(a) Deterioration due to the effects of various chemical or mechanical factors on the materials composing the property; i.e. rusting of metal parts, decay of wooden parts or discoloration and cracking of plastic parts.
(b) Wear and tear due to abrasion, friction between moving parts, impact, vibration or fatigue of the materials that make up the property.
2. Functional depreciation which is due to the decrease in the demand for the function of the equipment for which it was designed. Such depreciation is caused by the following:
(a) Inadequacy of the equipment.
(b) Obsolescence caused by the invention of more efficient equipment and machines to perform the same task.
(c) Change in the method of production.
(d) Change in style and design of the goods produced on the equipment.
(e) Transfer of population due to various causes.
3. Change in the price levels of similar property. If price levels rise during the life of the property, even if the original investment has been recovered through proper depreciation procedure, the recovered capital will be insufficient to provide an identical replacement. Thus, it is the capital that has depreciated, and not the property.
DEPRECIATION COST
The depreciation cost depends upon the physical or economic life of the equipment and its first cost.
a) The physical life of an equipment is the length of time during which it is capable of performing the function for which it was designed and manufactured.
b) The economic life of an equipment is the length of time during which it will operate at a satisfactory profit. Thus, even though the equipment can still perform its function, but it can only operate at a loss, then it is considered economically dead. Replacement is in order.
c) The first cost of any property includes the original purchase price, freight and transportation charges to the site, installation expense, initial taxes and permit to operate and all other expenses needed to put the equipment into operation.
d) The amount to be recovered, equal to the depreciation cost, is the difference between the first cost and the salvage value or scrap value of the equipment.
e) The salvage value, sometimes called the second-hand value is defined as the amount for which the equipment or the machine can be sold as second hand. It implies that the machine can still perform its function.
f) The scrap value or junk value is the amount that the equipment can be sold for, when disposed off as a junk. This implies that the equipment can not be use anymore for the function for which it was designed.
DETERMINATION OF DEPRECIATION COST
The methods often used to determine annual depreciation cost are the following :
1. Straight- line method
2. Sinking fund method
3. Matheson formula ( also known as Constant percentage method; Fixed percentage method; Declining balance method or Diminishing balance method )
4. Sum of years-digits method ( SYD method )
5. Service-output or Production-units method
Other methods are :
1. Straight-line plus average Interest formula
2. Double-rate declining-balance method
3. Operating day method
4. Retirement method
5. Annual inventory method
REQUIREMENTS FOR A DEPRECIATION METHOD
A depreciation method should fulfil the following requirements :
1. Payment to the depreciation fund should be equal to the loss in the value due to depreciation.
2. The method should be simple.
3. Prior to its adoption, approval of the method should be secured from the Bureau of Internal Revenue ( BIR )
4. To be satisfactory, the actual value of the equipment should, at all times, be equal to the book value. It will be necessary from time to time to check the actual value against the book value, and in case the two values are not in agreement, adjustments should be made.
VALUATION
Valuation is the process of determining the value of certain properties for definite reasons. Valuation is sometimes called appraisal and the person engaged in the task of valuation is called an appraiser.
Due to their technical knowledge, engineers are usually requested to solve problems in valuation under the following instances :
1. When second hand structures, equipment and machinery are to be purchased or sold.
2. When extractive or wasting assets such as mines, oil and gas wells, timber lands, and quarries are to be purchased or sold.
3. When two or more going enterprises are to be merged or consolidated.
4. When the value of a property is needed for expropriation by the government for highways or impounding reservoirs.
5. When the value of a property is needed for purposes of taxation or insurance.
6. When the rates to be charged by public utility companies are to be determined, their properties must be correctly evaluated.
7. When the management of an enterprise wishes to know the correct valuation of their property, in order to determine the financial soundness of the enterprise.
8. For the determination of penalties and or bonuses.
Terminologies related to Valuation :
1. The market value of a property is the amount which a willing buyer will pay to a willing seller for the property when neither one is under compulsion to buy or to sell.
2. The utility or use value of a property is what it is worth to the owner when in actual operation. A property that is in good operating condition has a higher value than one which is not operational.
3. The fair value is the value which is a disinterested third party, different from the buyer or seller, will determine in order to establish a price that is fair and acceptable to both the buyer and the seller.
4. The Book Value is the value of the equipment as shown on the account records of the business enterprise. It is the present value of the equipment which is the difference between the original cost and the accrued depreciation. The book value of a property is not equal to its actual value.
5. Going value or going-concern value is considered to be an intangible value which an actually operating concern has due to its operation. It is also considered as the difference between the value of the property as it stands ready for operation and its value as it would stand at completion of construction as an inert assembly of physical parts.
6. Goodwill value is that element of value which a business has earned through the favorable consideration and patronage of is customers arising from its well-known and well-conducted policies and operations. Well-known trade mark and well-known products have this value to great extent. Goodwill value is increase by good advertising, sound business policies and courteous selling of the product or of rendering service.
7. Salvage value of an equipment is the amount that can be obtained from the sale of the equipment as second hand. It is implied that the equipment has still some utility value. It is not always equal to the book value of the equipment at the time it is sold. It is affected by several factors relative to the equipment, as follows:
a) Condition of the equipment at the time of sale. An equipment in good condition will command a better salvage value than one in poor condition.
b) Current price of similar new equipment. If similar new equipment are currently being sold at much higher price than the original cost of the original equipment, then the salvage value will be more than the actual book value of the equipment at the time of sale.
c) Reason for selling. In certain cases, the seller is very keen on selling s certain piece of equipment because the same has not been operating economically. If the buyer should notice this, then the salvage value will be low.
d) Present condition of the market. The law of supply and demand will operate in this case. If similar goods are scarce, the salvage value of a property will be rather high. On the contrary, if the market is glutted with similar properties, then the salvage value will be low.
e) Ease or difficulty of removal of the equipment. In cases where a piece of equipment is easily removed from the premises of the company, the salvage value maybe fairly high. Difficulty in removing equipment from its premises will result in a low salvage value due to the expected high cost of removal.
f) Nature of the equipment. A standard piece of equipment, not subject to rapid changes in design or use, will usually command a better salvage value than a more specialized piece of equipment.
8. Scrap value or junk value of a machine is the amount the machine would sell or if disposed off as junk. The utility of the machine is considered to be zero.
9. Rate-base value is the value assigned to the property for the purpose of establishing rates. This is usually applied to public utility companies.
Source : Engineering Economy, 3rd edition by Matias Arreola
chapter 7 ( pages 153 - 189 ) and chapter 8 ( pages 190 - 206 )
Saturday, September 22, 2012
Thursday, September 6, 2012
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