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### TUTORIAL CENTRIFUGAL PUMP SYSTEMS

by marechausse 0 Comments 6 Viewed 0 Times

### Rhode Island's College- and Career-Ready Commitment - Achieve

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### NYS Mathematics Glossary* – Algebra 2/Trig - Regents Exam Prep ...

by Jimakon 0 Comments 21 Viewed 0 Times

NYS Mathematics Glossary* – Algebra 2/Trig *This glossary has been amended from the full SED Commencement Level Glossary of Mathematical Terms (available at http://www.emsc.nysed.gov/ciai/mst/math/glossary/home.html) to list only terms indicated to be at the Algebra 2/Trig level.) This Glossary, intended for teacher use only, provides an understanding of the mathematical terms used in the Regents-approved course entitled Algebra 2/Trig (as reflected in the NYS Mathematics Core Curriculum). A a + bi form The form of a complex number where a and b are real numbers, and i = −1 . abscissa The horizontal or x-coordinate of a two-dimensional coordinate system. absolute value The distance from 0 to a number n on a number line. The absolute value of a number n is indicated by n . Example: −3 = 3 , +3 = 3 , and 0 = 0 . absolute value equation An equation containing the absolute value of a variable. Example: x+3 = 9 absolute value function A function containing the absolute function of a variable. ⎧ x, x ≥ 0 ⎫ Example: f ( x) = x = ⎨ ⎬ ⎩ − x, x < 0 ⎭ absolute value inequality An inequality containing the absolute value of a variable. Example: x + 3 < 9 adjacent angles Two coplanar angles that share a common vertex and a common side but have no common interior points. Example: In the figure, ∠AOB and ∠BOC are a pair of adjacent angles, but ∠AOC and ∠BOD are not adjacent. A B C O D 2 adjacent sides Two sides of any polygon that share a common vertex. algebraic equation A mathematical statement that is written using one or more variables and constants which contains an equal sign. Examples: 3y + 5 = 1 2 x − 5 = 11 log 5 ( x − 3) = 2 2x = 1 8 algebraic expression A mathematical phrase that is written using one or more variables and constants, but which does not contain a relation symbol ( <, >, ≤, ≥, =, ≠ )...

### Algebra and Trigonometry Review Material - Department of Math

by Jimakon 0 Comments 7 Viewed 0 Times

Algebra and Trigonometry. Review Material. Department of Mathematics. Vanderbilt University. June 2, 2004. q  v u t v  y q Iu v  I g q   q   y t s q r r y    q rI  I sI s r q p i h u v q r  y q s q   y   I Ir y q   i y r q Iu v  y I y t v  y q   v sI    q  qI r y q   s v  y    h y   q p  v  e r q p i h  u v q r w r q x      v     }   } q |Iu s r q p i h  u v  yI  v r rI ~ q   uu v  I g r q  q  y   sr q p i h q xy p v q    y uu v s q  hux xx wI     © ¨       y {  qs q  j z r y w  I g s r q  q I q r v w  v x v u  s k sr y v I i y  q  y r q p  y   I g s r q  q I  y s   qI  y h t uu v  y  q s q   sI     © ¨     '    y s  q s q  j dn nn  m    h  r  h q   q  m q  nnn   o k yrqp  I g r q   q  y  s r q p i h  q u y  g q xI  v  q    v q xI I s y t u u v  y  q s q   s I    4   '  y o  q s q  j dn n  m    h   l k s r q p i h  qu y  g q xI I s y t r y s r q p i h    I   h y   y  q s q   sI     © ¨     ¨    y l  q s q  j k  I gyuu y  q   q r v s hu h u v  I  I s h q p uuI g q g s r q p i h   y s  q s q  j   '       q uu v  sI  q s v   I I r g  y wv g sI  j  d i   v h  q q g q p r q p i h   q x q  v s I e f e   s v  h s  s   q i qu q q   s q I i r q  q  wu q  q u t i y   v   w r q t y r t v  I xI  wp r y  d           I s v  s  q i qu q s I  I sIu wp  q pI r  s q  q p  v   q s     v  quu v  sI s   q  p y  y  yI   quu y  v  v   uu v  q   s   q  p y u v I  v i q   v i u h  q s h   v I s v p  s y i q     y i v q r v w q   q  I s  s I  v i q   v i I qu y r  v  r y t iI wr q x v wvu t s r q p i h g fed c b a ` ¥ ¤ QX UY ¤ £ QX ¡ ¥ S W V ¢ U ¥ T ¤ S R Q P    yI  v  y   q s I q  I g   q i qu q q i v s q    sI u  y  y  q g  v   q  y g d   «    m    h   d   «  m  h  § d   m    h   p d       m    h   d     § d   m    h   v ª ¦  % ©  \$ # © ¦  yI  h ¨ s v  v qr q g I  g  ¦ §  wp ¦  y s  q i qu q uu v  I g r q   q  y    y s  q i qu q uu v  y  q s q   q  y  q  q g  s  q s q r v ¦   v    s r q p i h   y  q r v w q   q  I s  su vx r q I q   I  q  hu  I r q x q  q r v ¥ ¤   v ¥ q  v   q  y g {   ¥ ¤  ¥ q d   e f e     ¥ q  d   e f e     ¥ q  d e   f e   ¥ ¤   d e   f e   ¥ ¤   k uu q g s v     '  '  £ ' r q Is  y   v  q ¢    I v   y      I  v   s g y  s   e  v q u  r I   I ¡  q u u q   q u I  g    I v   y        u v x r q   I q    v   s g y  s q x y p v q  I u r q p i h  q    y   e  v q u  r I  g y u u y  q  j     u v x r q   I q  j k   h q r h  I

### LAPORAN AKHIR - JICA

by Hermawan 0 Comments 36 Viewed 0 Times

### llustrative Guide to Classical Moulding Design for Cabinetry ...

by jacovic 0 Comments 21 Viewed 0 Times

Classical is a term that is often used loosely within the design community. In this age of modernism, traditionalism, and mixing design genres to fit individual tastes, the true sense of what is classical can get lost. It is true that Classical is most often associated with the Five Orders, but many miss the deeper understanding of classical proportions and overall beauty that can be adapted to fit many styles today. This booklet was created to give design professionals a broader understanding of classical design principals and show how they can be adapted today. More specifically, we explore the specific math and proportions that can be used for cabinetry, and the rooms that cabinetry are most often found in - the kitchen and bath. By tailoring this information to these specific applications, we hope that more design professionals will feel comfortable in basing their designs on something more than just taste, but rather a cultural style that has stood the test of time and is still very relevant today. Although kitchen and bathroom designs are based on modern conveniences and functionality, classical proportions still play a crucial role in making any design beautiful. An easy place to start determining good proportions is where your top cabinetry line will be, which should be based on ceiling height (unless the ceiling height is exceedingly tall). The guidelines below ensure that enough room is left to accommodate a cabinet crown and a ceiling crown. When the ceiling is unusually high, it is best to create your own ceiling line by allowing the lower edge of the ceiling crown, or entablature, to sit lower on the wall. You can calculate the rest of your proportions off this line. Below are examples of the Great Hall and Anteroom at Syon Park.

### Some Calculus Problems - Penn Math

by luan 0 Comments 14 Viewed 0 Times

... A por whih rel x does this improper integrl onvergec A how tht G(x + I) = xG(x) nd dedue tht G(n + I) = n3 for ny integer n ! HF QIF y g(t ) X R 3 R2 de¢nes  smooth urve in the plneF A sf g(H) = H nd kgH (t )k  D show tht for ny  ! HD kg( )k  F woreoverD show tht equlity n our if nd only if one hs g(t ) = vt where v is  unit vetor tht does not depend on t F A sf g(H) = HD gH (H) = H nd kgHH (t )k IPD give n upper ound estimte for kg(P)k F hen n this upper ound e hievedc QPF vet r(t ) de¢ne  smooth urve tht does not pss through the originF A sf the point a = r(t0 ) is  point on the urve tht is losest to the origin @nd not n end point of the urveAD show tht the position vetor r(t0 ) is perpendiulr to the tngent vetor rH (t0 ) F A ht n you sy out  point b = r(t1 ) tht is furthest from the originc QQF gonsider two smooth plne urves g1 ; g2 X (H; I) 3 R2 tht do not intersetF uppose 1 nd 2 re points on g1 nd g2 D respetivelyD suh tht the distne j1 2 j is miniE mlF rove tht the stright line 1 2 is norml to oth urvesF R QRF vet h(x; y; z) = H de¢ne  smooth surfe in R3 nd let  X= (; ; ) e  point not on the surfeF sf  X (x; y; z) is  point on the surfe tht is losest to  D show tht the line  is perpendiulr to the tngent plne to the surfe t  F QSF vet r(t ) desrie  smooth urve nd let V e  ¢xed vetorF sf rH (t ) is perpendiulr to V for ll t nd if r(H) is perpendiulr to V D show tht r(t ) is perpendiulr to V for ll t F QTF vet f (s) e ny differentile funtion of the rel vrile s F how tht u(x; t ) X= f (x + Qt ) hs the property tht ut = Qux F how tht u lso stis¢es the wve eqution utt = Wuxx F QUF vet u(x; y) e  smooth funtionF A sf ux = H with u(H; y) = sin(Qy) D ¢nd u(x; y) F A sf ux = Pxy with u(H; y) = sin(Qy) D ¢nd u(x; y) F A sf ux + uy = H with u(H; y) = sin(Qy) D ¢nd u(x; y) F ss there more thn one suh funtionc dA sf ux + uy = Q Pxy with u(H; y) = sin(Qy) D ¢nd u(x; y) F ss eA sf ux Puy = H with u(H; y) = sin(Qy) D ¢nd u(x; y) F ss there more thn one suh funtionc QVF vet r X= xi + yj nd V(x; y) X= p(x; y)i + q(x; y)j e @smoothA vetor ¢elds nd g  R smooth urve in the plneF sn this prolem s is the line integrl s = C V ¡ d r F por eh of the followingD either give  proof or give  ounterexmpleF A sf g is  vertil line segment nd q(x; y) = HD then s = HF A sf g is  irle nd q(x; y) = HD then s = HF A sf g is  irle entered t the origin nd p(x; y) = q(x; y) D then s = HF dA sf p(x; y) > H nd q(x; y) > HD then s > HF QWF vet g denote the unit irle entered t the origin of the plneD nd h denote the irle of rdius S entered t (P; I) D oth oriented ounterlokwiseF vet  denote the ring region etween these R urvesF sf  vetor ¢eld V stis¢es div V = HD show tht the line R integrl C V ¡ N ds = D V ¡ N ds = his extends immeditely to the sitution where g nd h re more generl urves nd  is the region etween themF por £uid £ow it is n expression of onservtion of mssD sine div V = H mens there re no soures or sinks in the region  F...

### Engineering Mechanics major – Course Dependency Map

by jacky 0 Comments 12 Viewed 0 Times

Engineering Mechanics major – Course Dependency Map 550.291 Linear Algebra / Differential Equations (or 110.201 and 110.302) Mathematics elective – 4 credits 560.348 or 550.310 Statistics 110.202 Calculus III or 110.211 Honors Multivariable Calculus 110.109 Calculus II Humanities / Social Science elective 6* * Humanities/Social Science Electives - total 18 credits required, some electives may carry more than 3 credits, so the electives might be achieved in less than six courses. Humanities / Social Science elective 5 Humanities / Social Science elective 4 * Technical Electives - total 18 credits required, some electives may carry more than 3 credits, so the elective requirements might be achieved in less than six courses. Technical Elective 5 - 3 credits Humanities / Social Science elective 3 Basic Science, Mathematics, and Humanities / Social Science in other departments: some courses have science and math prerequisites not mapped here. See isis.jhu.edu/classes for info. Technical Elective 4 – 3 credits Technical Elective 3 – 3 credits Humanities / Social Science elective 2 500.200 Computing for Engineers or other intro to programming options Humanities / Social Science elective 1 110.108 Calculus I 510.101 Intro to Materials Chemistry or 030.101 Intro to Chemistry 530.101/102, 530.105/106 Freshman Experiences I and Jaafar's DARPA Labs or other intro to engineering options BEGIN HERE Technical Elective 6* - 3 credits 171.102 / 173.112 Physics II and Lab 530.202 Dynamics 530.103/104 Intro to Mechanics I / II or 171.101 / 173.111 Physics I and Lab Key Required Course 530.201 Statics of Mechanics and Materials Tech Elective Required for next course: EM/ES Electives Concurrent: Technical Elective 2 – 3 credits 530.231 / 232 Thermodynamics and Lab 530.327 / 329 Intro to Fluid Mechanics and Lab 530.215 / 216 Mechanics Based Design and Lab or 530.405 Mechanics of Solids H/S Electives Basic Science and Math Suggested for next course: Technical Elective 1 – 3 credits 530.403/404 Senior Design I/II Engineering Mechanics elective 2 Engineering Mechanics elective 1 Engineering Science – solids / fluids elective Engineering Science – dynamics/ materials elective Engineering Science – fluids elective Engineering Science – solids elective ...

### Solar System Math - NASA Quest!

by queen01 0 Comments 15 Viewed 0 Times

Lesson 4 How do missions to different planets and moons compare in terms of payload size and cost? Introduction In this lesson, students will calculate the total mass that is needed to support a mission to a possible destination in the solar system. Students will calculate the mass needed to keep a crew of three astronauts alive for the duration of a mission, the amount of science materials that can be transported on each mission, and the total cost of a mission. Students will compare the costs relative to the amount of scientific materials that can be transported to determine which planets or moons would be the best place(s) to send humans in our solar system. Main Concept The more time required for a mission to a planet or a moon, the more crew survival resources are needed. This affects both the cost of the mission and the amount of room available for scientific instruments. Instructional Objectives During this lesson, students will: • Calculate the mass of the resources needed to sustain a three-person crew on a mission to a given planet or moon. • Calculate the proportion (as a fraction, decimal, or percent) of a crew vehicle that is available for scientific instruments for a particular destination and plot the proportion on a number line to compare it with other destinations. • Calculate the cost of a launch to each destination and create graphs to compare these costs and the amount of room that is needed for scientific instruments for each mission. Major Focus Skills Math • Ratio and proportion • Comparing and ordering fractions, decimals, and percents • Units of measurement (metric and standard) • Data collection and representation Major Focus Concepts Math • Fractions, decimals, and percents are used to represent relationships between numbers. • Estimation • Whole numbers, fractions, decimals, and percents can be placed on a number line to represent their relative values. ...

### Solar System Bead Distance Activity

by queen01 0 Comments 24 Viewed 0 Times

Our solar system is immense in size. We think of the planets as revolving around the sun but rarely consider how far each planet is from the sun or from each other. Furthermore, we fail to appreciate the even greater distances to the other stars. Astronomers refer to the distance from the sun to the Earth as one “astronomical unit” or AU. This unit provides an easy way to calculate the distances of the other planets from the sun and build a scale model with the correct relative distances. Instructional Objective: By calculation and through the construction of a scale model solar system (based on their calculations where age-appropriate), students will observe the relative distances of the planets, the asteroid belt and dwarf planet Pluto from each other and the sun including the increasingly vast distance spacings of planets in the outer solar system compared to the inner solar system. National Science Education Standards: Standard D: Earth in the Solar System National Math Education Standards: NM.5-8.5 Number Relationships NM.5-8.13 Measurement Vocabulary: Astronomical Unit - 1AU = approximately 150 million kilometers (93 million miles) (149,597,870,700 kilometers or 92,955,807,238 miles to be exact!) Activity: We will construct a distance model of the solar system to scale, using colored beads as planets. The chart below shows the planets and asteroid belt in order along with their distance from the sun in astronomical units. First, complete the chart by multiplying each AU distance by our scale factor of 10 centimeters per astronomical unit. Next, use the new distance to construct a scale model of our solar system. Start your model by cutting a 4.5 meter piece of string (5.0 meters if you are doing the Pluto extension). Use the distances in centimeters that you have calculated in the chart below to measure the distance from the sun on the string to the appropriate planet and tie the colored bead in place. When you are finished, wrap your string solar system around the cardboard holder. Note that the bead colors are rough approximations of the colors of the planets and the sun, ...

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