USA-AMC_12-AHSME-2013

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2013年AMC_12真题(A)

USA AMC/AHSME 2013 A
1. Square ABCD has side length 10. Point E is on BC , and the area of △ ABE is 40. What is BE? (A)4 (B)5 (C)6 (D)7 (E)8
2. A softball team played ten games, scoring 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 runs. They lost by one run in exactly five games. In each of the other games, they scored twice as many runs as their opponent. How many total runs did their opponents score? (A) 35 (B) 40 (C) 45 (D) 50 (E) 55
2 2 y , what is xy? x y
8. Given that x and y are distinct nonzero real numbers such that x (A)
1 4
(B)
1 2
(C) 1
(D) 2
(E) 4
9. In △ABC, AB = AC = 28 and BC = 20. Points D, E, and F are on sides AB, BC , and
15. Rabbits Peter and Pauline have three offspringFlopsie, Mopsie, and Cotton-tail. These five rabbits are to be distributed to four different a parent and a child. It is not required that every store gets a rabbit. In how many different ways can this be done? (A) 96 (B) 108 (C) 156 (D) 204 (E) 372

Capsense 设计指南

Document number: 001-78613 Rev **
赛普拉斯半导体 198 Champion Court San Jose, CA 95134-1709 电话（美国）：880.858.1810 电话（国际）：4 赛普拉斯半导体公司，2010-2012。此处所包含的信息可能会随时更改，恕不另行通知。除赛普拉斯产品的内嵌电路之外，赛普拉斯半导体公司不对任何其他电路的使用承担任何责任。也不根据专利或其他权利以明示或暗示的方式授予任何许可。除非与赛普拉斯签订明确的书面协议，否则赛普拉斯产品不保证能够用于或适用于医疗、生命支持、救生、关键控制或安全应用领域。此外，对于可能发生运转异常和故障并对用户造成严重伤害的生命支持系统，赛普拉斯不授权将其产品用作此类系统的关键组件。若将赛普拉斯产品用于生命支持系统中，则表示制造商将承担因此类使用而招致的所有风险，并确保赛普拉斯免于因此而受到任何指控。商标 PSoC Designer™、Programmable System-on-Chip™ 和 SmartSense™ 是赛普拉斯半导体公司的商标，PSoC® 和 CapSense® 是赛普拉斯半导体公司的注册商标。此处引用的所有其他商标或注册商标归其各自所有者所有。源代码所有源代码（软件和/或固件）均归赛普拉斯半导体公司（赛普拉斯）所有，并受全球专利法规（美国和美国以外的专利法规）、美国版权法以及国际条约规定的保护和约束。赛普拉斯据此向获许可者授予适用于个人的、非独占性、不可转让的许可，用以复制、使用、修改、创建赛普拉斯源代码的派生作品、编译赛普拉斯源代码和派生作品，并且其目的只能是创建自定义软件和/或固件，以支持获许可者仅将其获得的产品依照适用协议规定的方式与赛普拉斯集成电路配合使用。除上述指定的用途之外，未经赛普拉斯的明确书面许可，不得对此类源代码进行任何复制、修改、转换、编译或演示。免责声明赛普拉斯不针对此材料提供任何类型的明示或暗示保证，包括（但不仅限于）针对特定用途的适销性和适用性的暗示保证。赛普拉斯保留在不做出通知的情况下对此处所述材料进行更改的权利。赛普拉斯不对此处所述之任何产品或电路的应用或使用承担任何责任。对于可能发生运转异常和故障并对用户造成严重伤害的生命支持系统，赛普拉斯不授权将其产品用作此类系统的关键组件。若将赛普拉斯产品用于生命支持系统中，则表示制造商将承担因此类使用而招致的所有风险，并确保赛普拉斯免于因此而受到任何指控。产品使用可能受适用的赛普拉斯软件许可协议限制。

AMC1203中文资料

Copyright © 2008, Texas Instruments Incorporated
PRODUCTION DATA information is current as of publication date. Products conform to specifications per the terms of the Texas Instruments standard warranty. Production processing does not necessarily include testing of all parameters.
ABSOLUTE MAXIMUM RATINGS (1)
Over operating free-air temperature range, unless otherwise noted.
PARAMETER Supply voltage, VDD1 to GND1 or VDD2 to GND2 Analog input voltage at VIN+, VIN– Input current to any pin except supply pins Continuous total power dissipation Maximum junction temperature, TJ Human body model (HBM) JEDEC standard 22, test method A114-C.01 Electrostatic discharge (ESD), all pins Charged device Model (CDM) JEDEC standard 22, test method C101 Machine Model (MM) JEDEC standard 22, test method A115A (1) AMC1203 –0.3 to +6 GND1 – 0.3 to VDD1 + 0.3 ±10 +150 ±3000 ±1500 ±200 UNIT V V mA °C V V V

美国 AMC 伺服驱动器

连续电流 15 25
12.5 25
注意： 1、峰值电流的最大持续时间约为 2 秒。 2、最小电感适用于线电压远低于最高电压的情况，若不能满足条件可使用外部电感。 3、环路增益、限制电流、输入增益和零漂都能够使用内部电位器进行调节。
深圳市雷赛科技有限公司地址：深圳市南山区登良路 25 号天安南油工业区二栋三楼
VAC 30-130 30-130
峰值电流 16 30
连续电流 6
12.5 15 25 60 10
12.5 25 50
连续电流 8 15
无刷±10V 模拟量 AC 驱动器
型号 B25A20AC BE25A20AC BX25A20AC B30A40AC B40A40AC B60A40AC B100A40AC
BD30A8 BDC30A8
20-80 20-80
BD25A20 BD25A20I BDC40A20
40-190 40-190 60-190
峰值电流 15 30 30 25 25 40
连续电流 7.5 15 15 12.5 12.5 20
无刷 PWM 输入 AC 驱动器
型号 BD25A20AC
VAC 45-140
VDC 20-80 20-80 20-80 20-80 20-80 20-80 20-80 40-190 40-190 60-200 40-190 40-190 40-190 60-400 60-400 60-400 60-400
峰值电流 15 15 15 30 30 30 100 25 25 25 40 40 40 30 40 60 100
AZX 系列
描述
单
位
DC 输入电压范围 VDC
DC 母线过压限制 VDC

USA-AMC_12-AHSME-2010-44

2010A1What is(20−(2010−201))+(2010−(201−20))?(A)−4020(B)0(C)40(D)401(E)40202A ferry boat shuttles tourists to an island every hour starting at10AM until its last trip, which starts at3PM.One day the boat captain notes that on the10AM trip there were 100tourists on the ferry boat,and that on each successive trip,the number of tourists was1 fewer than on the previous trip.How many tourists did the ferry take to the island that day?(A)585(B)594(C)672(D)679(E)6943Rectangle ABCD,pictured below,shares50%of its area with square EF GH.Square EF GHshares20%of its area with rectangle ABCD.What is ABAD?A BCDEH(A)4(B)5(C)6(D)8(E)104If x<0,then which of the following must be positive?(A)x|x|(B)−x2(C)−2x(D)−x−1(E)3√x5Halfway through a100-shot archery tournament,Chelsea leads by50points.For each shota bullseye scores10points,with other possible scores being8,4,2,0points.Chelsea alwaysscores at least4points on each shot.If Chelsea’s next n shots are bulleyes she will be guaranteed victory.What is the minimum value for n?(A)38(B)40(C)42(D)44(E)466A palindrome,such as83438,is a number that remains the same when its digits are reversed.The numbers x and x+32are three-digit and four-digit palindromes,respectively.What is the sum of the digits of x?(A)20(B)21(C)22(D)23(E)24Thisﬁle was downloaded from the AoPS Math Olympiad Resources Page Page120107Logan is constructing a scaled model of his town.The city’s water tower stands40meters high,and the top portion is a sphere that holds100,000liters of water.Logan’s miniature water tower holds0.1liters.How tall,in meters,should Logan make his tower?(A)0.04(B)0.4π(C)0.4(D)4π(E)48Triangle ABC has AB=2·AC.Let D and E be on AB and BC,respectively,such that ∠BAE=∠ACD.Let F be the intersection of segments AE and CD,and suppose that CF E is equilateral.What is∠ACB?(A)60◦(B)75◦(C)90◦(D)105◦(E)120◦9A solid cube has side length3inches.A2-inch by2-inch square hole is cut into the center of each face.The edges of each cut are parallel to the edges of the cube,and each hole goes all the way through the cube.What is the volume,in cubic inches,of the remaining solid?(A)7(B)8(C)10(D)12(E)1510Theﬁrst four terms of an arithmetic sequence are p,9,3p−q,and3p+q.What is the2010th term of the sequence?(A)8041(B)8043(C)8045(D)8047(E)804911The solution of the equation7x+7=8x can be expressed in the form x=log b77.What is b?(A)715(B)78(C)87(D)158(E)15712In a magical swamp there are two species of talking amphibians:toads,whose statements are always true,and frogs,whose statements are always false.Four amphibians,Brian,Chris, LeRoy,and Mike live together in the swamp,and they make the following statements:Brian:”Mike and I are diﬀerent species.”Chris:”LeRoy is a frog.”LeRoy:”Chris is a frog.”Mike:”Of the four of us,at least two are toads.”How many of these amphibians are frogs?(A)0(B)1(C)2(D)3(E)413For how many integer values of k do the graphs of x2+y2=k2and xy=k not intersect?(A)0(B)1(C)2(D)4(E)814Nondegenerate ABC has integer side lengths,BD is an angle bisector,AD=3,and DC=8.What is the smallest possible value of the perimeter?(A)30(B)33(C)35(D)36(E)37201015A coin is altered so that the probability that it lands on heads is less than 12and when thecoin is ﬂipped four times,the probability of an equal number of heads and tails is 16.What is the probability that the coin lands on heads?(A)√15−36(B)6−√6√6+212(C)√2−12(D)3−√36(E)√3−1216Bernardo randomly picks 3distinct numbers from the set {1,2,3,4,5,6,7,8,9}and arrangesthem in descending order to form a 3-digit number.Silvia randomly picks 3distinct numbers from the set {1,2,3,4,5,6,7,8}and also arranges them in descending order to form a 3-digit number.What is the probability that Bernardo’s number is larger than Silvia’s number?(A)4772(B)3756(C)23(D)4972(E)395617Equiangular hexagon ABCDEF has side lengths AB =CD =EF =1and BC =DE =F A =r .The area of ACE is 70%of the area of the hexagon.What is the sum of all possible values of r ?(A)4√33(B)103(C)4(D)174(E)618A 16-step path is to go from (−4,−4)to (4,4)with each step increasing either the x -coordinateor the y -coordinate by 1.How many such paths stay outside or on the boundary of the square −2≤x ≤2,−2≤y ≤2at each step?(A)92(B)144(C)1568(D)1698(E)12,80019Each of 2010boxes in a line contains a single red marble,and for 1≤k ≤2010,the box in thekth position also contains k white marbles.Isabella begins at the ﬁrst box and successively draws a single marble at random from each box,in order.She stops when she ﬁrst draws a red marble.Let P (n )be the probability that Isabella stops after drawing exactly n marbles.What is the smallest value of n for which P (n )<12010?(A)45(B)63(C)64(D)201(E)100520Arithmetic sequences (a n )and (b n )have integer terms with a 1=b 1=1<a 2≤b 2anda nb n =2010for some n .What is the largest possible value of n ?(A)2(B)3(C)8(D)288(E)200921The graph of y =x 6−10x 5+29x 4−4x 3+ax 2lies above the line y =bx +c except at threevalues of x ,where the graph and the line intersect.What is the largest of those values?(A)4(B)5(C)6(D)7(E)822What is the minimum value of f (x )=|x −1|+|2x −1|+|3x −1|+···+|119x −1|?(A)49(B)50(C)51(D)52(E)53201023The number obtained from the last two nonzero digits of90!is equal to n.What is n?(A)12(B)32(C)48(D)52(E)6824Let f(x)=log10(sin(πx)·sin(2πx)·sin(3πx)···sin(8πx)).The intersection of the domain of f(x)with the interval[0,1]is a union of n disjoint open intervals.What is n?(A)2(B)12(C)18(D)22(E)3625Two quadrilaterals are considered the same if one can be obtained from the other by a rotation and a translation.How many diﬀerent convex cyclic quadrilaterals are there with integer sides and perimeter equal to32?(A)560(B)564(C)568(D)1498(E)22552010B1Makayla attended two meetings during her9-hour work day.Theﬁrst meeting took45 minutes and the second meeting took twice as long.What percent of her work day was spent attending meetings?(A)15(B)20(C)25(D)30(E)352A big L is formed as shown.What is its area?5228(A)22(B)24(C)26(D)28(E)303A ticket to a school play costs x dollars,where x is a whole number.A group of9th graders buys tickets costing a total of$48,and a group of10th graders buys tickets costing a total of $64.How many values of x are possible?(A)1(B)2(C)3(D)4(E)54A month with31days has the same number of Mondays and Wednesdays.How many of the seven days of the week could be theﬁrst day of this month?(A)2(B)3(C)4(D)5(E)65Lucky Larry’s teacher asked him to substitute numbers for a,b,c,d,and e in the expression a−(b−(c−(d+e)))and evaluate the rry ignored the parentheses but added and subtracted correctly and obtained the correct result by coincedence.The numbers Larry substituted for a,b,c,and d were1,2,3,and4,respectively.What number did Larry substitute for e?(A)−5(B)−3(C)0(D)3(E)520106At the beginning of the school year,50%of all students in Mr.Well’s math class answered ”Yes”to the question ”Do you love math”,and 50%answered ”No.”At the end of the school year,70%answered ”Yes”and 30%answered ”No.”Altogether,x %of the students gave a diﬀerent answer at the beginning and end of the school year.What is the diﬀerence between the maximum and the minimum possible values of x ?(A)0(B)20(C)40(D)60(E)807Shelby drives her scooter at a speed of 30miles per hour if it is not raining,and 20miles per hour if it is raining.Today she drove in the sun in the morning and in the rain in the evening,for a total of 16miles in 40minutes.How many minutes did she drive in the rain?(A)18(B)21(C)24(D)27(E)308Every high school in the city of Euclid sent a team of 3students to a math contest.Each participant in the contest received a diﬀerent score.Andrea’s score was the median among all students,and hers was the highest score on her team.Andrea’s teammates Beth and Carla placed 37th and 64th,respectively.How many schools are in the city?(A)22(B)23(C)24(D)25(E)269Let n be the smallest positive integer such that n is divisible by 20,n 2is a perfect cube,and n 3is a perfect square.What is the number of digits of n ?(A)3(B)4(C)5(D)6(E)710The average of the numbers 1,2,3,...,98,99,and x is 100x .What is x ?(A)49101(B)50101(C)12(D)51101(E)509911A palindrome between 1000and 10,000is chosen at random.What is the probability that itis divisible by 7?(A)110(B)19(C)17(D)16(E)1512For what value of x doeslog √2√x +log 2x +log 4(x 2)+log 8(x 3)+log 16(x 4)=40?(A)8(B)16(C)32(D)256(E)102413In ABC,cos(2A −B )+sin(A +B )=2and AB =4.What is BC ?(A)√2(B)√3(C)2(D)2√2(E)2√314Let a ,b ,c ,d ,and e be positive integers with a +b +c +d +e =2010,and let M be thelargest of the sums a +b ,b +c ,c +d ,and d +e .What is the smallest possible value of M ?(A)670(B)671(C)802(D)803(E)804201015For how many ordered triples (x,y,z )of nonnegative integers less than 20are there exactly two distinct elements in the set {i x ,(1+i )y ,z },where i =√−1?(A)149(B)205(C)215(D)225(E)23516Positive integers a,b,and c are randomly and independently selected with replacement fromthe set {1,2,3,...,2010}.What is the probability that abc +ab +a is divisible by 3?(A)13(B)2981(C)3181(D)1127(E)132717The entries in a 3×3array include all the digits from 1through 9,arranged so that theentries in every row and column are in increasing order.How many such arrays are there?(A)18(B)24(C)36(D)42(E)6018A frog makes 3jumps,each exactly 1meter long.The directions of the jumps are chosenindependently and at random.What is the probability the frog’s ﬁnal position is no more than 1meter from its starting position?(A)16(B)15(C)14(D)13(E)1219A high school basketball game between the Raiders and Wildcats was tied at the end of theﬁrst quarter.The number of points scored by the Raiders in each of the four quarters formed an increasing geometric sequence,and the number of points scored by the Wildcats in each of the four quarters formed an increasing arithmetic sequence.At the end of the fourth quarter,the Raiders had won by one point.Neither team scored more than 100points.What was the total number of points scored by the two teams in the ﬁrst half?(A)30(B)31(C)32(D)33(E)3420A geometric sequence (a n )has a 1=sin x,a 2=cos x,and a 3=tan x for some real numberx .For what value of n does a n =1+cos x ?(A)4(B)5(C)6(D)7(E)821Let a >0,and let P (x )be a polynomial with integer coeﬃcients such thatP (1)=P (3)=P (5)=P (7)=a ,andP (2)=P (4)=P (6)=P (8)=−a .What is the smallest possible value of a ?(A)105(B)315(C)945(D)7!(E)8!22Let ABCD be a cyclic quadrilateral.The side lengths of ABCD are distinct integers lessthan 15such that BC ·CD =AB ·DA .What is the largest possible value of BD ?(A) 3252(B)√185(C) 3892(D) 4252(E) 5332201023Monic quadratic polynomials P(x)and Q(x)have the property that P(Q(x))has zeroes at x=−23,−21,−17,and−15,and Q(P(x))has zeroes at x=−59,−57,−51,and−49.What is the sum of the minimum values of P(x)and Q(x)?(A)-100(B)-82(C)-73(D)-64(E)024The set of real numbers x for which1x−2009+1x−2010+1x−2011≥1is the union of intervals of the form a<x≤b.What is the sum of the lengths of these intervals?(A)1003335(B)1004335(C)3(D)403134(E)2026725For every integer n≥2,let pow(n)be the largest power of the largest prime that divides n.For example pow(144)=pow(24·32)=32.What is the largest integer m such that2010m divides5300n=2pow(n)?(A)74(B)75(C)76(D)77(E)78。

迈思肯(Microscan)2013最新产品手册

无论是生产个人消费类电子产品，还是医疗诊断设备，抑或是汽车零部件，迈思肯的解决方案都有助于实现多种关键性应用，例如质量控制，生产层面的在制品监测，引导货品的传送，零部件追溯，归类和批次跟踪等。
精确性迈思肯产品是高精密仪器。在各种任务中，无论是高速条码采集，还是利用机器视觉进行高精度导引，定位和坐标校正，迈思肯的产品都能进行复杂的数据采集，性能可靠。
联系信息
24
亚太区总部
3 ©2013 Microscan Systems, Inc.
数据采集技术
自动识别和符号体系
线性或一维条形码自20世纪70年代开始就已投入商业使用，是针对自动识别零件跟踪应用最为广泛的一类符号体系。如今越来越多的生产商使用二维码，例如Data Matrix 等，二维码可更灵活的进行打码并且具备更大的数据容量。众多行业明确规定了所必须使用的具体码制并规定了相关码制质量。
技术先导迈思肯的技术创新历史非常悠久。我们在20世纪80年代早期就发明了第一台激光二极管条形码扫描器以及Data Matrix二维码，在自动识别（Auto ID）行业掀起一场革命。我们凭借高级视觉和光源产品在机器视觉行业遥遥领先。
如今，迈思肯在机器视觉和自动识别领域不断开发新产品，仍然是公认的技术领先者。
检测 – 颜色或缺陷检测 – 零部件有/无检测 – 目标定位及引导
测量和校准 – 尺寸测量和级别设定 – 预配置测量，如交叉线或点对点距离
机器手引导 – 输出坐标以引导机器或工具进行精准定位
高速、复杂检测
完整性检查
形状检测
模式比较
测量
6
位置/角度检测
读取OCR
©2013 Microscan Systems, Inc.

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暖的手融进在民生的行列中心集合起来用热情们职责的神圣
热的爱通约在崇高的使命中来的民生人用激情们事业的光荣
来吧来吧手拉手起生命的彩虹地之间民生为先入我的忠诚地之间心连心起不变的承诺地之间民生为先写爱的永恒司源自训对待工作，务实高效

MSA2000简易管理手册v1.1_20140315

Created by Jeff，2014/3/15
Front panel components............................................................................. 23 Disk drive bay numbers .............................................................................. 24 Rear panel view – controller module .......................................................... 24 Rear panel components.............................................................................. 25 P2000 6Gb 3.5 12-drive enclosure .............................................................. 25 MSA2000 3Gb 3.5 12-drive enclosure ......................................................... 26 P2000G3 iSCSI .................................................................................................................27 Front panel components............................................................................. 27 Disk drive bay numbers .............................................................................. 28 Rear panel views – controller modules ....................................................... 28 Rear panel components.............................................................................. 29 P2000 6Gb 3.5 12-drive enclosure .............................................................. 30 MSA2000 3Gb 3.5 12-drive enclosure ......................................................... 30 P2000G3 SAS...................................................................................................................31 Front panel components............................................................................. 31 Disk drive bay numbers .............................................................................. 32 Rear panel view – controller module .......................................................... 32 Rear panel components.............................................................................. 33 P2000 6Gb 3.5 12-drive enclosure .............................................................. 33 MSA2000 3Gb 3.5 12-drive enclosure ......................................................... 34 2. MSA2000 管理方式............................................................................................................35

全美数学竞赛USA-AMC_12-AHSME-2009-44

2009A1Kim’sﬂight took oﬀfrom Newark at10:34AM and landed in Miami at1:18PM.Both cities are in the same time zone.If herﬂight took h hours and m minutes,with0<m<60,what is h+m?(A)46(B)47(C)50(D)53(E)542Which of the following is equal to1+11+11+1?(A)54(B)32(C)53(D)2(E)33What number is one third of the way from14to34?(A)13(B)512(C)12(D)712(E)234Four coins are picked out of a piggy bank that contains a collection of pennies,nickels,dimes, and quarters.Which of the following could not be the total value of the four coins,in cents?(A)15(B)25(C)35(D)45(E)555One dimension of a cube is increased by1,another is decreased by1,and the third is left unchanged.The volume of the new rectangular solid is5less than that of the cube.What was the volume of the cube?(A)8(B)27(C)64(D)125(E)2166Suppose that P=2m and Q=3n.Which of the following is equal to12mn for every pair of integers(m,n)?(A)P2Q(B)P n Q m(C)P n Q2m(D)P2m Q n(E)P2n Q m7Theﬁrst three terms of an arithmetic sequence are2x−3,5x−11,and3x+1respectively.The n th term of the sequence is2009.What is n?(A)255(B)502(C)1004(D)1506(E)80378Four congruent rectangles are placed as shown.The area of the outer square is4times that of the inner square.What is the ratio of the length of the longer side of each rectangle to the length of its shorter side?Thisﬁle was downloaded from the AoPS Math Olympiad Resources Page Page12009(A)3(B)√10(C)2+√2(D)2√3(E)49Suppose that f(x+3)=3x2+7x+4and f(x)=ax2+bx+c.What is a+b+c?(A)−1(B)0(C)1(D)2(E)310In quadrilateral ABCD,AB=5,BC=17,CD=5,DA=9,and BD is an integer.What is BD?DC BA(A)11(B)12(C)13(D)14(E)1511Theﬁgures F1,F2,F3,and F4shown are theﬁrst in a sequence ofﬁgures.For n≥3,F n is constructed from F n−1by surrounding it with a square and placing one more diamond on each side of the new square than F n−1had on each side of its outside square.For example,ﬁgure F3has13diamonds.How many diamonds are there inﬁgure F20?F1F2F34(A)401(B)485(C)585(D)626(E)76112How many positive integers less than1000are6times the sum of their digits?(A)0(B)1(C)2(D)4(E)12200913A ship sails 10miles in a straight line from A to B ,turns through an angle between 45◦and 60◦,and then sails another 20miles to C .Let AC be measured in miles.Which of the following intervals contains AC 2?1020A BC(A)[400,500](B)[500,600](C)[600,700](D)[700,800](E)[800,900]14A triangle has vertices (0,0),(1,1),and (6m,0),and the line y =mx divides the triangleinto two triangles of equal area.What is the sum of all possible values of m ?(A)−13(B)−16(C)16(D)13(E)1215For what value of n is i +2i 2+3i 3+···+ni n =48+49i ?Note:here i =√−1.(A)24(B)48(C)49(D)97(E)9816A circle with center C is tangent to the positive x and y -axes and externally tangent to thecircle centered at (3,0)with radius 1.What is the sum of all possible radii of the circle with center C ?(A)3(B)4(C)6(D)8(E)917Let a +ar 1+ar 21+ar 31+···and a +ar 2+ar 22+ar 32+···be two diﬀerent inﬁnite geometric series of positive numbers with the same ﬁrst term.The sum of the ﬁrst series is r 1,and thesum of the second series is r 2.What is r 1+r 2?(A)0(B)12(C)1(D)1+√52(E)218For k >0,let I k =10...064,where there are k zeros between the 1and the 6.Let N (k )bethe number of factors of 2in the prime factorization of I k .What is the maximum value of N (k )?(A)6(B)7(C)8(D)9(E)10200919Andrea inscribed a circle inside a regular pentagon,circumscribed a circle around the pen-tagon,and calculated the area of the region between the two circles.Bethany did the same with a regular heptagon (7sides).The areas of the two regions were A and B ,respectively.Each polygon had a side length of 2.Which of the following is true?(A)A =2549B (B)A =57B (C)A =B (D)A =75B (E)A =4925B 20Convex quadrilateral ABCD has AB =9and CD =12.Diagonals AC and BD intersect atE ,AC =14,and AED and BEC have equal areas.What is AE ?(A)92(B)5011(C)214(D)173(E)621Let p (x )=x 3+ax 2+bx +c ,where a ,b ,and c are complex numbers.Suppose thatp (2009+9002πi )=p (2009)=p (9002)=0What is the number of nonreal zeros of x 12+ax 8+bx 4+c ?(A)4(B)6(C)8(D)10(E)1222A regular octahedron has side length 1.A plane parallel to two of its opposite faces cutsthe octahedron into the two congruent solids.The polygon formed by the intersection of the plane and the octahedron has area a √b c ,where a ,b ,and c are positive integers,a and c are relatively prime,and b is not divisible by the square of any prime.What is a +b +c ?(A)10(B)11(C)12(D)13(E)1423Functions f and g are quadratic,g (x )=−f (100−x ),and the graph of g contains the vertexof the graph of f .The four x -intercepts on the two graphs have x -coordinates x 1,x 2,x 3,and x 4,in increasing order,and x 3−x 2=150.The value of x 4−x 1is m +n √p ,where m ,n ,and p are positive integers,and p is not divisible by the square of any prime.What is m +n +p ?(A)602(B)652(C)702(D)752(E)80224The tower function of twos is deﬁned recursively as follows:T (1)=2and T (n +1)=2T (n )for n ≥1.Let A =(T (2009))T (2009)and B =(T (2009))A .What is the largest integer k such thatlog 2log 2log 2...log 2B k timesis deﬁned?(A)2009(B)2010(C)2011(D)2012(E)201325The ﬁrst two terms of a sequence are a 1=1and a 2=1√3.For n ≥1,a n +2=a n +a n +11−a n a n +1.2009What is|a2009|? (A)0(B)2−√3(C)1√3(D)1(E)2+√32009B1Each morning of herﬁve-day workweek,Jane bought either a50-cent muﬃn or a75-cent bagel.Her total cost for the week was a whole number of dollars.How many bagels did she buy?(A)1(B)2(C)3(D)4(E)52Paula the painter had just enough paint for30identically sized rooms.Unfortunately,on the way to work,three cans of paint fell of her truck,so she had only enough paint for25rooms.How many cans of paint did she use for the25rooms?(A)10(B)12(C)15(D)18(E)253Twenty percent less than60is one-third more than what number?(A)16(B)30(C)32(D)36(E)484A rectangular yard contains twoﬂower beds in the shape of congruent isosceles right triangles.THe remainder of the yard has a trapezoidal shape,as shown.The parallel sides of the trapezoid have lengths15and25meters.What fraction of the yard is occupied by theﬂower beds?(A)18(B)16(C)15(D)14(E)135Kiana has two older twin brothers.The product of their ages is128.What is the sum of their three ages?(A)10(B)12(C)16(D)18(E)246By inserting parentheses,it is possible to give the expression2×3+4×5several values.How many diﬀerent values can be obtained?(A)2(B)3(C)4(D)5(E)620097In a certain year the price of gasoline rose by20%during January,fell by20%during February, rose by25%during March,and fell by x%during April.The price of gasoline at the end of April was the same as it had been at the beginning of January.To the nearest integer,what is x?(A)12(B)17(C)20(D)25(E)358When a bucket is two-thirds full of water,the bucket and water weigh a kilograms.When the bucket is one-half full of water the total weight is b kilograms.In terms of a and b,what is the total weight in kilograms when the bucket is full of water?(A)23a+13b(B)32a−12b(C)32a+b(D)32a+2b(E)3a−2b9Triangle ABC has vertices A=(3,0),B=(0,3),and C,where C is on the line x+y=7.What is the area of ABC?(A)6(B)8(C)10(D)12(E)1410A particular12-hour digital clock displays the hour and minute of a day.Unfortunately, whenever it is supposed to display a1,it mistakenly displays a9.For example,when it is 1:16PM the clock incorrectly shows9:96PM.What fraction of the day will the clock show the correct time?(A)12(B)58(C)34(D)56(E)91011On Monday,Millie puts a quart of seeds,25%of which are millet,into a bird feeder.On each successive day she adds another quart of the same mix of seeds without removing any seeds that are left.Each day the birds eat only25%of the millet in the feeder,but they eat all of the other seeds.On which day,just after Millie has placed the seeds,will the birdsﬁnd that more than half the seeds in the feeder are millet?(A)Tuesday(B)Wednesday(C)Thursday(D)Friday(E)Saturday12Theﬁfth and eighth terms of a geometric sequence of real numbers are7!and8!respectively.What is theﬁrst term?(A)60(B)75(C)120(D)225(E)31513Triangle ABC has AB=13and AC=15,and the altitude to BC has length12.What is the sum of the two possible values of BC?(A)15(B)16(C)17(D)18(E)1914Five unit squares are arranged in the coordinate plane as shown,with the lower left corner at the origin.The slanted line,extending from(a,0)to(3,3),divides the entire region into two regions of equal area.What is a?2009(A)12(B)35(C)23(D)34(E)4515Assume0<r<3.Below areﬁve equations for x.Which equation has the largest solutionx?(A)3(1+r)x=7(B)3(1+r/10)x=7(C)3(1+2r)x=7(D)3(1+√r)x=7(E)3(1+1/r)x=716Trapezoid ABCD has AD BC,BD=1,∠DBA=23◦,and∠BDC=46◦.The ratio BC:AD is9:5.What is CD?(A)79(B)45(C)1315(D)89(E)141517Each face of a cube is given a single narrow stripe painted from the center of one edge to the center of its opposite edge.The choice of the edge pairing is made at random and independently for each face.What is the probability that there is a continuous stripe encircling the cube?(A)18(B)316(C)14(D)38(E)1218Rachel and Robert run on a circular track.Rachel runs counterclockwise and completes a lap every90seconds,and Robert runs clockwise and completes a lap every80seconds.Both start from the start line at the same time.At some random time between10minutes and 11minutes after they begin to run,a photographer standing inside the track takes a picture that shows one-fourth of the track,centered on the starting line.What is the probability that both Rachel and Robert are in the picture?(A)116(B)18(C)316(D)14(E)51619For each positive integer n,let f(n)=n4−360n2+400.What is the sum of all values of f(n)that are prime numbers?2009(A)794(B)796(C)798(D)800(E)80220A convex polyhedron Q has vertices V 1,V 2,...,V n ,and 100edges.The polyhedron is cut byplanes P 1,P 2,...,P n in such a way that plane P k cuts only those edges that meet at vertex V k .In addition,no two planes intersect inside or on Q .The cuts produce n pyramids and a new polyhedron R .How many edges does R have?(A)200(B)2n (C)300(D)400(E)4n 21Ten women sit in 10seats in a line.All of the 10get up and then reseat themselves usingall 10seats,each sitting in the seat she was in before or a seat next to the one she occupied before.In how many ways can the women be reseated?(A)89(B)90(C)120(D)210(E)223822Parallelogram ABCD has area 1,000,000.Vertex A is at (0,0)and all other vertices are inthe ﬁrst quadrant.Vertices B and D are lattice points on the lines y =x and y =kx for some integer k >1,respectively.How many such parallelograms are there?(A)49(B)720(C)784(D)2009(E)204823A region S in the complex plane is deﬁned byS ={x +iy :−1≤x ≤1,−1≤y ≤1}.A complex number z =x +iy is chosen uniformly at random from S .What is the probability that 34+34i z is also in S ?(A)12(B)23(C)34(D)79(E)7824For how many values of x in [0,π]is sin −1(sin 6x )=cos −1(cos x )?Note:The functionssin −1=arcsin and cos −1=arccos denote inverse trigonometric functions.(A)3(B)4(C)5(D)6(E)725The set G is deﬁned by the points (x,y )with integer coordinates,3≤|x |≤7,3≤|y |≤7.How many squares of side at least 6have their four vertices in G ?2009(A)125(B)150(C)175(D)200(E)225。

2014年AMC_12真题(A)

3,
3
7. The first three terms of a geometric progression are term? (A) 1 (B)
7
3 , and
6
3 . What is the fourth
3
(C)
8
3
(D)
9
3
(E)
10
3
8. A customer who intends to purchase an appliance has three coupons, only one of which may be used: Coupon 1: 10% off the listed price if the listed price is at least $50 Coupon 2: $20 off the listed price if the listed price is at least $100 Coup on 3: 18% off the amount by which the listed price exceeds $100 For which of the following listed prices will coup on 1 offer a greater price reduction than either coup on 2 or coup on 3? (A) $179.95 (B) $199.95 (C) $219.95 (D) $239.95 (E) $259.95
(A) 2100
(B) 2220
(C) 3000
(D) 3120
(E) 25
14. Let a < b < c be three integers such that a, b, c is an arithmetic progression and a, c, b is a geometric progression. What is the smallest possible value of c? (A) − 2 (B) 1 (C) 2 (D) 4 (E) 6

UPC功能说明书

Standard Features:•Advanced Linear Amplifiers Provide Very Low Voltage Distortion, no Switching Noise, Fast Voltage and Current Slew Rates, Exceptionally Low Output Impedance and High Peak Current Capability• 1, 2, or 3 Phase Output Form selectable from front panel or bus command•20 to 5,000 Hz. Full Power Bandwidth Operation – 5Hz to 50KHz small signal bandwidth, 3dB at 10% of full voltage• Precision Voltage Programming – 0.05% with Continuous Self-Calibration (CSC) engaged • True-RMS Metering of Volts, Amps, and Power • GPIB (IEEE-488.2) or RS-232 Interface • Waveform Library – Arbitrary Waveform Generator• Up to 99 Programs with Associated Transients for Static and Dynamic Test Applications •UPC Studio Software SuiteAvailable Options:• Programmable Output Impedance• Harmonic Analysis and Waveform Synthesis • Peak Inrush Capture and Waveform Analysis (Available on models with UPC3 controller)•UPC Test Manager SoftwareUPC Manager Software SuiteMaster the Power of the Wave!UPC Manager Software gives you the tools neces-sary to quickly and easily operate your AC Power Source. With our graphical interface control all areas of your AC Power Source testing with simple presets, user prompts, test sequences, test plans and custom reports.Model 312AMXFREQUENCY CONVERSION R & D MANUFACTURING AEROSPACE MILITARYCUSTOM1, 2, or 1,200VA 20-5,000 HzModel 312AMXAs a member of Pacific Power’s AMX-Series popular family of high performance Linear AC Power Sources, the 312AMX offers the same low output voltage noise and distortion, ease of installation, and high AC waveform fidelity as found in all of Pacific Power’s Linear AC Power Sources. Control and operational features provide a high degree of versatility and ease of use for applications ranging from simple,manually controlled frequency conversion to harmonic testing and sophisticated programmable transient simulation.AC TEST POWERAll 312AMX models are equipped with a powerful micro-controller with the ability to operate as a fully integrated test system. This enables a variety of power conditions and transients to be applied to the device under test while metering and analyzing all output performance parameters. For higher power requirements, refer to the AMX & ASX series catalog.FREQUENCY/ VOLTAGE CONVERSIONThe 312AMX is an excellent source of stable AC Voltage over the frequency range of 20 to 5,000 Hz when using the high-end UPC-32 controller. Also available in 1,200 Hz maximum output frequency when using UPC3 or Manual controller. The output frequency is quartz-crystal stabilized. Output voltages up to 300V L-L in split phase mode and 260V L-L in three phase mode are available on the 312AMX model.PHASE CONVERSIONWith the ability to provide either single or two phase output, the 312AMX is a good choice to convert one-phase line voltage into precisely controlled split (two-phase) or three-phase output power.UPC SERIES CONTROLLERThree controller models are available in both manual and programmable control version. All controllers provide manual operation from the front panel. Programmable Controllers may be operated from the front panel or from a remote interface via RS 232 or GPIB.The Leader in AC Power TechnologyAn early pioneer in the development solid-state power conversion equipment, Pacific Power Source continues to develop, manufacture, and market both linear and high-performance PWM AC Power Sources. Pacific Power Source’s reputation as a market and technology leader is best demonstrated by its continuing investments in both research and development and world-wide customer support. With corporate owned offices in the United States, France, the United Kingdom, and China, local personalized support is always available.1Ø42Ø43Ø40-150V L-N 0-300V L-L0-150V L-N / 0-260V L-LNOTES:1. Rated output power is based on a combination of nominal output voltage, rated current and load power factor. Values stated represent the maximum capabilities of a given model (maximum power in split phase (Form2) direct coupled mode is 800VA). Consult factory for assistance in determining specific unit capabilities as they might apply to your application.2. Unit is operable as single phase with dual range capability or 3 phase. Output voltage range and 1/2/3 conversions are selected by front panel or bus commands.3. Vmax is output voltage with nominal input and full rated load applied.4. Available current will vary with output voltage and power factor. Current shown is per phase.Output RatingsThermal and Power Factor Rating CurvesAMX Power Source Specifications (PF = 1.0, V out > 25% F.S.)Input Power Requirements (47-63 Hz)312AMXOutput Frequency Line Regulation Load Regulation Ripple and Noise OUTPUT VOLTAGE-AC VOLTS RMSShort term overloads to 150% are permitted. Operating time before thermal shutdown or circuit breaker trip varies from sec-onds to several minutes depending upon line and temperature conditions.THERMAL RATING -AC CURRENT RMSShort tem overloads to 150% of rated current are permitted.Operating time before thermal shutdown or circuit breaker trip varies from seconds to several minutes depending upon line and temperature conditions.Rated Continuous Load Current as a Function of Ambient Temperature and Power Factor and Output Voltage at Nominal Input Line.The UPC Controlleris a highly versatile one, two, or threephase oscillator/signal generator designed to control any ofPacific Power’s AC Power Sources. Three controller models,UPC-3M, UPC-3, or UPC-32 are offered. To use the full 5KHz power bandwidth of the 312AMX, the UPC-32 controller isrequired.Controller ModelsOutput Control SpecificationsTotal Control, Metering, and Analysis of AC Power- Simple, Intuitive OperationWaveform ControlExternal Inputs/OutputsOutput MeteringUsing the front panel keyboard and display , all controllermodels provide for selection of power source output mode, cou-pling, voltage, and frequency. Selecting the correct UPC controller for a given application varies with your test requirement, desired features, and price.Both the UPC-3 and UPC-32 Controllers are available witheither RS-232 or GPIB remote interface. Commands are structured in accordance with SCPI (Standard Commands for Programmable Instruments).© 2012 Pacific Power Source, Inc. Subject to change without notice. #DS312AMX101217692 Fitch, Irvine, CA 92614 USAPhone: +1 949.251.1800 Fax: +1 949.756.0756 T oll Free: 800.854.2433E-mail:**********************19" (483mm)Ordering InformationAvailable Models312AMX-UPC3M312AMX-UPC3312AMX-UPC32 General/EnvironmentalMechanical SpecificationsSoftware/Firmware OptionsProtection and SafetyOrder Example312AMX-UPC32, V IN : 120VAC • 1,200VA, 3-Phase, AC Power Source with UPC-32 programmable controller.• Standard GPIB Interface•120VAC, 1 Phase Input VoltageTypical Delivery Items• AC Power Source• English Manuals (AC Source and Controller)• UPC Studio Software - (Download)• UPC Interactive LabVIEW TM Libraries (Download)• Compliance Certificate with Test data •CE Conformity Document (CE Models)。

2013年AMC_12真题(B)

8. Line 1 has equation 3x − 2y = 1 and goes through A = (−1, −2). Line 2 has equation y = 1 and meets line 1 at point B. Line 3 has positive slope, goes through point A, and meets 2 at point C. The area of △ABC is 3. What is the slope of 3 ? (A)
USA AMC 12/AHSME 2013 B
1. On a particular January day, the high temperature in Lincoln, Nebraska, was 16 degrees higher than the low temperature, and the average of the high and low temperatures was 3 . In degrees, what was the low temperature in Lincoln that day? (A) − 13 (B) − 8 (C) − 5 (D) 3 (E) 11
16. Let ABCDE be an equiangular convex pentagon of perimeter 1. The pairwise intersections of the lines that extend the side of the pentagon determine a five-pointed star polygon. Let s be the perimeter of the star. What is the difference between the maximum and minimum possible perimeter of s?

北美压铸协会压铸标准(中文)

北美压铸学会压铸件的产品规格标准NADCAProduct Specification Standards for DieCastings铝铝基质复合材料铜镁锌和锌铝合金二零零三年重新修订的最新版本(Revised for 2003)第五次出版(5th Edition)3. 合金数据( Alloy Data )1. 合金的相互对照名称(Alloy Cross Reference Designations)A：类傩于前一项，只是次要成分稍有变化。

B：铝合金压铸件的美联邦规格使用个别合金的铝协会代码名称。

军事代码名称被美联邦的规格所代替。

C：日本规格允许镁最大含量为0.3。

D：日本规格允许锌的最大含量为1.0。

E：德国工业标准DIN 1725规格允许锌最大为1.2，镁最大等于0.5。

F：德国工业标准DIN 1725规格允许镁含量最大为0.3。

G：在DIN 1725中所示的合金成分趋向于“基本的首要金属”而且杂质限制低很难使它直接与美国合金相联系。

注意：这些标准中的部分标准已废弃不用，但出于历史目的仍包括在这里。

最接近的相互参照资料请参考本章结尾有关外国合金代码名称和化学成分的表格。

所示的相互参照代码名称为符合普遍公认原始资料的合金规格。

这些参考资料适用于压铸条件下的金属，不应和金属锭的类傩规格混淆。

栏目中填有“----”表明这种特殊的合金还没有在所给的资料中注册。

UNS ---- 统一编制(Unified Numbering System)；AA ---- 铝协会(Aluminum Association)；FED ----美联邦规格(Federal Specifications)；MIL ---- 军事规格(Military Specifications)；JIS ---- 日本工业标准(Japanese Industrial Standard)；DIN ---- 德国工业标准(German Industrial Standard)；ANSI ---- 美国国家标准学会(American NationalStandards Institute)；SAE ---- 美国汽车工程师学会(Society of Automotive Engineers)；ASTM ---- 美国材料试验学会(American Society for Testing and Materials)；2. 铝合金(Aluminum Alloy)●选择铝合金(Selecting Aluminum Alloys)压铸铝合金的比重大约是2.7克/立方厘米，属于重量较轻的结构金属。

国家半导体产品命名规则

美国国家半导体(NS)产品命名规则概述美国国家半导体在销售的元件上进行标记，以便提供元件标识和制造的追溯性信息。

提供在元件上标记信息的方法取决于元件封装的大小和进行标记的可用区域，以及元件的性质和规格。

这里的信息描述了客户将观察到的大多数元件标记。

特定封装标记按每个元件的部件编号。

下面的链接讨论了常见的标记准则，以帮助了解与右侧示例中相类似的设备标记。

特别代码标准制造信息（第一行）小组件制造信息（第一行）典型元件描述（第二行）其他的信息（第三行和第四行）极小组件标记军用/航空标记强化塑料标记其他标记晶圆制造厂代码装配厂代码制造日期代码裸片批次代码元件系列，产品线和元件类型电气等级信息温度范围代码封装代码ROM 代码标记特别代码元件上的实际标记可能会与网上的定义有出入，以下的特别代码被解译成元件编号的真正代表字元。

美国国家半导体使用一些指定的字母来识别产品，例如“DD” Die Step Rev 会在元件标记中包含一个或两个“C” 或“AA”，另一个例子“BBBBB”则是一个5位数字的裸片检阅号码，它可被解码成“43ABE”的真正字元。

NS = 标准NS商标U = 晶圆制造厂代码Z = 装配厂代码X = 1-日期或 + 号代表“ES” 工程样本XY = 两个位的日期代码XYY = 三个位的日期代码XXYY = 四个位的日期代码TT = 两个位的裸片批次代码E# = 含铅成份种类 * (E0 - E7 per JESD97)BBBBB= 五个位的裸片批次代码DD = 一或两个位的Die Step RevSS = 晶圆筛选代码C = 版权标记M = 印在圈内的M> = ESD标记EP = 强化塑料识别A = 检查批次号码DIE-RUN-## = 10个位的晶圆批次/裸片批次号码I = 微型 SMD 引脚1指示V = 微型 SMD 一个位的裸片批次代码或“+” 号表示為工程样品“ES”* - 假如空间容许标准制造信息（第一行）元件标记的第一行提供如下所示的制造信息。

2017-2020AMC真题和答案

2020 AMC 12A Problems Problem 1Carlos took of a whole pie. Maria took one third of the remainder. What portion of the whole pie was left?Problem 2The acronym AMC is shown in the rectangular grid below with grid linesspaced unit apart. In units, what is the sum of the lengths of the line segments that form the acronym AMCProblem 3A driver travels for hours at miles per hour, during which her cargets miles per gallon of gasoline. She is paid per mile, and her only expense is gasoline at per gallon. What is her net rate of pay, in dollars per hour, after this expense?Problem 4How many -digit positive integers (that is, integers between and , inclusive) having only even digits are divisible byProblem 5The integers from to inclusive, can be arranged to form a -by-square in which the sum of the numbers in each row, the sum of the numbers in each column, and the sum of the numbers along each of the main diagonals are all the same. What is the value of this common sum?Problem 6In the plane figure shown below, of the unit squares have been shaded. What is the least number of additional unit squares that must be shaded so that the resulting figure has two lines of symmetryProblem 7Seven cubes, whose volumes are , , , , , , and cubic units, are stacked vertically to form a tower in which the volumes of the cubes decrease from bottom to top. Except for the bottom cube, the bottom face of each cube lies completely on top of the cube below it. What is the total surface area of the tower (including the bottom) in square units?Problem 8What is the median of the following list of numbersProblem 9How many solutions does the equation have on the intervalProblem 10There is a unique positive integer suchthat What is the sum of the digitsofProblem 11A frog sitting at the point begins a sequence of jumps, where each jump is parallel to one of the coordinate axes and has length , and the direction of each jump (up, down, right, or left) is chosen independently at random. The sequence ends when the frog reaches a side of the square withvertices and . What is the probability that thesequence of jumps ends on a vertical side of the squareProblem 12Line in the coordinate plane has the equation . Thisline is rotated counterclockwise about the point to obtain line . What is the -coordinate of the -intercept of lineProblem 13There are integers , , and , each greater than 1, suchthat for all . What is ?Problem 14Regular octagon has area . Let be the area ofquadrilateral . What isProblem 15In the complex plane, let be the set of solutions to andlet be the set of solutions to . What is the greatest distance between a point of and a point ofProblem 16A point is chosen at random within the square in the coordinate plane whose vertices are and . Theprobability that the point is within units of a lattice point is . (A point is a lattice point if and are both integers.) What is to the nearest tenthProblem 17The vertices of a quadrilateral lie on the graph of , and the -coordinates of these vertices are consecutive positive integers. The area of thequadrilateral is . What is the -coordinate of the leftmost vertex?Problem 18Quadrilateral satisfies, and . Diagonals and intersect at point , and . What is the area of quadrilateral ?Problem 19There exists a unique strictly increasing sequence of nonnegativeintegers suchthat What isProblem 20Let be the triangle in the coordinate plane with vertices , ,and . Consider the following five isometries (rigid transformations) of the plane: rotations of , , and counterclockwise around the origin, reflection across the -axis, and reflection across the -axis. How many ofthe sequences of three of these transformations (not necessarily distinct) will return to its original position? (For example, a rotation, followed by a reflection across the -axis, followed by a reflection across the -axis will return to its original position, but a rotation, followed by a reflection across the -axis, followed by another reflection across the -axis will not return to its original position.)Problem 21How many positive integers are there such that is a multiple of , and the least common multiple of and equals times the greatest common divisor of andProblem 22Let and be the sequences of real numbers suchthat for all integers , where . What isProblem 23Jason rolls three fair standard six-sided dice. Then he looks at the rolls and chooses a subset of the dice (possibly empty, possibly all three dice) to reroll. After rerolling, he wins if and only if the sum of the numbers face up on the three dice is exactly . Jason always plays to optimize his chances of winning. What is the probability that he chooses to reroll exactly two of the dice?Problem 24Suppose that is an equilateral triangle of side length , with the property that there is a unique point inside the triangle suchthat , , and . What isProblem 25The number , where and are relatively prime positive integers, has the property that the sum of all realnumbers satisfying is , where denotes thegreatest integer less than or equal to and denotes the fractional part of . What is2020 AMC 12A Answer Key1. C2. C3. E4. B5. C6. D7. B8. C9. E10.E11.B12.B13.B14.B15.D16.B17.D18.D19.C20.A21.D22.B23.A24.B25.C2020 AMC 12B Problems Problem 1What is the value in simplest form of the followingexpression?Problem 2What is the value of the followingexpression?Problem 3The ratio of to is , the ratio of to is , and the ratioof to is . What is the ratio of to ?Problem 4The acute angles of a right triangle are and , where andboth and are prime numbers. What is the least possible value of ?Problem 5Teams and are playing in a basketball league where each game results in a win for one team and a loss for the other team. Team has won of itsgames and team has won of its games. Also, team has won moregames and lost more games than team How many games hasteam played?Problem 6For all integers the value of is always whichof the following?Problem 7Two nonhorizontal, non vertical lines in the -coordinate plane intersect to form a angle. One line has slope equal to times the slope of the other line. What is the greatest possible value of the product of the slopes of the two lines?Problem 8How many ordered pairs of integers satisfy theequationProblem 9A three-quarter sector of a circle of radius inches together with its interior can be rolled up to form the lateral surface area of a right circular cone by tapingtogether along the two radii shown. What is the volume of the cone in cubicinches?Problem 10In unit square the inscribedcircle intersects at and intersects at a point different from What isProblem 11As shown in the figure below, six semicircles lie in the interior of a regular hexagon with side length so that the diameters of the semicircles coincide with the sides of the hexagon. What is the area of the shaded region—inside the hexagon but outside all of the semicircles?Problem 12Let be a diameter in a circle of radius Let be a chord in the circle that intersects at a point suchthat and What isProblem 13Which of the following is the value ofProblem 14Bela and Jenn play the following game on the closed interval of the real number line, where is a fixed integer greater than . They take turns playing, with Bela going first. At his first turn, Bela chooses any real number in theinterval . Thereafter, the player whose turn it is chooses a real numberthat is more than one unit away from all numbers previously chosen by either player. A player unable to choose such a number loses. Using optimal strategy, which player will win the game?Problem 15There are 10 people standing equally spaced around a circle. Each person knows exactly 3 of the other 9 people: the 2 people standing next to her or him, as well as the person directly across the circle. How many ways are there for the 10 people to split up into 5 pairs so that the members of each pair know each other?Problem 16An urn contains one red ball and one blue ball. A box of extra red and blue balls lie nearby. George performs the following operation four times: he draws a ball from the urn at random and then takes a ball of the same color from the box and returns those two matching balls to the urn. After the four iterations the urn contains six balls. What is the probability that the urn contains three balls of each color?How many polynomials of theform , where , , ,and are real numbers, have the property that whenever is a root, sois ? (Note that )Problem 18In square , points and lie on and , respectively, so that Points and lie on and , respectively, and points and lie on so that and . See the figure below. Triangle , quadrilateral ,quadrilateral , and pentagon each has area Whatis ?Square in the coordinate plane has vertices at thepoints and Consider the following four transformations: a rotation of counterclockwise around the origin; a rotation of clockwise around the origin; a reflection across the -axis; and a reflection across the -axis.Each of these transformations maps the squares onto itself, but the positions of the labeled vertices will change. For example, applying and then wouldsend the vertex at to and would send thevertex at to itself. How many sequences of transformations chosen from will send all of the labeled vertices back to theiroriginal positions? (For example, is one sequenceof transformations that will send the vertices back to their original positions.)Problem 20Two different cubes of the same size are to be painted, with the color of each face being chosen independently and at random to be either black or white. What is the probability that after they are painted, the cubes can be rotated to be identical in appearance?Problem 21How many positive integers satisfy(Recallthat is the greatest integer not exceeding .)Problem 22What is the maximum value of for real values ofProblem 23How many integers are there such that whenever are complex numbers such thatthen the numbers are equally spaced on the unit circle in the complex plane?Problem 24Let denote the number of ways of writing the positive integer as a product where , the are integers strictly greater than , and the order in which the factors are listed matters (that is, two representations that differ only in the order of the factors are counted as distinct).For example, the number can be written as , , and ,so . What is ?Problem 25For each real number with , let numbers and be chosen independently at random from the intervals and , respectively, and let be the probability thatWhat is the maximum value of2020 AMC 12B Answer Key1. C2. A3. E4. D5. C6. D7. C8. D9. C10. B11. D12. E13. D14. A15. C16. B17. C18. B19. C20. D21. C22. C23. B24. A25. BThe area of a pizza with radius is percent larger than the area of a pizza with radius inches. What is the integer closest to ?Solution Supposeis of . What percent of is ?Solution A box containsred balls,green balls, yellow balls,blue balls, white balls, and black balls. What is the minimum numberof balls that must be drawn from the box without replacement to guarantee that at least balls of a single color will be drawn?SolutionWhat is the greatest number of consecutive integers whose sum is ?SolutionTwo lines with slopes andintersect at . What is the area of the triangle enclosed by these two lines and the line?SolutionThe ﬁgure below shows line with a regular, inﬁnite, recurring pattern of squares and line segments.How many of the following four kinds of rigid motion transformations of the plane in which this ﬁgure is drawn, other than the identity transformation, will transform this ﬁgure into itself?some rotation around a point of linesome translation in the direction parallel to linethe reﬂection across linesome reﬂection across a line perpendicular to lineSolutionMelanie computes the mean , the median, and the modes of the values that are the dates in the months of . Thus her data consist of , , . . . , , , , and . Let be the median of the modes. Which of the following statements is true?SolutionProblem 2Problem 3Problem 4Problem 5Problem 6Problem 7For a set of four distinct lines in a plane, there are exactly distinct points that lie on two or more of the lines. What is the sum of allpossible values of ?Solution A sequence of numbers is deﬁned recursively by, , and for all . Then can be written as , whereandare relatively prime positive inegers. What is Solution The ﬁgure below shows circles of radius within a larger circle. All the intersections occur at points of tangency. What is the area ofthe region, shaded in the ﬁgure, inside the larger circle but outside all the circles of radius?Solution For some positive integer , the repeating base- representation of the (base-ten) fraction is. What is ?Solution Positive real numbers and satisfy and. What is ?Problem 8Problem 9Problem 10Problem 11Problem 12Solution How many ways are there to paint each of the integers either red, green, or blue so that each number has a different colorfrom each of its proper divisors?Solution For a certain complex number, the polynomial has exactly 4 distinct roots. What is?Solution Positive real numbers andhave the property that and all four terms on the left are positive integers, where denotes the base- logarithm. What is?Solution The numbers are randomly placed into the squares of a grid. Each square gets one number, and each of thenumbers is used once. What is the probability that the sum of the numbers in each row and each column is odd?Solution Let denote the sum of the th powers of the roots of the polynomial . In particular, ,, and . Let , , and be real numbers such that for ,, What is?Solution A sphere with center has radius . A triangle with sides of length and is situated in space so that each of its sides is tangent to the sphere. What is the distance between and the plane determined by the triangle?SolutionIn with integer side lengths,What is the least possible perimeter for ?Problem 13Problem 14Problem 15Problem 16Problem 17Problem 18Problem 19Real numbers between and , inclusive, are chosen in the following manner. A fair coin is ﬂipped. If it lands heads, then it is ﬂipped again and the chosen number is if the second ﬂip is heads and if the second ﬂip is tails. On the other hand, if the ﬁrst coin ﬂip is tails, then the number is chosen uniformly at random from the closed interval . Two random numbersandare chosen independently in thismanner. What is the probability that?Solution Let What is Solution Circles and , both centered at , have radii and , respectively. Equilateral triangle , whose interior lies in the interior of but in the exterior of , has vertex on , and the line containing side is tangent to . Segments and intersect at ,and . Thencan be written in the form for positive integers ,, , with . What is ?Solution Deﬁne binary operations andby for all real numbers and for which these expressions are deﬁned. The sequence is deﬁned recursively byand for all integers . To the nearest integer, what is ?SolutionFor how many integers between and , inclusive, isan integer? (Recall that .)Problem 21Problem 22Problem 23Problem 24Copyright © 2019 Art of Problem SolvingLet be a triangle whose angle measures are exactly , , and . For each positive integer deﬁne to be the foot of the altitude from to line . Likewise, deﬁne to be the foot of the altitude from to line, and to be the foot of the altitude from to line. What is the least positive integer for whichis obtuse?Solution2019 AMC 12A (Problems • Answer Key • Resources (/Forum/resources.php?c=182&cid=44&year=2019))Preceded by2018 AMC 12B Problems Followed by 2019 AMC 12B Problems1 •2 •3 •4 •5 •6 •7 •8 •9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18• 19 • 20 • 21 • 22 • 23 • 24 • 25All AMC 12 Problems and SolutionsThe problems on this page are copyrighted by the Mathematical Association of America ()'s American Mathematics Competitions ().Retrieved from "https:///wiki/index.php?title=2019_AMC_12A_Problems&oldid=101818"See also2019 AMC 12A Answer Key1. E2. D3. B4. D5. C6. C7. E8. D9. E10. A11. D12. B13. E14. E15. D16. B17. D18. D19. A20. B21. C22. E23. D24. D25. E2019 AMC 12B Answer Key1. D2. E3. E4. C5. B6. A7. A8. A9. B10. E11. D12. D13. C14. C15. E16. A17. D18. C19. B20. C21. B22. C23. C24. C25. C2018 AMC 12A ProblemsA large urn contains balls, of which are red and the rest are blue. How many of the blue balls must be removed so that the percentage of red balls in the urn will be ? (No red balls are to be removed.)SolutionWhile exploring a cave, Carl comes across a collection of -pound rocks worth each, -pound rocks worth each, and -pound rocks worth each. There are at least of each size. He can carry at most pounds. What is the maximum value, in dollars, of the rocks he can carry out of the cave?SolutionSolutionAlice, Bob, and Charlie were on a hike and were wondering how far away the nearest town was. When Alice said, "We are at least 6 miles away," Bob replied, "We are at most 5 miles away." Charlie then remarked, "Actually the nearest town is at most 4 miles away." It turned out that none of the three statements were true. Letbe the distance in miles to the nearest town. Which of the following intervals is the set of all possible values of ?Solution What is the sum of all possible values of for which the polynomials andhave a root in common?Solution For positive integers andsuch that , both the mean and the median of the set are equalto . What is ?SolutionFor how many (not necessarily positive) integer values of is the value of an integer?SolutionAll of the triangles in the diagram below are similar to iscoceles triangle , in which . Each of the 7 smallest triangles has area 1, andhas area 40. What is the area of trapezoid ?Solution Which of the following describes the largest subset of values ofwithin the closed interval for which for everybetweenand , inclusive?Solution How many ordered pairs of real numbers satisfy the following system of equations?SolutionA paper triangle with sides of lengths 3,4, and 5 inches, as shown, is folded so that point falls on point . What is the length in inches of the crease?Problem 5Problem 6Problem 7Problem 8Problem 9Problem 10Problem 11Solution Let be a set of 6 integers taken fromwith the property that ifand are elements of with , thenis not a multiple of . What is the least possible value of an element in Solution How many nonnegative integers can be written in the form where for ?Solution The solutions to the equation, where is a positive real number other than or , can be written as where and are relatively primepositive integers. What is ?Solution A scanning code consists of a grid of squares, with some of its squares colored black and the rest colored white. There must be at least one square of each color in this grid of squares. A scanning code is called if its look does not change when the entire square is rotated by a multiple of counterclockwise around its center, nor when it is reflected across a line joining opposite corners or a line joining midpoints of opposite sides. What is the totalnumber of possible symmetric scanning codes?Solution Which of the following describes the set of values of for which the curvesand in the real -plane intersect at exactly points?SolutionFarmer Pythagoras has a field in the shape of a right triangle. The right triangle's legs have lengths 3 and 4 units. In the corner where those sides meet at a right angle, he leaves a small unplanted square so that from the air it looks like the right angle symbol. The rest of the field is planted. The shortest distance from to the hypotenuse is 2 units. What fraction of the field is planted?Problem 12Problem 13Problem 14Problem 15Problem 16Problem 17SolutionTriangle with and has area . Let be the midpoint of, and let be the midpoint of . The angle bisector of intersects andat and , respectively. What is the area of quadrilateral ?Solution Letbe the set of positive integers that have no prime factors other than , , or . The infinite sum of the reciprocals of the elements of can be expressed as , where and are relatively prime positive integers. What is ?Solution Triangle is an isosceles right triangle with . Let be the midpoint of hypotenuse . Points and lie on sidesand ,respectively, so that andis a cyclic quadrilateral. Given that triangle has area , the length can be written as , where ,, and are positive integers andis not divisible by the square of any prime. What is the value of?Solution Which of the following polynomials has the greatest real root?Solution The solutions to the equations and where form the vertices of a parallelogram in the complex plane. The areaof this parallelogram can be written in the formwhereand are positive integers and neither nor is divisible by the square of any prime number. What is Solution In and Points andlie on sides and respectively, so that Let andbe the midpoints of segments and respectively. What is the degree measure of the acute angle formed by lines and Solution Alice, Bob, and Carol play a game in which each of them chooses a real number between 0 and 1. The winner of the game is the one whose number is between the numbers chosen by the other two players. Alice announces that she will choose her number uniformly at random from all the numbers between 0 and 1, and Bob announces that he will choose his number uniformly at random from all the numbers between and Armed with this information, what number should Carol choose to maximize her chance of winning? Solution For a positive integer and nonzero digits , , and , let be the -digit integer each of whose digits is equal to ; let be the-digit integer each of whose digits is equal to , and let be the -digit (not -digit) integer each of whose digits is equal to . What is the greatest possible value offorwhich there are at least two values of such that ?SolutionProblem 18Problem 19Problem 20Problem 21Problem 22Problem 23Problem 24Problem 25See also2018 AMC 12A (Problems • Answer Key • Resources)Preceded by 2017 AMC 12B ProblemsFollowed by 2018 AMC 12B Problems1 ·2 ·3 ·4 ·5 ·6 ·7 ·8 ·9 · 10 · 11 · 12 · 13 · 14 · 15 · 16 · 17 · 18 · 19 · 20 · 21 · 22 · 23 · 24 · 25All AMC 12 Problems and SolutionsThe problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.Retrieved from "/wiki/index.php?title=2018_AMC_12A_Problems&oldid=94197"Category: AMC 12 ProblemsCopyright © 2018 Art of Problem Solving2018 AMC 12A Answer Key1. D2. C3. E4. D5. E6. B7. E8. E9. E10. C11. D12. C13. D14. D15. B16. E17. D18. D19. C20. D21. B22. A23. E24. B25. DRetrieved from "/wiki/index.php?title=2018_AMC_12A_Answer_Key&oldid=90552"Copyright © 2018 Art of Problem Solving2018 AMC 12B ProblemsKate bakes 20-inch by 18-inch pan of cornbread. The cornbread is cut into pieces that measure 2 inches by 2 inches.How many pieces of cornbread does the pan contain?SolutionSam drove 96 miles in 90 minutes. His average speed during the first 30 minutes was 60 mph (miles per hour), and his average speed during the second 30 minutes was 65 mph. What was his average speed, in mph, during the last 30minutes?Solution A line with slope 2 intersects a line with slope 6 at the point . What is the distance between the -intercepts ofthese two lines? Solution A circle has a chord of length , and the distance from the center of the circle to the chord is . What is the area of thecircle?Solution How many subsets ofcontain at least one prime number?Solution Suppose cans of soda can be purchased from a vending machine for quarters. Which of the following expressionsdescribes the number of cans of soda that can be purchased fordollars, where 1 dollar is worth 4 quarters?SolutionWhat is the value ofSolutionProblem 2Problem 3Problem 4Problem 5Problem 6Problem 7Problem 8Line segment is a diameter of a circle with . Point, not equal toor, lies on the circle. As point moves around the circle, the centroid (center of mass) of traces out a closed curve missing two points. To the nearest positive integer, what is the area of the region bounded by this curve?SolutionWhat isSolution A list of positive integers has a unique mode, which occurs exactly times. What is the least number of distinct values that can occur in the list?SolutionA closed box with a square base is to be wrapped with a square sheet of wrapping paper. The box is centered on the wrapping paper with the vertices of the base lying on the midlines of the square sheet of paper, as shown in the figureon the left. The four corners of the wrapping paper are to be folded up over the sides and brought together to meet at the center of the top of the box, point in the figure on the right. The box has base length and height . What is the area of the sheet of wrapping paper?Solution Side of has length . The bisector of angle meets at , and . The set of all possiblevalues of is an open interval . What is ?Problem 9Problem 10Problem 11Problem 12Solution Square has side length . Point lies inside the square so thatand . The centroids of, ,, and are the vertices of a convex quadrilateral. What is the area of that quadrilateral?Solution Joey, Chloe, and their daughter Zoe all have the same birthday. Joey is 1 year older than Chloe, and Zoe is exactly 1 year old today. Today is the first of the 9 birthdays on which Chloe's age will be an integral multiple of Zoe's age. What will be the sum of the two digits of Joey's age the next time his age is a multiple of Zoe's age?SolutionHow many odd positive 3-digit integers are divisible by 3 but do not contain the digit 3?Solution The solutions to the equation are connected in the complex plane to form a convex regular polygon,three of whose vertices are labeled and . What is the least possible area ofSolutionLet and be positive integers such thatand is as small as possible. What is ?Problem 13Problem 14Problem 15Problem 16Problem 17。

可伸缩的显示器[发明专利]

专利名称：可伸缩的显示器
专利类型：发明专利
发明人：J.波特,P.V-T.勒,J.卢瑟,D.N.劳比申请号：CN201680032452.5
申请日：20160616
公开号：CN107613809A
公开日：
20180119
专利内容由知识产权出版社提供
摘要：本发明提供了一种可伸缩的显示器，所述可伸缩的显示器可以从显示器外壳腔中竖立并且倾斜到指定角度以获得最佳的显示特性。

一个实例可以包括以下各项中的至少一个：显示器外壳腔；显示器；安装至所述显示器外壳腔内的所述显示器的轨道；以及安置在所述轨道上的导螺杆，所述导螺杆旋转地将所述轨道和所述显示器从所述显示器外壳腔中升起来。

申请人：安玛思有限责任公司
地址：美国德克萨斯州
国籍：US
代理机构：北京市柳沈律师事务所
代理人：宋西
更多信息请下载全文后查看。

ASHRAEStandard62.1-2013andStandard90.1-2013…

Technical Report 1MechanicalASHRAE Standard 62.1-2013 and Standard 90.1-2013 EvaluationAuthor: Kale MullikinAdvisor: Donghyun RimSeptember 18, 2014ContentsProject Summary (2)Executive Summary (2)ASHRAE standard 62.1-2013 (3)Section 5 (3)Summary of ASHRAE 62.1 (7)Ventilation Rate Procedure Analysis (8)Summary of Ventilation Rate Procedure (10)ASHRAE standard 90.1-2013 (11)Section 5: Building Envelope (11)Section 6: Heating, Ventilating, and Air Conditioning (13)Section 7: Service Water Heating (13)Section 8: Power (13)Section 9: Lighting (13)Section 10: Other Equipment (14)Summary of ASHRAE 90.1 (15)Appendix (16)Project SummaryThe Medical Office Building is located in North-East United States and is to house many medical offices as well as some examination rooms and a physical therapy area. The building is two stories with a total square footage of 72,706.The main heating and cooling of the building will be supplied by two roof top units with a VAV system to regulate the air in the building. There are also five separate ductless split-system units that will serve areas that generate more heat than the rest of the building.Executive SummaryThis technical report was created to analyze the Medical Office Building and determine if it meets the requirements of ASHRAE 62.1-2013 and 90.1-2013.ASHRAE 62.1 specifies minimum ventilation rates and other requirements to provide an air quality that is acceptable for human occupation. Since the Medical Office Building is a healthcare facility, it is very important that the building complies with this standard. This building does comply with 62.1. There was only one minor specification that was not met and that was bird screens on the intakes of the roof top units. This can be easily improved post construction if it proves to be a problem.ASHRAE 90.1 is intended to set minimum requirements for energy efficiency of buildings. Due to the fact that the Medical Office Building was not intended to obtain a LEED rating, the building adhered to compliance but did not go above and beyond. The standard requires that there be energy saving controls on the lights and mechanical units as well as minimizing the amount of air to leak in or out of the building.ASHRAE standard 62.1-2013Section 55.1 Ventilation Air DistributionDesign for Air Balancing: System will be equipped with 100% modulating based economizer system. Fresh air will be measured and controlled with minimum and maximum fresh air setpoints that will be programmable at the human interface.Plenum Systems: This building does not make use of plenum supply and return. Therefore this section does not apply.Documentation: Minimum requirements for air balancing and testing shall be taken fromNEBB’s “Procedural Standards for Testing, Adjusting, and Balancing of EnvironmentalSystems.” Testing, adjusting, and balancing shall be done by a firm certified by NEBB.5.2 Exhaust Duct Location: Exhaust fans will be located on the ceiling allowing for negative pressure of exhaust ducts. Exhaust fans will also comply with AMCA requirements.5.3 Ventilation System Controls: System will be equipped with an automatic economizer cycle with maximum and minimum fresh air set points adjustable at a human interface to maintain required fresh air ventilation.5.4 Airstream SurfacesResistance to Mold Growth:The duct materials in this building are composed of galvanized sheet steel complying with ASTM A 653/A 653M having a G90 coating, PVC-coated galvanized steel complying with ASTM A 653/A 653M having a G90 coating, carbon-steel sheets ASTM A 366/A366M, stainless steel ASTM A 480/A480M type 316, aluminum sheets ASTM B 209 alloy 3003 temper H14.Resistance to Erosion: This building has sheet metal ducts which are excluded from thissection. The duct liner present in some of the ducts will be coated to prevent the erosion of glass fibers.5.5 Outdoor Air IntakesLocation: The closest exhaust fan is exhausting class 2 air and is further than 10 feet awayfrom the inlet of the roof top units specified in drawings. Other fresh air inlets are located on the ground floor and there are no exhaust near outlets or loading areas near these inlets.Rain Entrainment and Intrusion: Rain entrainment and intrusion is prevented by a downward facing hood on the intake of the roof top unit as well as linked damper blades and a damper filter.Snow Entrainment: Roof access doors are provided as well as walking pads placed on the roof leading to the roof top units.Bird Screens: Bird screens are called out on the roof top exhaust fans but are not called out on the intakes for the roof top units.5.6 Local Capture of Contaminants: Separate exhaust fans have been provided for all the rooms that require direct venting to the outside.5.7 Combustion Air: Fuel-burning appliances are located in the roof top units and therefore have plenty of air for combustion as well as venting.5.8 Particulate Matter Removal: A pleated cartridge type pre-filter of minimum MERV 8 has been provided in accordance with ASHRAE standard 52.1.5.9 Dehumidification SystemsRelative Humidity: The climate of the area already has a low humidity so humidifiers havebeen added to better control the humidity of the building. Humidity set points are adjustable at the operator’s interface station was well as monitoring the relative humidity.Exfiltration: Exfiltration is easily controlled by the presence of VAV boxes in different zones to control the amount of air entering the room which can easily be adjusted to keep the building pressurized.5.10 Drain PansDrain Pan Slope: Drain pans are sloped to comply with ASHRAE 62.Drain Outlet: Threaded nipples are mounted on both sides of the drain pan.Drain Seal: No negative static pressure is present in the roof top unit at the drain pan therefore there is no need for a drain seal.Pan Size: The drain pan will span the whole area under the roof top unit and be a minimum of two inches deep.5.11 Finned-Tube Coils and Heat ExchangersDrain Pans: A stainless steel formed drain pan has been provided in accordance withASHRAE 62.1.Finned-Tube Coil Selection for Cleaning: Easy access to upstream and downstream of thecoil has been provided as well as detailed instructions on how to clean the coils.5.12 Humidifiers and Water-Spray SystemsWater Quality: The humidifier being used is a self-contained humidifier that will use citywater which meets potable water requirements.Obstructions: The location of the humidifier with relation to manifolds in ducts, air handling units and occupied space has been coordinated to ensure proper humidifier operation.5.13 Access for Inspection, Cleaning, and MaintenanceEquipment Clearance: The ventilation equipment is located on the roof with adequate space between the two units therefore providing enough room for inspection and maintenance.Ventilation Equipment Access: Access doors have been provided for inspection andmaintenance of the ventilation equipment.Air Distribution System: Access doors have been provided in the ducts at major areas such as dampers and sensors.5.14 Building Envelope and Interior SurfacesBuilding Envelope: The building will be wrapped in a vapor air barrier and all seams andjoints will have flashing and be caulked to keep moisture and air out.Condensation on Interior Surfaces: Insulation will be provided for ducts and piping wherecondensation could possibly be present due to the cooler nature of the pipes and ducts.5.15 Buildings with Attached Parking Garages: The Medical Office Building does not have an attached parking garage. Therefore this section is not applicable.5.16 Air Classification and RecirculationClassification: Most of the air in this building is classified as class 1. The restrooms areclassified as class 2 and have exhaust fans that vent directly outside.Redesignation: Air in this building will not be cleaned or mixed.Recirculation Limitations: Class 2 air in this building will not be recirculated. Class 2 air will be vented directly outside.Documentation: There is no change of classification from the ASHRAE standard.5.17 Requirements for Buildings Containing ETS Areas and ETS-Free Areas: There are no ETS areas in this building.Summary of ASHRAE 62.1It can be said that the Medical Office Building is in compliance with ASHRAE 62.1. The only section found that the building was not in compliance with was section 5.5-Bird Screens. Although the building is not in compliance with this section, this can easily be fixed once the building is completed.Ventilation Rate Procedure AnalysisVentilation rate calculations are preformed to determine the amount of outdoor air needed in a building to provide a healthy environment for people to live and work in. In the Medical Office Building, there are two roof top units and they were both analyzed because the building is not very large and has many different rooms.Supporting EquationsBreathing Zone Outdoor Airflow (V bz)V bz= R p × P z+ R a × A zA z = the net occupiable floor area of the ventilation zone (ft2)P z = the number of people in the ventilation zone during typical usageR p = outdoor airflow rate required per person (table 6.2.2.1)R a = outdoor airflow rate required per unit area (table 6.2.2.1)Zone Outdoor Airflow (V oz)V oz= V bz/E zV bz = breathing zone outdoor airflowE z = zone air distribution effectiveness is 1.0 due to ceiling supply of cool airPrimary Outdoor Air Fraction (Z pz)Z pz= V oz/V pzV oz = zone outdoor airflowV pz = zone primary airflowUncorrected Outdoor Air Intake (V ou)V ou= D∑all zones (R p× P z) + ∑all zones (R a × A z)D = occupant diversity is taken to be 1Outdoor Air Intake (V ot)V ot= V ou/E vV ou = uncorrected outdoor air intakeE v = system ventilation efficiency (from table 6.2.5.2)Summary of Ventilation Rate ProcedureThe medical office building is in compliance with the ventilation rate procedure. Roof top unit one is compliant by about 1,000 cfm and roof top unit 2 is compliant by about 500 cfm. An opportunity for improvement could be to split the zones that roof top unit 2 has to handle in half and use two more roof top units so there would be slightly more outdoor air cfm to work with. For roof top unit 1, the nominal outside air (∑V oz) was the same as the required outside air (V ot). For roof top unit 2, the nominal outside air (∑V oz) was less than the required outside air (V ot).RTU-1∑V oz = 3267 cfm V ot = 3267 cfmRTU-2∑V oz = 4272 cfm V ot = 6213 cfmTable 1: Comparison of RTU-1 and RTU-2 nominal and required outside airASHRAE standard 90.1-2013Section 5: Building Envelope5.1 Scope: The Medical Office Building is located in North-East United States. This location has very moist climate which requires that the air be conditioned before it enters the building to improve the comfort of the occupants.5.4 Mandatory Provisions: The building has design elements to reduce air leakage out of the building such as an air barrier, vestibules at the main entrances of the building, and sealants at all joints around windows and doors and any other areas that air my possibly leak in.Figure 1: US Climate Zones5.5 Prescriptive Building Envelope Option: The walls at the Medical Office Building are commonly built up in the following fashion:•Brick veneer•Air space•2” rigid insulation•Air/vapor barrier•5/8” high density glass fiber reinforced sheathing•6” structural steel studs•R-13 batt insulation•5/8” mold resistant gypsum wallboardThis wall makeup easily complies with the R-10 continuous insulation requirement and the R-13 filled cavity requirement from table 5.5-5 of ASHRAE 90.1. There is a 6” requirement for roof insulation which satisfies the R-30 continuous insulation required for the roof also from table 5.5-5 of ASHRAE 90.1.According to section 5.5.4 of ASHRAE standard 90.1, vertical fenestration must not exceed 40% of the total vertical building surfaces and skylights may not exceed 3% of the fenestration of the roof.Building Face Total Wall Area (SF) Fenestration (SF)North 7423 2764East 4705 710South 7682 1971West 5959 2346Total 25769 7791% Fenestration 30.23Table 2: Vertical FenestrationRoof Area (SF) Fenestration (SF)40637 540%Fenestration 1.33Table3: Roof FenestrationSection 6: Heating, Ventilating, and Air Conditioning6.4 Mandatory Provisions: The roof top units are equipped with an economizer cycle which will take into account when the building is occupied and when it is not to adjust the amount of conditioning needed to save energy. All the ductwork and piping will be insulated to conserve energy and reduce condensation.6.5 Economizers: The economizers are expected to comply with all parts of section 6.5.1.1 which also have been called out in the specifications. The VAV system in this building will have static pressure sensors to monitor the air flow through the VAV box.Section 7: Service Water HeatingThe water heated in this building is not used for heating the building, it is for domestic use only. The heaters and storage tanks for domestic water heating do meet the requirements given in table 7.8 of ASHRAE.Section 8: PowerPower to the Medical Office Building will be supplied by a 480/277 3 phase 4 wire source. There will be a 600KW emergency generator on site to provide emergency power since this is a medical building and emergency power is very important. The power in this building meets the requirements for voltage drop, energy monitoring, etc. given in the ASHRAE standard.Section 9: LightingTable 9.5.1 was used to determine the lighting power density for the Medical Office Building. The building area type used was health-care clinic and the power density for this is 0.90 W/ft2. The total building area is 72,706 sf.The building meets the ASHRAE requirements for lighting using different switches to control the lighting depending on occupancy.Section 10: Other EquipmentAll the electric motors in the building are compliant with the requirements of the Energy Independence and Security Act of 2007. The elevators also meet the requirements for lighting, ventilation and standby mode.Summary of ASHRAE 90.1The Medical Office Building is in compliance with ASHRAE 90.1. The building envelope meets building envelope requirements as well as requirements for heating, ventilation, and air conditioning, service water heating, power, lighting, and other equipment.AppendixVentilation Rate Calculations:• A value of 0.8 was used for E z because there is a ceiling supply of warm air at 15 F or more above space temperature and a ceiling return.•Maximum Z p value for each system is highlighted in green.。

FAMOS_Getting_started

© 2013 imc Meßsysteme GmbHimc Meßsysteme GmbH • Voltastraße 5 • 13355 Berlin • Germany2Table Of Contentsimc FAMOS Users Manual (4)1.1 imc customer support - hotline (4)1.2 Important Notes (5)1.2.1 Guidelines1.2.1.1 Guarantee of Year 2000 conformity (5)1.2.1.2 Certificates and Quality Management (5) (6)1.3 imc Guarantee and Software-License Agreement (6)1.4 Product ImprovementIntroduction (7)2.1 Foreword (7)2.2 Additional Help Resources (8)2.3 System Requirements (9)2.4 Installation (10)2.5 Start (11)2.6 imc License Manager (11)2.6.1 General2.6.1.1 About this manual (11)2.6.1.2 System prerequisites (12) (12)2.6.1.3 Installation2.6.1.4 imc Dongle (13)2.6.1.5 Definition of terms (14) (16)2.6.2 User Interface2.6.2.1 Licenses activated (16)2.6.2.2 Activation (18)2.6.2.3 Administration (26)2.6.2.4 Deactivating (32)2.6.3 Network license (37)2.6.3.1 Instructions for administrators (37)2.6.3.2 What does the user need to do? (37)2.6.4 Trial version license (39) (40)2.7 imc FAMOS PackagesUser Interface (43)3.1 Introduction (44)3.2 Variables List3.2.1 Overview (44)3.2.2 Operation (44)3.2.3 Options (46) (47)3.3 The Functions List3.3.1 Overview (47) (48)3.3.2 Operation (50)3.4 Editor Box3.4.1 Overview (50)3.4.2 Editing Text (51)3.4.3 Active line, executing formulas (52)3.4.4 Help and Assistant (52) (52)3.5 Output Box (53)3.6 The Plug-in box (54)3.7 File MenuTable Of Contents3 (55)3.8 Variable Menu (56)3.9 Sequence Menu (58)3.10 Extra Menu (59)3.11 Project Menu (61)3.12 Window Menu (62)3.13 "?" (Help) MenuTutorial (63)4.1 Introduction (63)4.2 Starting FAMOS (64)4.3 Specifying Directories (65)4.4 Loading Files (66)4.5 Showing Variables (66)4.6 Zooming (67)4.7 Unzooming (67)4.8 Measuring (68)4.9 Viewing Variable Properties (69)4.10 Interpolation (71)4.11 More Waveforms in Curve Window (74)4.12 Changing a Formula (74)4.13 Single Values (75)4.14 Calculations (76)4.15 Waveform Editor (Data Editor) (76)4.16 Saving Results (77)4.17 Deleting Variables (77)4.18 Spectrum (78)4.19 Complex Waveforms (79)4.20 Creating Sequences (80)4.21 Executing Sequences (81)4.22 Changing Sequences (81)4.23 Saving Sequences (81)4.24 Favorites (82)4.25 Using the File Browser to load files (84)4.26 Loading and Displaying Files from a Directory (85)4.27 Loading and Displaying Files from Different Directories Index (86)4imc FAMOS Users Manualimc FAMOS Users Manual1.1 imc customer support - hotlineGermany:imc Meßsysteme GmbHPhone: 030 / 46 70 90 - 26Fax: 030 / 4 63 15 76WWW:e-mail:hotline@imc-berlin.deFor our international partners see and click to International DistributorsWhen requesting telephone consultation, please be prepared to state the software revision and have this manual present. Thanks!1.2 Important NotesPlease be sure to read!Dear system user,1.Before using, please always verify that this manual version matches the software version which youhave obtained. If it does not, or if you discover any discrepancies, please contact our Customer Support right away (see: imc Customer Support - Hotline).2.Please also be advised that the software you have obtained, as well as the associated Users Manualare directed toward competent and instructed users and not uninitiated one-time users.3.Please also be aware that continuously and rapidly advancing developments in the field of software cancause portions of the Users Manual to become outdated and make it necessary to obtain updates. If you notice any discrepancies of this type, we request that you contact our Customer Support by the telephone number above.4.We also request you contact our hotline number if you find material in the manual which you believecould be misunderstood and thereby lead to personal injury.Your partners at imc Meßsysteme GmbH.Important Notes5 1.2.1 Guidelines1.2.1.1 Guarantee of Year 2000 conformityWe certify that our software products imcDevices, imc-CRONOS, LOOK, imc FAMOS1, SEARCH, Filter Design, FRAME and Online-FRAME as well as our hardware products busDAQ, SPARTAN, imc CRONOS-PL(SL), imc C-Series, imc C1, imc F1 and F2 and imc-CRONOS meet the "C-EURO YEAR 2000" requirements. There should be no problems in the interpretation of dates. All data recorded after the year 1980 (the year DOS was introduced) will be correctly interpreted until the year 2079.This means in particular (i.a.):Processing of the date will at no time lead to system interruptions.Date-based processing operations return the same results regardless of the value for the datasupplied, whether prior to 2000 A.D. or after (up until 2079 A.D.), unless otherwise defined.The value for the date is defined either explicitly or by an unequivocal algorithm or by a derivablerule, in all interfaces and memory areas.1Some imc FAMOS sequences return the year number in two digits (see Manual "imc FAMOS Function Reference"). Your application may require testing for this circumstance.1.2.1.2 Certificates and Quality Managementimc holds DIN-EN-ISO-9001 certification since May 1995.Current certificates and information about the imc quality system can be foundon the WEB http://www.imc-berlin.de/en:Customer Support / Quality AssuranceFor further information, please contact our hotline.6imc FAMOS Users Manual1.3 imc Guarantee and Software-License Agreementimc Limited Warranty*Subject to the general terms and conditions of imc Meßsysteme GmbH.*The specifications stated in this documentation are subject to change without prior notice.imc may hold rights to patents, trademarks, copyrights and other intellectual property, to which the statements in this documentation refer. This does not imply that the purchaser of this imc product receives any of these rights, excepting such which are explicitly provided for in the written license agreement.1.4 Product ImprovementDear Reader!We at imc hope that you find this manual helpful and easy to use. To help us in further improving this documentation, we would appreciate hearing any comments or suggestions you may have.In particular, feel free to give us feedback regarding the following:Terminology or concepts which are poorly explainedConcepts which should be explained in more depthGrammar or spelling errorsPrinting errorsPlease send your comments to the following address:imc Meßsysteme GmbHintegrated measurement & controlCustomer Service DepartmentVoltastrasse 5D - 13355 BerlinTelephone: +49 (30) 46 70 90 - 26Fax: +49 (30) 46 3 15 76e-mail: hotline@imc-berlin.deForeword7 Introduction2.1 Forewordimc FAMOS (F ast A nalysis and M onitoring o f S ignals) is a software program for analysis and evaluation of measurement results. With an extensive range of functions conceived especially for the needs of measurement and control applications, imc FAMOS eliminates much of your routine work in a comfortable fashion.With imc FAMOS, you can process large waveforms quickly and efficiently and create computational procedures using standard mathematical notation. No specialized programming expertise is required!Furthermore, imc FAMOS offers powerful means for displaying your data in charts or tables and for printing these in individually designed reports.imc FAMOS processes measured data produced by imc devices (e.g. imc CRONOS, imc C-Series, imc µMUSYCS). The scope of functions also includes a large number of import- and export filters for common file formats (e.g. the standard formats of different manufacturers of measurement devices).The task of importing data into an analysis program which are not expressed in a directly supported file format is often the first and most difficult problem involved with analyzing measured data. Toward this end, imc FAMOS offers support in a variety of ways: for simple ASCII formats, for example, a flexible and easily configured Assistant is provided. For more complex formats, the imc File Assistant can be used, by which means the user can personally create import filter, even without possessing any programming skills.imc FAMOS is principally conceived for use in offline evaluation of data and cannot be used to control measurement instrumentsimc FAMOS can be expanded with add-on modules and function libraries. Expansions are available which, for example, make it possible to design digital filters or to classify measurement data. Furthermore you can add your own self-written function libraries to imc FAMOS.Required ReadingThe following chapters contain important information concerning the installation and operation imc FAMOS. We highly recommend going through this manual - even if you are familiar with Windows applications in general. With graphics-oriented programs such as imc FAMOS and other MS-Windows apps, most of the functions can be largely learned without referring to the instructions, due to the program’s clear and intuitive design. However, it is still recommended that you observe the entire instructions in order to be able to use certain functions which are more interesting than obvious.Following successful installation, we recommend working through the chapter'Tutorial' in order to get quickly acquainted with the workings of imc FAMOS.Note2.2 Additional Help ResourcesTo supplement this manual, additional information and help are available in the form of online help files, which are included with the installation of imc FAMOS. Along with the context-sensitive imc FAMOS Online Help, which mainly presents excerpts of the manual, you can also find other help topics specially tailored to beginners or to users who changed from other imc FAMOS versions. The imc Start menu contains the calls to the display of these help topics. Here you will additionally find the complete manuals in PDF format in the submenu "Manuals".imc FAMOS Update-InfoThis section is particularly interesting for users who are already familiar with previous imc FAMOS versions. Here you can find an overview of the technical innovations implemented in this version as well as notes which simplify learning the difference.8Introductionimc FAMOS ReadMeThis presents info on changes and extensions in imc FAMOS which were implemented after this manual went to print.2.3 System RequirementsSupported operating systems:Windows XP (SP3 or higher), Windows Vista SP1, Windows 7, Windows 8, Windows 2008 Server Additional runtime environment:Microsoft .NET 4.0 Runtime Environment (included in the delivery)The following minimum system configuration is required:PC with Pentium microprocessor or higher512 MB RAM (or minimum requirement of the operating system respectively)Hard disk with at least 200 MB available disk spaceCD-ROM driveModern graphics card and appropriate color monitor with usable screen resolution of at least 800 x 600 pixels and High-Color (16-bit color resolution) color outputMouse or trackballThe following items are not required, but can greatly improve the performance of imc FAMOS: Extended memory >= 1 GBTrue Color (32-bit color resolution), screen resolution 1024*768 or betterColor printerLarge, fast hard disk with more than 2GB available disk space.In order to be able to import or export files in Microsoft ® Excel format (*.xls), Excel must be installed on the same computer. The following versions are supported:Excel 95, Excel 97, Excel 2000, Excel 2002 (XP), Excel 2003, Excel 2007Excel 2010 (except "Starter Edition")System Requirements9 2.4 InstallationWindows must be correctly installed and all system prerequisites must be assured before installing imc FAMOS.To install FAMOS, start the program "setup_ImcFamos.exe" from the root directory of the installation CD.Alternatively you can select the "Software" icon and subsequently the command "Install".Select the edition of FAMOS to install:Follow the Assistant's instructions and select your preferred language for the online help files and example files like projects, sequences and dialogs.In the subsequent dialog, the license agreement appears. Once you have accepted its provisions, select the installation folder to which to copy all the files.The installation folder must be on the PC's local hard drive. FAMOS cannot be installed on a network drive.This base directory will be structured with various subdirectories where, for example, sample files will be deposited. The subdirectory \BIN, for instance, contains all executable files and program libraries; the subdirectory "\SEQ" sample sequences (macros); the subdirectory "\DAT" has measurement data files containing information in various data formats.At installation, you must also supply a name for the program group; the installation program will then supplement the Windows Start menu with a corresponding entry. If, for instance, you specify "imc" as your group name, you will be able to call the program from the submenu "Start/ Programs/ imc".10Introduction2.5 StartStart FAMOS either via the corresponding entry in the Windows Start menu, or by clicking on the shortcut on the Windows-Desktop which was created during the installation, or directly by calling the file "FAMOS.exe" from the Windows Explorer.LicensingAs of the version FAMOS 6.1, the software license is administered by a License Manager. A detailed description is located in the next section. Earlier versions had been copyright-protected by a hardlock (dongle). As of FAMOS 6.1 this will no longer be required. If you wish to exchange a FAMOS hardlock for the License Manager, please contact the imc Customer Support.This document refers to the user's manual for detailed information. You can now begin by working through the chapter Tutorial. The subsequent chapters provide an overview of the User Interface.Start112.6 imc License Manager2.6.1 GeneralThe imc License Manager enables you to activate and display imc software products requiring a license.imc License ManagerWhen you acquire an imc software product you receive an activation key. After installing the product, the licensing process is performed using the License Manager.The program can be activatedlocally, for the PC: the software can be run exclusively on this PC.on the imc Dongle: In this case the software can be run on any PC where a) the software has beeninstalled and b) the imc Dongle is connected.2.6.1.1 About this manualThis documentation refers to license manager version 2.0.12Introduction2.6.1.2 System prerequisitesOperating system:Windows XP SP2, Windows Vista, Windows 7Software prerequisites:Microsoft .Net Framework 4.0Rights:Higher than guest rights2.6.1.3 InstallationBy default, the License Manager is installed along with the program purchased (FAMOS, imc Studio etc.).For this purpose, manual installation is not required.If the License Manager is needed on a PC where no activated imc software is present, it must be installed manually. This is necessary for the purposes of activation / deactivation without Internet on the PC having Internet access if that PC does not have imc software installed.To do this, start imcLM_Setup on the installation CD in the folder LicenseManager.Additionally, when setting up a network server, the service imc License Service "IMC-LI" is required, installed by imc LM_SetupServer.After installation, the service "IMC-LI" starts automatically.Also observe the Internet settings which are required for correct functioning.imc License Manager13 2.6.1.4 imc DongleIf multiple computers are running the imc products, you can transfer the licenses to an imc Dongle. The Dongle then activates the operating computer.Toward this end, the License Manager supports a mixture of licenses; such which are linked to a specific computer, such which may be available via a network server, and such which are read by the Dongle.License typesWith an imc Dongle, only first licenses, their updates, and "DEMO" licenses can be activated.Network licenses and second activations are not possible with imc Dongles.Important constraint: If a license is activated on an imc Dongle, then no second activation is available any longer for this license.Software versionThe imc Dongle is supported as of license manager version 1.3.StructureThe imc Dongle consists of 2 USB devices:USB-HID protected Dongle partUSB-Flash free memory with the licenses (2GB)Plugging/unplugging an imc DongleIn order to use the licenses on an imc Dongle, the imc Dongle must be connected at the start of the program to be licensed. If the imc Dongle is unplugged during the program's runtime, a message appears to prompt the user to plug in. If the user does not comply, the License Manager closes the program after 1 min. It is also possible to save the program and close it manually, if the imc Dongle is no longer available.If the only licenses on the imc Dongle are ones which are not needed, then it can be unplugged even while using an imc program requiring licensing.Transfer of a license from the Dongle to PC or vise-versaAn activated license can be deactivated at any time. Following deactivation, the license is available for another PC or imc Dongle and can be re-transferred. Since any activation and deactivation is always registered on the imc Server, either direct or indirect connection to the Internet is required.Use of the imc Dongle in virtual machinesWhen the imc Dongle is used with a virtual machine, both USB device parts (USB-HID,USB-Flash) must be adjusted to the VM (Connect (Disconnect from host)).14Introduction2.6.1.5 Definition of terms"Activation""Activation" denotes the procedure for obtaining a license to use a software product.Computer-specific data (the fingerprint) are combined with certain data for theproduct to obtain the license. Following installation of a program, it must first beactivated before it can be run."Activation file"The "activation file" is a transport file for computer-specific data and activated licenses with whose help it is possible to activate computers not having Internetaccess.Full version In contrast to updates and upgrades, the version of the software which can be run without the installation or activation of any further components.imc Dongle USB-Dongle, on which a product license can be activated.This then replaces the computer-bound licensing."License" A "license" is the entitlement to use a software product on a computer."License Key"By purchasing an imc software product, you acquire a"License Key", which is assigned to you as the customer. A imc products requiring a license which youpurchase are assigned to this "License Key".The License Key must be carefully kept and may not be made available to thirdparties.The "License Key" thus does not pertain to a single product but to you as aregistered user.Additional activations of the program on this computer are thus made possible bymeans of this License Key. Toward this end, ensure that the same License Key isused. In particular, when making repeat orders, be able to state the License Key."License file"The "License file" contains all licenses activated for the local computer."Network license"Network licenses are licenses which are not attached to a single PC. Within the network, a server is set up which has a certain number of available licenses. Allcomputers having access to this server obtain a license by dynamic assignment.Under certain conditions (see the corresponding product documentation), when youpurchase a network license for N users, you obtain an additional N single-userlicenses. These single-user licenses, however, do not enable a second activation."Product"A "product" is a software package appearing in the price list, e.g. FAMOS Professional."Product bundle"The "product bundle" contains multiple products, e.g. FAMOS Professional and the Spectral Kit."Second activation"Under certain conditions, a program can be activated on a second computer.However, special note must be made that the program may never be used on bothcomputers simultaneously. A second activation is possible if a single-user license(not a network license) was purchased and the corresponding productdocumentation indicates the possibility of a second activation. The "secondactivation" enables an additional activation if one activation has already beenperformed on a different computer. It is provided for purposes of use by he sameuser on a mobile PC or a home computer.The second activation is also attached to the particular computer.imc License Manager15 Second activation can be omitted if the license is activated on the imc Dongle.Please note that the second activation does not constitute a second activation, but instead enables the same license, for practical purposes, to be used sometimes on one computer and sometimes on another, without the inconvenient need for repeatedly transferring the license from one computer to the other."Single-user (license)"A license which entitles a program to be used on one computer. Upon activation, the license is transferred to a computer. This means that the license is attached to this computer. Under certain conditions, it is possible to perform a second license activation; see below.Trial version A trial version is a full version having an expiration date, attached to a single computer, and possibly subject to other limitations; see the corresponding chapter.Update The enhancement of a program to a higher and newer version. For instance, an update from FAMOS 6.0 to 6.1Upgrade The enhancement of a program or a related program to a more powerful version16Introduction2.6.2 User Interface2.6.2.1 Licenses activatedA license is activated locally for either a PC or for the imc Dongle. A local license is bound to a certain PCand cannot be transferred to a different PC. The process of activating a license involves transferring data which uniquely identify the PC. The PC's data are then permanently associated with the activated license for one product.If the license was linked to the imc Dongle, it can be used independently of any particular PC. In order to be able to run the software on any PC, the software must be installed and the imc Dongle possessing the appropriate license must be connected.The table in the branch Licenses activated lists all software products which have been activated on this PC and/or on the connected imc Dongle. If you wish to see all of a Licence Key's possible software products, use the menu item Administration > License overview.There are various views which can be selected for the table:Summary:In the view "Summary", the relevant information for the installed products is listed.The comment indicates whether the was obtained via the imc DONGLE connected, or via a network service or from the PC’s hard drive.Dependencies:"Dependencies" indicates whether the version of the software product is a full eine full version or was licensed by meansof updates.imc License Manager17 Detailed view:"Detailed view" lists all components which are automatically licensed along with the software product. Activations:"Activations" shows the points in time at which licenses are activated as a demo, full version or update.Expired Licences:Here, demo versions whose term has expired are listed.18Introduction2.6.2.2 ActivationIn order to activate your product directly, Internet access is necessary. If the computer for which the software is intended does not have Internet access, it is possible to activate the license via a different computer. On this topic, see Computers without Internet access.2.6.2.2.1 Via InternetThe inputs needed for activating a license for a product are to be entered in the sequence of pages belonging to the Activation Assistant. If and entries are missing, it is not possible to proceed to the next page. The controls "Start", "Back" and "Next" allow switching between the Assistant's pages.imc License Manager1920Introduction2.6.2.2.1.1 Single Location (License)With direct Internet access, proceed as follows:Step 1:After installing the program, open the imc License ManagerStep 2:Click on ActivationStep 3:Select Via InternetGo to Contact DataStep 4:Here, enter your contact data. Keep a record of these with the License Key, sincethese data absolutely must match for any subsequent activation.Proceed with Next on page 3.Step 5:For activation, these are the available selections:Attention: The contact data for the single user license and the second activationmust be identical.1.Enabling Trial Version: Select Trial Version and freeware if you have not yet purchasedthe software and you wish to test the software without a License Key.2.Entering the License Key: If you have purchased the program, enter the License Keyhere.Activate the single-user licenseActivate a network license on the computer which is to serve as the license server.Second activation of a single-user license is only possible if the single user licensehasalready been activated once and the conditions or the second activation are met.Step 6:By clicking on "Next", the system accesses the Internet to research whether there is already an available license for your version (page 4). Subsequently, page 5 appears with the list ofthe available products.Example: a license for FAMOSProducts do not appear if the license is already activated on the computer.Products do not appear if the license is already activated on a different computer.Products do not appear if no product had been purchased which has the License Keyentered.Products do not appear if they are already a part of a product bundle which is activated onthe computer.Trial versions do not appear if a full version has already been activated.Updates and upgrades do not appear if the corresponding full versions have already beenactivated.If your product does not appear, please contact the Customer Support.Step 7:On page 6, the encoded data are transmitted.Step 8:A click on Next activates the license via Internet (page 7). Subsequently, the successful activation is indicated on page 8.If a single-user license has already been transferred to a computer, under certain conditions it may be transferred to a second computer. This second activation is performed in the same way as the first one, except that in step 5 the option Second activation must be selected.Entries for the second activationNotesThe contact data and the License Key must match those for the first activation.The "second license" can not be installed on a computer on which there is already a single user license.The contact data sent pertain to the "second computer"Please note the conditions which apply to the second activation.A second isn't available if the first activation is saved on the imc Dongle.After starting the imc License Manager all activated licenses are displayed, see here.。

美国能源之星V7．0标准将于11月中旬生效

美国能源之星V7．0标准将于11月中旬生效
佚名
【期刊名称】《质量与认证》
【年(卷),期】2018(0)4
【摘要】美国环保署日前发布实施电脑产品能源之星V7．0标准的具体时间，V7．0标准将于2018年11月16日生效。

2018年7月2日以后，停止提交新产品认证至V6．1。

2018年11月16日后制造的任何电脑产品必须符合V7．0的要求，才能获得ENERGYSTAR标志。

【总页数】1页(P21-21)
【关键词】美国环保署;标准;生效;能源;电脑产品;产品认证
【正文语种】中文
【中图分类】TV551.31
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2013A 1Square ABCD has side length 10.Point E is on BC ,and the area of ABE is 40.What is BE ?(A)4(B)5(C)6(D)7(E)8A B CDE 2A softball team played ten games,scoring 1,2,3,4,5,6,7,8,9,and 10runs.They lost by one run in exactly ﬁve games.In each of the other games,they scored twice as many runs as their opponent.How many total runs did their opponents score?(A)35(B)40(C)45(D)50(E)553A ﬂower bouquet contains pink roses,red roses,pink carnations,and red carnations.One third of the pink ﬂowers are roses,three fourths of the red ﬂowers are carnations,and six tenths of the ﬂowers are pink.What percent of the ﬂowers are carnations?(A)15(B)30(C)40(D)60(E)704What is the value of22014+2201222014−22012?(A)−1(B)1(C)53(D)2013(E)24024This ﬁle was downloaded from the AoPS Math Olympiad Resources PagePage 120135Tom,Dorothy,and Sammy went on a vacation and agreed to split the costs evenly.During their trip Tom paid $105,Dorothy paid $125,and Sammy paid $175.In order to share the costs equally,Tom gave Sammy t dollars,and Dorothy gave Sammy d dollars.What is t −d ?(A)15(B)20(C)25(D)30(E)356In a recent basketball game,Shenille attempted only three-point shots and two-point shots.She was successful on 20%of her three-point shots and 30%of her two-point shots.Shenille attempted 30shots.How many points did she score?(A)12(B)18(C)24(D)30(E)367The sequence S 1,S 2,S 3,···,S 10has the property that every term beginning with the third is the sum of the previous two.That is,S n =S n −2+S n −1for n ≥3.Suppose that S 9=110and S 7=42.What is S 4?(A)4(B)6(C)10(D)12(E)168Given that x and y are distinct nonzero real numbers such that x +2x =y +2y ,what is xy ?(A)14(B)12(C)1(D)2(E)49In ABC ,AB =AC =28and BC =20.Points D,E,and F are on sides AB ,BC ,and AC ,respectively,such that DE and EF are parallel to AC and AB ,respectively.What is the perimeter of parallelogram ADEF ?AB CDE F2013(A)48(B)52(C)56(D)60(E)7210Let S be the set of positive integers n for which 1n has the repeating decimal representation0.ab =0.ababab ···,with a and b diﬀerent digits.What is the sum of the elements of S ?(A)11(B)44(C)110(D)143(E)15511Triangle ABC is equilateral with AB =1.Points E and G are on AC and points D and Fare on AB such that both DE and F G are parallel to BC .Furthermore,triangle ADE and trapezoids DF GE and F BCG all have the same perimeter.What is DE +F G ?A BCD EF G(A)1(B)32(C)2113(D)138(E)5312The angles in a particular triangle are in arithmetic progression,and the side lengths are 4,5,x .The sum of the possible values of x equals a +√b +√c where a,b ,and c are positiveintegers.What is a +b +c ?(A)36(B)38(C)40(D)42(E)4413Let points A =(0,0),B =(1,2),C =(3,3),and D =(4,0).Quadrilateral ABCD is cut into equal area pieces by a line passing through A .This line intersects CD at point p q ,r s ,where these fractions are in lowest terms.What is p +q +r +s ?(A)54(B)58(C)62(D)70(E)7514The sequencelog 12162,log 12x ,log 12y ,log 12z ,log 1212502013is an arithmetic progression.What is x ?(A)125√3(B)270(C)162√5(D)434(E)225√615Rabbits Peter and Pauline have three oﬀspringFlopsie,Mopsie,and Cotton-tail.These ﬁverabbits are to be distributed to four diﬀerent pet stores so that no store gets both a parent and a child.It is not required that every store gets a rabbit.In how many diﬀerent ways can this be done?(A)96(B)108(C)156(D)204(E)37216A ,B ,C are three piles of rocks.The mean weight of the rocks in A is 40pounds,the meanweight of the rocks in B is 50pounds,the mean weight of the rocks in the combined piles A and B is 43pounds,and the mean weight of the rocks in the combined piles A and C is 44pounds.What is the greatest possible integer value for the mean in pounds of the rocks in the combined piles B and C ?(A)55(B)56(C)57(D)58(E)5917A group of 12pirates agree to divide a treasure chest of gold coins among themselves asfollows.The k th pirate to take a share takes k 12of the coins that remain in the chest.Thenumber of coins initially in the chest is the smallest number for which this arrangement will allow each pirate to receive a positive whole number of coins.How many coins doe the 12th pirate receive?(A)720(B)1296(C)1728(D)1925(E)385018Six spheres of radius 1are positioned so that their centers are at the vertices of a regularhexagon of side length 2.The six spheres are internally tangent to a larger sphere whose center is the center of the hexagon.An eighth sphere is externally tangent to the six smaller spheres and internally tangent to the larger sphere.What is the radius of this eighth sphere?(A)√2(B)32(C)53(D)√3(E)219In ABC ,AB =86,and AC =97.A circle with center A and radius AB intersects BC atpoints B and X .Moreover BX and CX have integer lengths.What is BC ?(A)11(B)28(C)33(D)61(E)7220Let S be the set {1,2,3,...,19}.For a,b ∈S ,deﬁne a b to mean that either 0<a −b ≤9orb −a >9.How many ordered triples (x,y,z )of elements of S have the property that x y ,y z ,and z x ?(A)810(B)855(C)900(D)950(E)98821Consider A =log(2013+log(2012+log(2011+log(···+log(3+log 2)···)))).Which of thefollowing intervals contains A ?2013(A)(log2016,log2017)(B)(log2017,log2018)(C)(log2018,log2019)(D)(log2019,log2020)(E)(log2020,log2021)22A palindrome is a nonnegatvie integer number that reads the same forwards and backwards when written in base10with no leading zeros.A6-digit palindrome n is chosen uniformly at random.What is the probability that n11is also a palindrome?(A)825(B)33100(C)720(D)925(E)113023ABCD is a square of side length √3+1.Point P is on AC such that AP=√2.The squareregion bounded by ABCD is rotated90◦counterclockwise with center P,sweeping out aregion whose area is1c (aπ+b),where a,b,and c are positive integers and gcd(a,b,c)=1.What is a+b+c?(A)15(B)17(C)19(D)21(E)2324Three distinct segments are chosen at random among the segments whose end-points are the vertices of a regular12-gon.What is the probability that the lengths of these three segments are the three side lengths of a triangle with positive area?(A)553715(B)443572(C)111143(D)81104(E)22328625Let f:C→C be deﬁned by f(z)=z2+iz+1.How many complex numbers z are there such that Im(z)>0and both the real and the imaginary parts of f(z)are integers with absolute value at most10?(A)399(B)401(C)413(D431(E)4412013B1On a particular January day,the high temperature in Lincoln,Nebraska,was16degrees higher than the low temperature,and the average of the high and low temperatures was3◦.In degrees,what was the low temperature in Lincoln that day?(A)−13(B)−8(C)−5(D)3(E)112Mr Green measures his rectangular garden by walking two of the sides andﬁnds that it is15 steps by20steps.Each or Mr Green’s steps is two feet long.Mr Green expect half a pound of potatoes per square foot from his garden.How many pounds of potatoes does Mr Green expect from his garden?(A)600(B)800(C)1000(D)1200(E)14003When counting from3to201,53is the51st number counted.When counting backwards from 201to3,53is the n th number counted.What is n?(A)146(B)147(C)148(D)149(E)1504Ray’s car averages40miles per gallon of gasoline,and Tom’s car averages10miles per gallon of gasoline.Ray and Tom each drive the same number of miles.What is the cars’combined rate of miles per gallon of gasoline?(A)10(B)16(C)25(D)30(E)405The average age of33ﬁfth-graders is11.The average age of55of their parents is33.What is the average age of all of these parents andﬁfth-graders?(A)22(B)23.25(C)24.75(D)26.25(E)286Real numbers x and y satisfy the equation x2+y2=10x−6y−34.What is x+y?(A)1(B)2(C)3(D)6(E)87Jo and Blair take turns counting from1to one more than the last number said by the other person.Jo starts by saying”1”,so Blair follows by saying”1,2”.Jo then says”1,2,3”,and so on.What is the53rd number said?(A)2(B)3(C)5(D)6(E)88Line 1has equation3x−2y=1and goes through A=(−1,−2).Line 2has equation y=1 and meets line 1at point B.Line 3has positive slope,goes through point A,and meets 2 at point C.The area of ABC is3.What is the slope of 3?(A)23(B)34(C)1(D)43(E)3220139What is the sum of the exponents of the prime factors of the square root of the largest perfect square that divides12!?(A)5(B)7(C)8(D)10(E)1210Alex has75red tokens and75blue tokens.There is a booth where Alex can give two red tokens and receive in return a silver token and a blue token,and another booth where Alexcan give three blue tokens and receive in return a silver token and a red token.Alex continuesto exchange tokens until no more exchanges are possible.How many silver tokens will Alexhave at the end?(A)62(B)82(C)83(D102(E)10311Two bees start at the same spot andﬂy at the same rate in the following directions.BeeA travels1foot north,then1foot east,then1foot upwards,and then continues to repeatthis pattern.Bee B travels1foot south,then1foot west,and then continues to repeat thispattern.In what directions are the bees traveling when they are exactly10feet away fromeach other?(A)A east,B west(B)A north,B south(C)A north,B west(D)A up,B south(E)A u 12Cities A,B,C,D,and E are connected by roadsAB,AD,AE,BC,BD,CD,DE.How many diﬀerent routes are there from A to B that use each road exactly once?(Such a routewill necessarily visit cities more than once.)A B CDE(A)7(B)9(C)12(D)16(E)18201313The internal angles of quadrilateral ABCD form an arithmetic progression.Triangles ABD and DCB are similar with∠DBA=∠DCB and∠ADB=∠CBD.Moreover,the angles in each of these two triangles also form an arithmetic progression.In degrees,what is the largest possible sum of the two largest angles of ABCD?(A)210(B)220(C)230(D240(E)25014Two non-decreasing sequences of nonnegative integers have diﬀerentﬁrst terms.Each se-quence has the property that each term beginning with the third is the sum of the previous two terms,and the seventh term of each sequence is N.What is the smallest possible value of N?(A)55(B)89(C)104(D144(E)27315The number2013is expressed in the form2013=a1!a2!···a m! b1!b2!···b n!,where a1≥a2≥···≥a m and b1≥b2≥···≥b n are positive integers and a1+b1is as small as possible.What is|a1−b1|?(A)1(B)2(C)3(D4(E)516Let ABCDE be an equiangular convex pentagon of perimeter1.The pairwise intersections of the lines that extend the side of the pentagon determine aﬁve-pointed star polygon.Let s be the perimeter of the star.What is the diﬀerence between the maximum and minimum possible perimeter of s?(A)0(B)12(C)√5−12(D)√5+12(E)√517Let a,b,and c be real numbers such thata+b+c=2,anda2+b2+c2=12What is the diﬀerence between the maximum and minimum possible values of c?(A)2(B)103(C)4(D)163(E)20318Barbara and Jenna play the following game,in which they take turns.A number of coins lie on a table.When it is Barbara’s turn,she must remove2or4coins,unless only one coin remains,in which case she loses her turn.When it is Jenna’s turn,she must remove1or3 coins.A coinﬂip determines who goesﬁrst.Whoever removes the last coin wins the game.Assume both players use their best strategy.Who will win when the game starts with2013 coins and when the game starts with2014coins?2013(A)Barbara will win with 2013coins,and Jenna will win with 2014coins.(B)Jenna will win with 2013coins,and whoever goes ﬁrst will win with 2014coins.(C)Barbara will win with 2013coins,and whoever goes second will win with 2014coins.(D)Jenna will win with 2013coins,and Barbara will win with 2014coins.(E)Whoever goes ﬁrst will win with 2013coins,and whoever goes second will win with 2014coins.19In triangle ABC ,AB =13,BC =14,and CA =15.Distinct points D ,E ,and F lie on segments BC ,CA ,and DE ,respectively,such that AD ⊥BC ,DE ⊥AC ,and AF ⊥BF .The length of segment DF can be written as m n ,where m and n are relatively prime positive integers.What is m +n ?(A)18(B)21(C)24(D 27(E)3020For 135◦<x <180◦,points P =(cos x,cos 2x ),Q =(cot x,cot 2x ),R =(sin x,sin 2x )andS =(tan x,tan 2x )are the vertices of a trapezoid.What is sin(2x )?(A)2−2√2(B)√3−6(C)3√2−5(D −34(E)1−√321Consider the set of 30parabolas deﬁned as follows:all parabolas have as focus the point(0,0)and the directrix lines have the form y =ax +b with a and b integers such that a ∈{−2,−1,0,1,2}and b ∈{−3,−2,−1,1,2,3}.No three of these parabolas have a common point.How many points in the plane are on two of these parabolas?(A)720(B)760(C)810(D 840(E)87022Let m >1and n >1be integers.Suppose that the product of the solutions for x of theequation8(log n x )(log m x )−7log n x −6log m x −2013=0is the smallest possible integer.What is m +n ?(A)12(B)20(C)24(D 48(E)27223Bernardo chooses a three-digit positive integer N and writes both its base-5and base-6representations on a ter LeRoy sees the two numbers Bernardo has written.Treating the two numbers as base-10integers,he adds them to obtain an integer S .For example,if N =749,Bernardo writes the numbers 10,444and 3,245,and LeRoy obtains the sum S =13,689.For how many choices of N are the two rightmost digits of S ,in order,the same as those of 2N ?(A)5(B)10(C)15(D 20(E)2524Let ABC be a triangle where M is the midpoint of AC ,and CN is the angle bisector of∠ACB with N on AB .Let X be the intersection of the median BM and the bisector CN .In addition BXN is equilateral and AC =2.What is BN 2?(A)10−6√27(B)29(C)5√2−3√38(D)√26(E)3√3−45.201325Let G be the set of polynomials of the formP(z)=z n+c n−1z n−1+···+c2z2+c1z+50,where c1,c2,···,c n−1are integers and P(z)has n distinct roots of the form a+ib with a andb integers.How many polynomials are in G?(A)288(B)528(C)576(D992(E)1056The problems on this page are copyrighted by the Mathematical Association of America’s American Mathematics Competitions.。