USA-AMC_8-2007-42

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AMCA-210-2007

-Refined the conversion from in. wg to Pa, which necessitated small but important changes in the constants used in I-P equations
Authority
ANSI/AMCA 210 - ANSI/ASHRAE 51 was approved by the membership of the Air Movement and Control Association on July 28, 2006 and by ASHRAE on March 17, 2008. It was approved by ANSI and became an American National Standard on August 17, 2007.
Air Movement and Control Association International 30 West University Drive Arlington Heights, IL 60004-1893 U.S.A.
or
AMCA International, Incorporated c/o Federation of Environmental Trade Associations 2 Waltham Court, Milley Lane, Hare Hatch Reading, Berkshire RG10 9TH United Kingdom
© 2008 by the Air Movement and Control Association International, Inc. and the American Society of Heating, Refrigerating, and Air Conditioning Engineers

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

2006年AMC8试题答案

This Solutions Pamphlet gives at least one solution for each problem on this year’s exam and shows that all the problems can be solved using material normally as-sociated with the mathematics curriculum for students in eighth grade or below. These solutions are by no means the only ones possible, nor are they necessarily superior to others the reader may devise.We hope that teachers will share these solutions with their students. However, the publication, reproduction, or communication of the problems or solutions of the AMC 8 during the period when students are eligible to participate seriously jeopardizes the integrity of the results. Dissemination at any time via copier, telephone, e-mail, World Wide Web or media of any type is a violation of the competition rules.Correspondence about the problems and solutions should be addressed to:Ms. Bonnie Leitch , AMC 8 Chair / bleitch@548 Hill Avenue, New Braunfels, TX 78130Orders for prior year Exam questions and Solutions Pamphlets should be addressed to:Attn: Publications American Mathematics Competitions University of Nebraska-Lincoln P .O. Box 81606Lincoln, NE 68501-1606Copyright © 2006, The Mathematical Association of AmericaT he M aTheMaTical a ssociaTion of a MericaAmerican Mathematics Competitions 22nd AnnualAMC 8(American Mathematics Contest 8)Solutions PamphletTuesday, NOVEMBER 14, 20061.(D)Mindy’s total was approximately 2+5+10=$17.2.(C)On the AMC 8a student’s score is the number of problems answered cor-rectly.So Billy’s score is 13.Because there is no penalty for guessing,if he wants to increase his score,he probably should ﬁll in the last ﬁve answers.3.(A)When Elisa started,she completed a lap in 2510=2.5minutes.Now she cancomplete a lap in 2412=2minutes.She has improved her lap time by 2.5−2=0.5or 12minute.4.(B)Ignore the number of complete revolutions because they do not aﬀect direc-tion.One-fourth of the distance around the circle clockwise from west is north.Three-fourths of the distance counterclockwise around the circle from north is east.Chenille’s spinner points east.5.(D)Divide the larger square into 8congruent triangles,as shown,4of which make up the smaller square.ABD The area of the smaller square is 48or 12of the area of the larger square,so thearea of the smaller square is equal to 30.6.(C)11422442The perimeter is 4+2+1+4+2+4+1+2=20inches.OREach rectangle has perimeter =2l +2w =2(4)+2(2)=8+4=12inches.When the two rectangles are positioned to form the T,a two-inch segment of each rectangle is inside the T and is not on the perimeter of the T.So the perimeter of the T is 2(12)−2(2)=24−4=20inches.7.(B)Because circumference C =2πr and circle Y has circumference 8π,itsradius is 8π2π=4.Because area A =πr 2and circle Z has area 9π,its radius is √9=3.Ordering the radii gives 3<π<4,so the circles in ascending order ofradii length are Z ,X and Y .8.(E)Because 200−96=104of those surveyed were male,104−26=78of those surveyed are male listeners.Listen Don’t Listen Total Male7826104Female583896Total 13664200The percentage of males surveyed who listen to KAMC is 78104×100%=75%.9.(C)Note that in each fraction,the numerator is the same as the denominatorin the next fraction,so they divide.The product of ¡32×¡4¡3×¡5¡4×...×2006$$$2005=20062=1003.10.(A)When the area of a rectangle is 12square units and the sides are integers,the factors of 12are the possible lengths of the sides.In point form,the side lengths could be (1,12),(2,6),(3,4),(4,3),(6,2)and (12,1).Only graph A ﬁts these points.11.(C)The sum of the digits of a two-digit number is at most 9+9=18.Thismeans the only possible perfect square sums are 1,4,9and 16.Each square has the following two-digit possibilities:1:104:40,31,22,139:90,81,72,63,54,45,36,27,1816:97,88,79There are 17two-digit numbers in all.12.(D)Note that 70%of 10is 7,80%of 20is 16and 90%of 30is 27.Antonetteanswers 7+16+27=50problems correctly out of 60problems in all.Her overall score is 5060or 83.3%.13.(D)Between 8:30and 9:00AM Cassie travels 6miles.At 9:00Cassie and Brianare only 56miles apart.After 9:00,because they are both biking towards each other,the distance between them decreases at the rate of 12+16=28miles per hour.At that rate,it will take them 5628=2hours to meet.So they will meetat 11:00AM.14.(B)Bob takes 45−30=15more seconds per page than Chandra.So thediﬀerence in their total reading times is 760·15=11,400seconds.Bob will spend 11,400more seconds reading than Chandra.15.(C)The ratio of time it takes Bob to read a page to the time it takes Chandrato read a page is45:30or3:2,so Bob should read23of the number of pagesthat Chandra reads.Divide the book into5parts,each with7605=152pages.Chandra will read theﬁrst3·152=456pages,while Bob reads the last2·152= 304pages.ORIf Chandra reads x pages,she will read for30x seconds.Bob has to read760−x pages,and this takes him45(760−x)seconds.Because Chandra and Bob read the same amount of time,30x=45(760−x).Solving for x,30x=45·760−45x,75x=45·760,x=45·76075=456.So Chandra will read theﬁrst456pages.16.(E)The least common multiple of20,45and30is22·32·5=ing theLCM,in180seconds Alice reads18020=9pages,Chandra reads18030=6pagesand Bob reads18045=4pages.Together they read a total of19pages in180seconds.The total number of seconds each reads is76019·180=7200.17.(B)Because the sum of a number from spinner Q and a number from spinner Ris always odd,the sum of the numbers on the three spinners will be odd exactly when the number from spinner P is even.Because2is the only even number onspinner P,the probability of getting an odd sum is13.18.(D)Four black andﬁve white squares are visible on each of the six faces of thecube.So59of the surface will be white.19.(D)Because triangles ABD and ECD are congruent and triangle ABC isisosceles,EC=AB=BC=11.That means BD=112or5.5.20.(C)Each of the six players played5games,and each game involved two players.So there were6·52=15games.Helen,Ines,Janet,Kendra and Lara won a totalof4+3+2+2+2=13games,so Monica won15−13=2games.21.(A)Using the volume formula lwh=V,the volume of water in the aquariumis100×40×37=148,000cm3.When the rock is put in,the water and the rock will occupy a box-shaped region with volume148,000+1000=149,000cm3.The volume of the water and the rock is100×40×h,where h is the new height of the water.The new volume=4000h=149,000cm3,so the new height ish=1490004000=37.25cm.After adding the rock,the water rises37.25−37=0.25cm.ORBecause the shape of the rock is irrelevant,we may assume that the rock is shaped like a rectangular box with base measuring100cm×40cm and height hing the volume formula,100×40×h=1000,so h=1000100×40=0.25cm.When the rock is put into the aquarium,the water level will rise by0.25cm.22.(D)If the lower cells contain A,B and C,then the second row will containA+B and B+C,and the top cell will contain A+2B+C.To obtain the smallest sum,place1in the center cell and2and3in the outer ones.The top number will be7.For the largest sum,place9in the center cell and7and8in the outer ones.This top number will be33.The diﬀerence is33−7=26. 23.(A)The counting numbers that leave a remainder of4when divided by6are4,10,16,22,28,34,....The counting numbers that leave a remainder of3when divided by5are3,8,13,18,23,28,33,....So28is the smallest possible number of coins that meets both conditions.Because4×7=28,there are no coins left when they are divided among seven people.ORIf there were two more coins in the box,the number of coins would be divisible by both6and5.The smallest number that is divisible by6and5is30,so the smallest possible number of coins in the box is28.24.(A)We can decompose CDCD into CD×100+CD=CD(101).That meansthat A=1and B=0.The sum is1+0=1.25.(B)There are one odd and two even numbers showing.Because all primesother than2are odd and the sum of an even number and an odd number is odd,the common sum must be odd.That means2must be opposite59and the common sum is2+59=61.The other two hidden numbers are61−44=17and61−38=23.The average of2,17and23is2+17+233=423=14.TheAmerican Mathematics Competitionsare Sponsored byThe Mathematical Association of AmericaThe Akamai FoundationContributorsAmerican Mathematical Association of Two Year CollegesAmerican Mathematical SocietyAmerican Society of Pension ActuariesAmerican Statistical AssociationArt of Problem SolvingCanada/USA MathcampCanada/USA MathpathCasualty Actuarial SocietyClay Mathematics InstituteConsortium for Mathematics & its ApplicationsInstitute for Operations Research and the Management SciencesL. G. Balfour CompanyMu Alpha ThetaNational Council of Teachers of MathematicsNational Assessment & TestingPedagoguery Software Inc.Pi Mu EpsilonSociety of ActuariesU.S.A. Math Talent SearchW. H. Freeman and CompanyWolfram Research Inc.。

多模式光谱稳定激光模块说明书

Multimode Spectrum Stabilized Laser Module Series − Lab VersionsInstallation and Operation Manual Document Number LASER-785-LAB-02-0409Office: 830 Douglas Ave., Dunedin, FL, USA 34698 Phone 727.733.2447 Fax 727.733.3962 8 a.m.– 8 p.m. (Mon-Thu), 8 a.m.– 6 p.m. (Fri) EST E-mail:********************(General sales inquiries) **********************(Questions about orders) ***************************(Technical support)WARNING Protective Eye Wear Should Be Worn When Using This Instrument - Intense Radiation Present See Important Safety Notices inside.AdditionalOffices: 666 Gubei Road, Kirin Tower, Suite 601B, Changning District,Shanghai, PRC. 200336Phone 86.21.5206.8686Fax 86.21.5206.8686******************************Sales and Support CenterGeograaf 24, 6921 EW DUIVEN, The NetherlandsPhone 31-26-3190500Fax 31-26-3190505E-Mail **********************Regional HeadquartersMaybachstrasse 1173760 OstfildernPhone 49-711 34 16 96-0Fax 49-711 34 16 96-85E-Mail ******************Copyright © 2009 Ocean Optics, Inc.All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, by any means, electronic, mechanical, photocopying, recording, or otherwise, without written permission from Ocean Optics, Inc.This manual is sold as part of an order and subject to the condition that it shall not, by way of trade or otherwise, be lent, re-sold, hired out or otherwise circulated without the prior consent of Ocean Optics, Inc. in any form of binding or cover other than that in which it is published. TrademarksMicrosoft, Windows, Windows 95, Windows 98, Windows Me, Windows NT, Windows 2000, Windows XP and Excel are either registered trademarks or trademarks of Microsoft Corporation.Limit of LiabilityEvery effort has been made to make this manual as complete and as accurate as possible, but no warranty or fitness is implied. The information provided is on an “as is” basis. Ocean Optics, Inc. shall have neither liability nor responsibility to any person or entity with respect to any loss or damages arising from the information contained in this manual.Important Safety Notices The Class IIIB laser described here produces a laser emission of 785 nm with output power levels exceeding 350 mW. All models except the –S are designed to be used in a fiber-coupled configuration (-S is designed for SMA coupling); any other configuration may expose the user to hazardous radiation.This laser is safe to operate, provided the user pays attention to all safety warnings:1.Post warnings in the area of the laser beam to alert those present.2.Keep all unauthorized personnel out of the area where the laser is operated to avoid potentiallyhazardous exposure to eyes and skin.3.Whenever the laser is running and the beam is not in use, it is good operating practice tomechanically block the path.4.Never look directly into the laser source or scattering laser light from any reflective surface.Never sight down the beam into the source.5.Maintain experimental setup at low heights to prevent inadvertent beam-eye contact.6.As a precaution against accidental exposures to the output beam or its reflection, operators shouldwear laser safety glasses attenuated to the wavelength being generated.Important Safety NoticesSources for additional information and assistance on laser safety are the following: Center for Device and Radiological HealthOffice of Compliance2098 Gaither Rd.Rockville, MD 20850Tel: 301 594 4654Fax: 301 594 4672Laser Institute of America12424 Research Parkway, Suite 125Orlando, FL 32826Tel: 407 380 1553Fax: 407 380 5588Table of Contents About This Manual (iii)Document Purpose and Intended Audience (iii)Document Summary (iii)Product-Related Documentation (iii)Upgrades (iii)Chapter 1: Introduction (1)Overview (1)Lab Version Models (2)Features (2)Package Contents (3)Additional Equipment Required (3)Chapter 2: Set-up and Operation (5)Overview (5)Set-up (5)Set-up for Operation in Internal Power Preset Mode (6)Set-up for Operation to Control Power Through the Front Panel (7)Set-up for Operation in External Power Control Mode (8)Operation (8)Operation in Internal Power Preset Mode (8)Operation Controlling Power Through the Front Panel (9)Operation in External Power Control Mode (10)Using the Remote Interlock Feature (10)Shutting Down the Laser (11)Index (13)Table of ContentsAbout This ManualDocument Purpose and Intended AudienceThis document provides you with information to get your laser set up and operating. Document SummaryChapter DescriptionChapter 1: Introduction Contains a list of product features and packagecontents.Chapter 2: Set-up and Operation Provides instructions for setting up and operating thelaser.Product-Related Documentation•Multimode Spectrum Stabilized Laser Subsystem Installation and Operation ManualYou can access documentation for Ocean Optics products by visiting our website at. Select Technical → Operating Instructions, then choose the appropriate document from the available drop-down lists. Or, use the Search by Model Number field at the bottom of the web page.You can also access operating instructions for Ocean Optics products on the Software and Technical Resources CD included with the system.Engineering-level documentation is located on our website at Technical → Engineering Docs. UpgradesOccasionally, you may find that you need Ocean Optics to make a change or an upgrade to your system. To facilitate these changes, you must first contact Customer Support and obtain a Return Merchandise Authorization (RMA) number. Please contact Ocean Optics for specific instructions when returning a product.About This ManualChapter 1IntroductionOverviewThe Multimode Spectrum Stabilized Laser Subsystem Series – Lab Versions consists of three models of continuous wave lasers designed specifically for Raman spectroscopy (see Lab Version Models). These laser models feature an internal 350 mW spectrum stabilized laser module that contains an integral Thermo-Electric Cooler (TEC) and thermistor for monitoring the internal temperature of the laser platform. The laser has narrow spectral lines, is compact and features a hermetically sealed laser component, making it optimal for industrial and medical applications.The unit comes complete with a laser-enable switch for safety, a safety key lockout, and an emergency shut-off switch.Multimode Spectrum Stabilized Laser Subsystem1: IntroductionSpectral Output Captured with HR4000 SpectrometerLab Version ModelsThis document covers the installation and operation of the following laser models:•LASER-785-IP-LAB − 785 nm spectrum stabilized multi-mode laser with > 350mW of fiber-coupled output power•LASER-785-LAB-ADJ − 785 nm spectrum stabilized multi-mode laser with > 350mW of fiber-coupled, adjustable output power. Also features an LED display and an output power control dial.•LASER-785-IP-ADJ-S − 785 nm spectrum stabilized multi-mode laser with > 350mW of SMA-coupled, adjustable output power. Also features an LED display and an output power control dial. In addition, the LASER-785-IP-OEM laser is available. This is a single-mode laser with >350mW of fiber-coupled output power. This version is documented in the Multimode Spectrum Stabilized Laser Subsystem Installation and Operation Manual. See Product-Related Documentation for more information.FeaturesThe laser provides the following features:•>350 mW Fiber Coupled or SMA-coupled (-S model) Output Power•Narrow Spectral Line width of only 0.2 nm•Thermo-Electric Cooler (TEC)•Low Power consumption (< 5.5 W)1: Introduction •Remote Interlock, Safety Key Lock-out and Emergency shut-off•LED display for output power setting (Models LASER-785-LAB-ADJ and LASER-785-LAB-ADJ-S only)•Output power control dial (Models LASER-785-LAB-ADJ and LASER-785-LAB-ADJ-S only) Package ContentsOne (1) Ocean Optics Multimode Stabilized LaserOne (1) ThermistorOne (1) power cordTwo (2) Master Power keysOne (1) remote plugAdditional Equipment RequiredThe following equipment, available from Ocean Optics, is also required to use your laser: Safety goggles (R-2001-GL goggles from Ocean Optics are recommended)1: IntroductionChapter 2Set-up and OperationOverviewThis section provides instructions for setting up and operating the laser. Read all instructions and warnings carefully before attempting to install and operate your laser.Set-upThe laser set-up procedure differs, depending on whether you are going to control the output power automatically via the Internal Preset mode (Model LASER-785-IP-LAB), manually through the unit’s front panel (Models LASER-785-LAB-ADJ and LASER-785-LAB-ADJ-S), or remotely (all models).Laser Rear Panel View2: Set-up and OperationSet-up for Operation in Internal Power Preset ModeUse these set-up instructions for the Internal Power Preset mode (Model LASER-785-IP-LAB).►Procedure1.Make sure that the master Power key is in the vertical (“Off’) position.2.Connect the 120V AC power plug to the power connector on the rear of the unit.3.Plug the other end of the power cord into a standard 110/120V electrical outlet.4.Connect a FC/PC Multi-mode fiber patch cord to the FC/PC bulkhead connector on the frontpanel of the unit.5.Note that this laser is configured with a remote interlock on the rear panel. The laser has an RJ-11(4-pin telephone jack) that is prewired to provide a closed loop connection for the interlock.Removal of the RJ-11 connector or a break in the closed loop circuit provided will result in alaser interrupt and the system will be reset to standby mode. You can reconfigure the RJ-11connector to provide a closed loop that interactively couples with their system or facility byreplacing the short length of wire with longer closed loop connections, if desired.6.Ensure that the Emergency Shut-off switch (EMO) is in the “ready” position by turning the redbutton clockwise until it pops out slightly.7.You are now ready to turn on the laser module. Go to Operation in Internal Power Preset Mode.2: Set-up and Operation Set-up for Operation to Control Power Through the Front PanelUse these set-up instructions when you want to control the laser power through the unit’s front panel (Models LASER-785-LAB-ADJ and LASER-785-LAB-ADJ-S).►Procedure1.Make sure that the master Power key is in the vertical (“Off’) position.2.Connect the 120V AC power plug to the power connector on the rear of the unit.3.Plug the other end of the power cord into a standard 110/120V electrical outlet.4.Connect an SMA 905 connectorized multi-mode fiber patch cord to the SMA bulkhead connectoron the front panel of the unit.5.Note that this laser is configured with a remote interlock on the rear panel. The laser has an RJ-11(4-pin telephone jack) that is prewired to provide a closed loop connection for the interlock.Removal of the RJ-11 connector or a break in the closed loop circuit provided will result in alaser interrupt and the system will be reset to Standby mode. You can reconfigure the RJ-11connector to provide a closed loop that interactively couples with their system or facility byreplacing the short length of wire with longer closed loop connections, if desired.6.Ensure that the Emergency Shut-off switch (EMO) is in the “ready” position by turning the redbutton clockwise until it pops out slightly.7.You are now ready to turn on the laser module. Go to Operation Controlling Power Through theFront Panel.2: Set-up and OperationSet-up for Operation in External Power Control ModeThe Model LASER-785-IP-LAB laser is designed for operation in the Internal Power Preset mode and the Models LASER-785-LAB-ADJ and LASER-785-LAB-ADJ-S are designed for operation through their front panel controls. However, the laser provides you with the capability (via an external port on the back panel) of adjusting the power remotely via computer or signal generator in External Power Control mode. Use these set-up instructions for the External Power Control mode. See for Operation in External Power Control Mode operation instructions in this mode.►Procedure1.Make sure that the laser power is not operating by pressing the Laser On switch and assuring thatthe Laser On LED on the front panel is not lit.2.Set the Mode Selection switch on the rear panel to External (the amber Operating Mode LEDwill light).3.Connect a BNC cable to the Control port on the rear panel.4.Go to Operation in External Power Control Mode to operate the laser in External Power Controlmode.OperationRead the following warning before attempting to use the laser:WARNINGSDO NOT LOOK DIRECTLY INTO THE LASER. LASER RADIATION ISHAZARDOUS TO THE EYES.AVOID DIRECT EXPOSURE TO THE BEAM.Operation in Internal Power Preset ModeUse this procedure to operate the Model LASER-785-IP-LAB laser in the Internal Power Preset mode.►Procedure1.Turn the master Power key (on the rear panel) 90 degrees clockwise to the horizontal “ON”position. The green System Power LED (on the front panel) lights indicating that system power is on.2: Set-up and Operation2.Push the Laser On switch (on the front panel). The red LED on the front panel lights to indicatethat the laser is in operation. The laser turns on approximately 2 seconds after the switch ispressed.NoteNote that the switch returns to the center position after you press it. At this point, it canfunction as a manual reset.3.In the event of a power interruption, power failure or interlock break, the laser is automaticallydisabled. To re-enable it, toggle the Laser On switch to back to the ON position. Operation Controlling Power Through the Front PanelUse this procedure to control the laser power through the unit’s front panel (Models LASER-785-LAB-ADJ and LASER-785-LAB-ADJ-S).►Procedure1.Turn the master Power key (on the rear panel) 90 degrees clockwise to the horizontal “ON”position. The green System Power LED (on the front panel) lights indicating that system power is on.2.Turn the laser adjustment dial on the front panel to the desired drive current setting. The setting isdisplayed on the front panel LED.3.Push the Laser On switch (on the front panel). The red LED on the front panel lights to indicatethat the laser is in operation. The laser turns on approximately 2 seconds after the switch ispressed.2: Set-up and OperationNoteNote that the switch returns to the center position after you press it. At this point, it canfunction as a manual reset.4.In the event of a power interruption, power failure or interlock break, the laser is automaticallydisabled. To re-enable it, toggle the Laser On switch to back to the ON position.Operation in External Power Control ModeThe Multimode Spectrum Stabilized Laser provides the capability of adjusting the power remotely via computer or signal generator in External Power Control mode. Use the following procedure: ►Procedure1.Make sure that a BNC cable is connected to the Control port on the rear panel as described in Set-up for Operation in External Power Control Mode.2.Apply a DC bias between 0 (zero power) and 1 (full power) Volt to modulate the laser or toadjust the laser’s output power. The unit can be modulated at rates up to approximately 300 KHz.3.Push the Laser On switch (on the front panel). The laser then outputs a variable amount if outputpower dependent on the DC bias voltage that has been applied to the Control port on the rearpanel.Using the Remote Interlock FeatureThe Remote Interlock is a safety feature that automatically shuts down the laser when a trigger such as a door or an enclosure opening occurs. You may decide to enable a remote interlock mechanism when integrating the laser into a laboratory or system environment.The interlock is located on the rear panel and uses an RJ-11 plug. The Remote Interlock is normally an open circuit, so the provided RJ-11 connector or a user-configured closed loop interconnect MUST be in place for proper function of the laser module. To enable the Remote Interlock, you must obtain an RJ-11 plug (or modify the plug provided) and create a closed circuit between the two signal terminals of the plug and insert the closed-circuit RJ-11 plug into the Interlock jack.The laser functions normally when is senses a closed circuit, but it will disable laser output when it detects an open circuit. To re-enable the laser function, you must make sure that the interlock is a closed circuit, and then manually reset the laser by toggling the Laser On switch on the front panel to the ON position.2: Set-up and Operation Shutting Down the LaserUse the following procedure when you are finished using the laser and need to shut it down.►Procedure1.Push the Laser On toggle switch (on the front panel) to turn the laser off. Make sure that theLaser On LED goes off.2.Turn the master Power key (on the rear panel) 90 degrees to the vertical “off” position. The greenSystem Power LED (on the front panel) goes off indicating that system power is off.3.Disconnect the fiber or SMA cords and power cable as needed.2: Set-up and OperationIndexCControl Power Through Front Panel set-up, 7Controlling Power Through the Front Panel operation, 9Ddocumentaudience, iiipurpose, iiisummary, iiiEequipmentrequired, 3External PowCOntrol modeoperation, 10External Power Control modeset-up, 8Ffeatures, 2IInternal Power Preset modeoperation, 8set-up, 6introduction, 1Mmanual operationset-up, 6, 7, 9models, 2Ooperation, 8Controlling Power Through the Front Panel, 9 Extarnal Power Control mode, 10Internal Power Preset mode, 8Ppackage contents, 3product-related documentation, iiiRrear panel, 5Remote Interlock, 10remote operationset-up, 8required equipment, 3Sset-up, 5Control Power Through Front Panel, 7External Power Control mode, 8Internal Power Preset mode, 6manual operation, 6, 7, 9remote operation, 8shut down, 11spectral output, 2Uupgrades, iiiIndex。

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。

美国AMC第8届数学竞赛_(2005)

2005年全美中学数学分级能力测验- - AMC8中文试题与参考答案一、21st AMC8 2005中文试题1.小妮将一数乘以2得到60. 不过，她应当将这个数除以2才会得到正确的答案。

正确的答案应该是多少？(A) 7.5 (B) 15 (C) 30 (D) 120 (E) 2402.卡尔某天在文具店买了每个美金$2.5元的资料夹5个. 这个文具店在卡尔买后的隔天降价20%. 假如卡尔多等一天才买, 问他可以节省多少元？(A) $1.00 (B) $2.00 (C) $2.50 (D) $2.75 (E) $5.003.至少要将下图正方形ABCD中多少个空白的小正方形涂黑后, 才可以使得着色后的图形是对称于对角线BD？(A) 1 (B) 2 (C) 3 (D) 4 (E) 54.一个正方形与一个三角形的周长相等. 三角形的三边长分别为6.1公分、8.2公分及9.7公分. 此正方形的面积是多少平方公分？(A) 24 (B) 25 (C) 36 (D) 48 (E) 645.汽水有以6罐一捆、12罐一捆及24罐一捆三种包装方式出售. 至少要买多少捆才会刚好买到90罐汽水？(A) 4 (B) 5 (C) 6 (D) 8 (E) 156. 设d 是一位数字. 有多少个数值d 可以使得2.00d 5>2.005？ (A) 0 (B) 4 (C) 5 (D) 6 (E) 107. 小明先往南走了12公里, 再往东走了34公里, 最后再往南走了12公里. 小明从出发点到最后停止点的直线距离是多少公里？ (A) 1 (B) 114 (C) 112 (D) 314(E) 28. 设m 及n 为正奇数. 下列哪一个也是奇数？(A) 3m n + (B) 3m n - (C) 2233m n + (D) 2(3)nm + (E) 3mn9. 在四边形ABCD 中, 边AB 及BC 的长均为10, 边CD 及DA 的长均为17, 且角ADC ∠为60︒. 对角线AC 的长是多少？(A) 13.5 (B) 14 (C) 15.5 (D) 17 (E) 18.510. 小乔从他家到学校已经走了一半的距离时发现会迟到. 于是, 后半段路程他用跑的, 他跑的速度是走的速度的3倍. 小乔花了6分钟从他家走到学校一半的路程. 从家到学校他共花了多少分钟？ (A) 7 (B) 7.3 (C) 7.7 (D) 8 (E) 8.311.某百货公司售货需外加6%的货物税. 此百货公司外套专柜减价期间, 一件美金$90元的外套减价20%. 杰克与比尔两位店员各自独力计算账单. 杰克是先将$90元加上6%的税金, 再将此所得的金额减去20%. 比尔是先将$90元减少20%, 再将此所得的金额加上6%的税金. 杰克最后所得的结果减去比尔最后所得的结果是多少元？(A) -$1.06 (B) -$0.53 (C) $0 (D) $0.53 (E) $1.0612.大猩猩艾尔从5月1日到5月5日共吃了100根香蕉. 牠每天都比前一天多吃6根香蕉. 艾尔在5月5日吃了多少根香蕉？(A) 20 (B) 22 (C) 30 (D) 32 (E) 3413.如图, 多边形ABCDEF的面积为52, 其中8BC=,AB=, 9 FA=.5问DE EF+是多少？(A) 7 (B) 8 (C) 9 (D) 10 (E) 1114.由十二支篮球队组成的小联盟分成两区, 每区各有六支球队. 每队与自己区内的其它球队各赛两场, 与另一区的每支球队各赛一场. 这个小联盟要安排多少场球赛?(A) 80 (B) 96 (C) 100 (D) 108 (E) 19215.有多少种不同的等腰三角形, 它们的边长都是整数且周长是23？(A) 2 (B) 4 (C) 6 (D) 9 (E) 1116. 马丁是有5只脚的火星人, 他的抽屉内装满了袜子, 袜子都是红色、白色或蓝色, 且每种颜色的袜子至少有5只. 每次马丁都是不看地任意拿出一只袜子. 马丁必须要从抽屉中拿出多少只袜子, 才可以保证有5只相同颜色的袜子？(A) 6 (B) 9 (C) 12 (D) 13 (E) 1517. 越野田径队跑步训练的成绩, 所用时间与跑的距离之关系如下图. 哪一位学生的平均速率最快？(A) 安祺 (B) 筱蕙 (C) 宗浩 (D) 婉琪 (E) 大维18. 有多少个三位数可被13整除？ (A) 7 (B) 67 (C) 69 (D) 76 (E) 7719. 图中梯形ABCD 的周长是多少？(A) 180 (B) 188 (C) 196 (D) 200 (E) 204A20. 小明和小华在一个用12个点将圆周等分好的圆周上, 在这些点上玩移动的游戏. 这些点按顺时针的方向从1号标到12号. 两人都从12号开始. 小明和小华分别依顺时针和逆时针方向移动. 每回小明走5步, 小华走9步(每走一步, 表示移动一个点的距离). 当两人停在同一点上时游戏结束. 从开始到结束共进行了几回？(A) 6 (B) 8 (C) 12 (D) 14 (E) 2421. 顶点都是用下图中之点的三角形有多少个？(A) 9 (B) 12 (C) 18 (D) 20 (E) 2422. 某公司卖三种不同大小盒子装的清洁剂：小盒(S)、中盒(M)及大盒(L). 中盒比小盒价格贵小盒价格的50%, 而所装的清洁剂比大盒少大盒容量的20%. 大盒所装的清洁剂是小盒的两倍, 而比中盒价格贵中盒价格的30%. 这三种盒装, 依购买者而言, 按照最划算到最不划算的顺序排列是什么？ (A) SML (B) LMS (C) MSL (D) LSM (E) MLS23. 如图所示, 等腰直角三角形ABC 内部包含一个面积2π的半圆. 此半圆的圆心O 在斜边AB 上且和AC 及BC 相切. 三角形ABC 的面积是多少？ (A) 6 (B) 8 (C) 3π (D) 10 (E) 4π24. 某计算器只有[1+]及[2⨯]两个按键. 当你按其中一个键时, 计算器会自动显示结果. 例如：计算器原来显示的是“9”, 你按[1+], 它会显示“10”. 如果你再按[2⨯], 它会显示“20”. 若开始显示的是“1”, 最少需按几次键才会显示“200”？ (A) 8 (B) 9 (C) 10 (D) 11 (E) 1225. 如图所示, 正方形的边长为2且与圆有相同的中心. 圆的内部和正方形外部所围区域面积的总和, 与圆的外部和正方形内部所围区域面积的总和相等. 圆的半径是多少？(A)(B)(C) 32(D) (E)二、21st。

2004年AMC8试题(英)20

INSTRUCTIONS 1.DO NOT OPEN THIS BOOKLET UNTIL YOUR PROCTOR TELLS YOU.2.This is a twenty-five question multiple choice test. Each question is followed by answers marked A, B, C, D and E. Only one of these is correct.3. Mark your answer to each problem on the AMC 8 Answer Form with a #2 pencil. Check the blackened circles for accuracy and erase errors and stray marks completely. Only answers properly marked on the answer form will be graded.4. There is no penalty for guessing. Your score on this test is the number of correct answers.5. No aids are permitted other than scratch paper, graph paper, rulers, erasers, and calculators that are accepted for use on the SAT. No problems on the test will require the use of a calculator.6. Figures are not necessarily drawn to scale.7. Before beginning the test, your proctor will ask you to record certain informa-tion on the answer form.8. When your proctor gives the signal, begin working on the problems. You will have 40 minutes to complete the test.9.When you finish the exam, sign your name in the space provided on the Answer Form.The Committee on the American Mathematics Competitions reserves the right to re-examine students before deciding whether to grant official status to their scores. The Committee also reserves the right to disqualify all scores from a school if it determines that the required security procedures were not followed.The publication, reproduction or communication of the problems or solutions of the AMC 8 during the period when students are eligible to participate seriously jeopardizes the integrity of the results. Duplication at any time via copier, telephone, e-mail, World Wide Web or media of any type is a violation of the competition rules.T he M aTheMaTical a ssociaTion of a MericaAmerican Mathematics Competitions 20th AnnualAMC 8(American Mathematics Contest 8)Tuesday, NOVEMBER 16, 20041.On a map,a12-centimeter length represents72kilometers.How many kilome-ters does a17-centimeter length represent?(A)6(B)102(C)204(D)864(E)12242.How many diﬀerent four-digit numbers can be formed by rearranging the fourdigits in2004?(A)4(B)6(C)16(D)24(E)813.Twelve friends met for dinner at Oscar’s Overstuﬀed Oyster House,and eachordered one meal.The portions were so large,there was enough food for18 people.If they share,how many meals should they have ordered to have just enough food for the12of them?(A)8(B)9(C)10(D)15(E)18The following information is needed to solve problems4,5and6.Ms.Hamilton’s eighth-grade class wants to participate in the an-nual three-person-team basketball tournament.nce,Sally,Joy and Fred are chosen for the team.In how many ways can thethree starters be chosen?(A)2(B)4(C)6(D)8(E)105.The losing team of each game is eliminated from the tournament.If sixteenteams compete,how many games will be played to determine the winner?(A)4(B)7(C)8(D)15(E)166.After Sally takes20shots,she has made55%of her shots.After she takes5more shots,she raises her percentage to56%.How many of the last5shots did she make?(A)1(B)2(C)3(D)4(E)57.An athlete’s target heart rate,in beats per minute,is80%ofthe theoretical maximum heart rate.The maximum heart rate isfound by subtracting the athlete’s age,in years,from220.To thenearest whole number,what is the target heart rate of an athletewho is26years old?(A)134(B)155(C)176(D)194(E)2438.Find the number of two-digit positive integers whose digits total7.(A)6(B)7(C)8(D)9(E)109.The average of theﬁve numbers in a list is54.The average of theﬁrst twonumbers is48.What is the average of the last three numbers?(A)55(B)56(C)57(D)58(E)5910.Handy Aaron helped a neighbor114hours on Monday,50minutes on Tuesday,from8:20to10:45on Wednesday morning,and a half-hour on Friday.He is paid$3per hour.How much did he earn for the week?(A)$8(B)$9(C)$10(D)$12(E)$1511.The numbers-2,4,6,9and12are rearranged according to these rules:1.The largest isn’tﬁrst,but it is in one of theﬁrst three places.2.The smallest isn’t last,but it is in one of the last three places.3.The median isn’tﬁrst or last.What is the average of theﬁrst and last numbers?(A)3.5(B)5(C)6.5(D)7.5(E)812.Niki usually leaves her cell phone on.If her cell phone is on butshe is not actually using it,the battery will last for24hours.Ifshe is using it constantly,the battery will last for only3hours.Since the last recharge,her phone has been on9hours,and duringthat time she has used it for60minutes.If she doesn’t talk anymore but leaves the phone on,how many more hours will the battery last?(A)7(B)8(C)11(D)14(E)1513.Amy,Bill and Celine are friends with diﬀerent ages.Exactly one of the following statements is true.I.Bill is the oldest.II.Amy is not the oldest.III.Celine is not the youngest.Rank the friends from the oldest to the youngest.(A)Bill,Amy,Celine(B)Amy,Bill,Celine(C)Celine,Amy,Bill(D)Celine,Bill,Amy(E)Amy,Celine,Bill14.What is the area enclosed by the geoboard quadrilateral below?(A)15(B)1812(C)2212(D)27(E)4115.Thirteen black and six white hexagonal tiles were used to create theﬁgure below.If a newﬁgure is created by attaching a border of white tiles with the same size and shape as the others,what will be the diﬀerence between the total number of white tiles and the total number of black tiles in the newﬁgure?(A)5(B)7(C)11(D)12(E)1816.Two600ml pitchers contain orange juice.One pitcher is13fulland the other pitcher is25full.Water is added toﬁll each pitchercompletely,then both pitchers are poured into one large con-tainer.What fraction of the mixture in the large container is orange juice?(A)18(B)316(C)1130(D)1119(E)111517.Three friends have a total of6identical pencils,and each one has at least onepencil.In how many ways can this happen?(A)1(B)3(C)6(D)10(E)1218.Five friends compete in a dart-throwing contest.Each one hastwo darts to throw at the same circular target,and each individ-ual’s score is the sum of the scores in the target regions that arehit.The scores for the target regions are the whole numbers1through10.Each throw hits the target in a region with a diﬀer-ent value.The scores are:Alice16points,Ben4points,Cindy7points,Dave 11points,and Ellen17points.Who hits the region worth6points?(A)Alice(B)Ben(C)Cindy(D)Dave(E)Ellen19.A whole number larger than2leaves a remainder of2when divided by each ofthe numbers3,4,5and6.The smallest such number lies between which two numbers?(A)40and49(B)60and79(C)100and129(D)210and249(E)320and36920.Two-thirds of the people in a room are seated in three-fourths ofthe chairs.The rest of the people are standing.If there are6empty chairs,how many people are in the room?(A)12(B)18(C)24(D)27(E)3621.Spinners A and B are spun.On each spinner,the arrow is equally likely to landon each number.What is the probability that the product of the two spinners’numbers is even?(A)14(B)13(C)12(D)23(E)3422.At a party there are only single women and married men withtheir wives.The probability that a randomly selected woman issingle is 25.What fraction of the people in the room are marriedmen?(A)13(B)38(C)25(D)512(E)3523.Tess runs counterclockwise around rectangular block JKLM .She lives at cornerJ .Which graph could represent her straight-line distance from home?JL M K(A)timed i s t a n c e(B)time d i s t a n c e (C)d i s t a n c e(D)timed i s t a n ce (E)time d i s t a n c e24.In the ﬁgure,ABCD is a rectangle and EF GH is a ing themeasurements given in the ﬁgure,what is the length d of the segment that is perpendicular to HE and F G ?)0,-*+./@!#"$$"!#(A)6.8(B)7.1(C)7.6(D)7.8(E)8.125.Two 4×4squares intersect at right angles,bisecting their intersecting sides,asshown.The circle’s diameter is the segment between the two points of intersec-tion.What is the area of the shaded region created by removing the circle from thesquares?(A)16−4π(B)16−2π(C)28−4π(D)28−2π(E)32−2πSOLUTIONSYour School Manager will be sent at least one copy of the 2004 AMC 8 Solutions Pam-phlet. It is meant to be loaned to students (but not duplicated).WRITE TO USComments about the problems and solutions for this AMC 8 should be addressed to:Ms. Bonnie Leitch, AMC 8 Chair / bleitch@548 Hill Avenue, New Braunfels, TX 78130Comments about administrative arrangements should be addressed to:MAA American Mathematics Competitions / amcinfo@American Mathematics Competitions, University of Nebraska-LincolnP.O. Box 880658, Lincoln, NE 68588-0658AMC 10 & AMC 12The AMC 10 and AMC 12 are 25-question, 75-minute contests with 5 choices of answers for each problem (A through E). Schools with high scoring students on the AMC 8 will receive an Invitation Brochure for the 2005 AMC 10. The best way to prepare for these upper level contests is to study exams from previous years. Orders for all publications listed below should be addressed to:American Mathematics CompetitionsATTN: PublicationsP.O. Box 81606Lincoln, NE 68501-1606PUBLICATIONSMINIMUM ORDER: $10 (Before handling fee), PAYMENTS IN US FUNDS ONLY. U.S.A. and Canadian orders must be prepaid and will be shipped UPS/DHL or AIRMAIL.Shipping & Handling charges for Publication Orders:Order TOTAL Shipping Charge$10.00 -- $40.00 $7.00$40.01 -- $50.00 $9.00$50.01 -- $75.00 $12.00$75.01 -- UP $15.00Make checks payable to the American Mathematics Competitions; or give your Visa or Mas-terCard number, expiration date and cardholder’s home address.International Orders: Do NOT prepay; an invoice will be sent to you.Each price is for an exam and its solutions for one year. Specify the years you want and how many copies of each exam. All prices effective to September 1, 2005.AMC 8 (Junior High/Middle School contests), 1986-2003, $1.00 per copy per year. AMC 10 (9th and 10th grade High School contests) 2000-2004. $1.00 per copy per year.AMC 12 (11th & 12th grade High School contests), 1990-2004, $1.00 per copy per year.2004AMC 8DO NOT OPEN UNTILTUESDAY, NOVEMBER 16, 2004 **Administration On An Earlier Date Will Disqualify Your School’s Results** 1. All information (Rules and Instructions) needed to administer this exam iscontained in the TEACHERS’ MANUAL, which is outside of this package.PLEASE READ THE MANUAL BEFORE NOVEMBER 16, 2004. Noth-ing is needed from inside this package until November 16.2. Your PRINCIPAL or VICE-PRINCIPAL must verify on the AMC 8 CER-TIFICATION FORM that you followed all rules associated with the conduct of the exam.3. The Answer Forms must be mailed First Class to the AMC office no laterthan 24 hours following the exam.4. THE AMC 8 IS TO BE ADMINISTERED DURING A CONVENIENT40 MINUTE PERIOD. THE EXAM MAY BE GIVEN DURING AREGULAR MATH CLASS.5. The publication, reproduction or communication of the problems or solutions of thistest during the period when students are eligible to participate seriously jeopardizes the integrity of the results. Duplication at any time via copier, telephone, e-mail, World Wide Web or media of any type is a violation of the competition rules.Major SponsorsThe Mathematical Association of America –– MAA / University of Nebraska – Lincoln –– UN-L /ContributorsAkamai Foundation / American Mathematical Association of Two Year Colleges – AMATYC / American Mathematical Society –– AMS / American Society of Pension Actuaries –– ASPA / American Statistical Association –– ASA / Art of Problem Solving www.artofproblemsolvingcom/ Canada/USA Mathcamp / Canada/USA Mathpath / Casualty Actuarial Society –– CAS / Clay Mathematics Institute –– CMI Institute for Operations Research and the Management Sciences –– INFORMS / L. G. Balfour & Company / Mu Alpha Theta –– MA Q / National Council of Teachers of Mathematics –– NCTM / Pedagoguery Software, Inc. Pi Mu Epsilon –– PME / Society of Actuaries –– SOA / USA Math Talent Search www.artofproblemsolvingcom/USAMTS/AoPS_U_About.phP W. H. Freeman & Company /。

AATCC TM 8-2007

AATCC takes no position respecting the validity of any patent rights asserted in connection with any item mentioned in this test method. Users of this test method are expressly advised that determination of the validity of any such patent rights, and the risk of infringement of such rights, are entirely their own responsibility.This test method is subject to revision at any time by the responsible technical committee and must be reviewed every five years and if not revised, either reaffirmed or withdrawn. Your comments are invited either for revision of this test method or for additional methods and should be addressed to the AATCC Technical Center. Your comments will receive careful consideration at a meeting of the responsible technical committee, which you may attend. If you feel that your comments have not received a fair hearing, you should make your views known to Christopher S. Leonard, Technical Director, at the address shown below.This test method is copyrighted by AATCC, PO Box 12215, Research Triangle Park, NC 27709 USA. Individual reprints (single or multiple copies) of this method may be obtained by contacting AATCC at the above address or tel: 919-549-3526; fax: 919-549-8933, or e-mail: orders@.AATCC License Agreement: This test method is copyrighted by the American Association of Textile Chemists and Colorists (AATCC), PO Box 12215, 1 Davis Drive, Research Triangle Park, NC USA. All rights reserved.AATCC grants you a license as follows: The right to download an electronic file of this AATCC test method for temporary storage on one computer for purposes of viewing, and/or printing one copy of the AATCC test method for individual use. Neither the electronic file nor the hard copy print may be reproduced in any way. In addition, the electronic file may not be distributed elsewhere over computer networks or otherwise. The hard copy print may only be distributed to other employees for their internal use within your organization. This test method is not for resale.Copyright © 2007 American Association of Textile Chemists and ColoristsAATCC Technical Manual/2008TM 8-200717Developed in 1936 by AATCC Commit-tee RA38; revised 1937, 1952, 1957,1961, 1969, 1972, 1985, 1988, 1996,2004, 2005, 2007; reaffirmed 1945;1989; editorially revised and reaffirmed 1968, 1974, 1977, 1981, 1995, 2001;editorially revised 1986, 2002. Partly equivalent to ISO 105-X12.1. Purpose and Scope1.1 This test method is designed to de-termine the amount of color transferred from the surface of colored textile materi-als to other surfaces by rubbing. It is ap-plicable to textiles made from all fibers in the form of yarn or fabric whether dyed,printed or otherwise colored. It is not rec-ommended for use for carpets or for prints where the singling out of areas may be too small using this method.1.2 Test procedures employing white test cloth squares, both dry and wet with water, are given.1.3 As washing, drycleaning, shrink-age, ironing, finishing, etc., may affect the degree of color transfer from a mate-rial, the test may be made before, after, or before and after any such treatment.2. Principle2.1 A colored test specimen is rubbed with white crock test cloth under con-trolled conditions.2.2 Color transferred to the white test cloth is assessed by a comparison with the Gray Scale for Staining or the Chro-matic Transference Scale and a grade is assigned.3. Terminology3.1 colorfastness, n.—the resistance of a material to change in any of its color characteristics, to transfer of its color-ant(s) to adjacent materials, or both, as a result of the exposure of the material to any environment that might be encoun-tered during the processing, testing, stor-age or use of the material.3.2 crocking, n.—a transfer of color-ant from the surface of a colored yarn or fabric to another surface or to an adjacent area of the same fabric principally by rubbing.4. Safety PrecautionsNOTE: These safety precautions are for information purposes only. The pre-cautions are ancillary to the testing proce-dures and are not intended to be all inclu-sive. It is the user’s responsibility to usesafe and proper techniques in handling materials in this test method. Manufac-turers MUST be consulted for specific details such as material safety data sheets and other manufacturer’s recommenda-tions. All OSHA standards and rules must also be consulted and followed.4.1 Good laboratory practices should be followed. Wear safety glasses in all laboratory areas.5. Apparatus and Materials5.1 AATCC Crockmeter or comparable alternate apparatus (see 13.2, 13.3 and Fig. 1).5.2 Test Cloth, cut in 50 mm squares (see 13.4).5.3 AATCC Chromatic Transference Scale (see 13.5).5.4 Gray Scale for Staining (see 13.5).5.5 White AATCC Textile Blotting Paper (see 13.5).5.6 Specimen Holder for Crockmeter (see 13.3).5.7 In-house poor crocking cloth.5.8 Crockmeter V erification Cloth.This item may be used in lieu of an in-house poor crocking cloth when such poor in-house crocking cloth is not avail-able (see 13.15).6. Verification6.1 Verification checks on the opera-tion of the test and the apparatus should be made routinely and the results kept in a log. The following observations and corrective actions are extremely impor-tant to avoid incorrect test results where abnormal crock images can result and in-fluence the rating process.6.2 Use the Crockmeter Verification Cloth or in-house poor crocking fabricwith known behavior and conduct three dry and wet crock tests.6.2.1 A poor circular image with un-even dye pick-up may indicate the crock-ing finger needs resurfacing (see 13.6).6.2.2 A double, elongated image may indicate a loose clip (see 13.6).6.2.3 A stretched and streaked crock image may be due to mounting the crock square diagonally.6.2.4 Scuff marks to the sides of the specimen indicate the loops to the wire clips are positioned downwards and are not high enough to prevent rubbing the specimen surface.6.2.5 A streak in the center of the crock cloth image and in the direction of rub-bing may mean the top of the metal base is warped and not flat. This will require a brace insert to square up the tester base.6.2.6 If specimen holders are used,place the holder over the specimen on the tester base. Move the crocking finger on the crocking arm to the most forward po-sition and observe whether it hits the in-side edge of the holder. If this occurs,move the holder slightly forward for all tests. Without correction, this problem will cause a dark area on one side of the crocking image.6.2.7 Confirm the wet pick-up tech-niques (see 9.2).6.2.8 Replace the abrasive paper on the tester base if it is smooth to the touch in the crocking area compared to the adja-cent area, or if slippage of the specimen is noticed (see 13.7).6.2.9 In routine testing, observe if mul-tiple streaks are on the crocking image.Position specimen normally with the long dimension oblique to the warp and fill-ing. If the direction of rubbing falls along a twill line or surface pattern, etc., then streaks may occur. If they do occur,slightly adjust the angle for testing.7. Test Specimens7.1 Two specimens are used, one each for the dry and the wet tests.7.1.1 Additional specimens may be used to increase the precision of the aver-age (see 12.1).7.2 Cut specimens at least 50 × 130 mm (2.0 × 5.1 in.) and position for testing pref-erably with the long dimension oblique to warp and filling or wales and courses.7.2.1 Larger or full width lab samples may be used without cutting individual specimens, when multiple tests are needed and when using for production testing.AATCC Test Method 8-2007Colorfastness to Crocking: AATCC Crockmeter MethodFig. 1—Crockmeter.Copyright © 2007 American Association of Textile Chemists and Colorists18TM 8-2007AATCC Technical Manual/20087.3 Yarns. Knit a piece of fabric at least 50 × 130 mm, or wind yarn tightly on a suitable form at least 50 × 130 mm with the yarn running in the long direction; or otherwise stretched (see 13.8).8. Conditioning8.1 Prior to testing, precondition and condition the test specimens and the crock squares for crock testing as di-rected in ASTM D 1776, Conditioning Textiles for Testing. Condition each spec-imen for at least 4 h in an atmosphere of 21 ± 1°C (70 ± 2°F) and 65 ± 2% RH by laying each test specimen or crock square separately on a screen or perforated shelf of conditioning rack.9. Procedures9.1 Dry Crocking Test.9.1.1 Place a test specimen on the base of the Crockmeter resting flat on the abra-sive cloth with its long dimension in the direction of rubbing (see 13.6 and 13.7).9.1.2 Place specimen holder over speci-men as an added means to prevent slippage.9.1.3 Mount a white test cloth square,the weave parallel with the direction of rubbing, over the end of the finger which projects downward from the weighted sliding arm. Use the special spiral wire clip to hold the test square in place. Posi-tion the clip with loops upward. If the loops point downward they can drag against the test specimen.9.1.4 Lower the covered finger onto the test specimen. Beginning with the finger positioned at the front end, crank the meter handle 10 complete turns at the rate of one turn per second to slide the covered finger back and forth 20 times. Set and run the motorized tester for 10 complete turns. Refer to individual specifications for any other required number of turns.9.1.5 Remove the white test cloth square, condition (see 8.1) and evaluate as directed in Section 10. In the case of napped, brushed or sanded material when loose fiber might interfere with the rating,remove the extraneous fibrous material by pressing lightly on the crock circle with the sticky side of cellophane tape before evaluating.9.2 Wet Crocking Test.9.2.1 Establish technique (see 13.10)for preparing wet crock cloth squares by weighing a conditioned square, then thor-oughly wet out white testing square in distilled water. Prepare only one square at a time.9.2.2 Weigh dry crock square. Using a syringe tube, graduated pipette or auto-matic pipetter, draw up water in mL to 0.65 times weight of crocking square. If crocking square weight equals 0.24 gm,the mL used would be 0.24 × 0.65 = 0.16mL. Lay crocking square on white plasticmesh over a dish. Apply water evenly over crocking square and weigh the wet square. Calculate wet pickup according to instructions in AATCC Methods 8 and 116, Colorfastness to Crocking test meth-ods. If needed, adjust the amount of water used to wet the square and using a new crocking square, repeat steps. When 65 ±5% wet pickup is achieved, record the amount of water used. Draw up the re-corded amount of water into the syringe tube, graduated pipette or automatic pi-petter for each wet crocking performed during the current day. Repeat this pro-cess each day.9.2.3 Avoid evaporative reduction of the moisture content below the specified level before the actual crock test is run.9.2.4 Continue as directed in 9.1.9.2.5 Air dry the white test square, then condition (see 8.1) before evaluating. In the case of napped, brushed or sanded material when loose fiber might interfere with the rating, remove the extraneous fibrous material by pressing lightly on the crock circle with the sticky side of cello-phane tape before evaluating.10. Evaluation10.1 Rate the amount of color trans-ferred from the specimen to the white test square under examination by means of the Chromatic Transference Scale or the Gray Scale for Staining (see 13.11 and 13.14).10.2 Back the test square with three layers of white test cloth while evaluating.10.3 Rate dry and wet crocking fast-ness by means of the Gray Scale for Staining or the 9-step AATCC Chromatic Transference Scale. (Usage of these scales is discussed in AATCC Evaluation Procedures 2, 3 and 8, respectively.)Grade 5—negligible or no color transfer.Grade 4.5—color transfer equivalent to Step 4-5 on the Gray Scale for Staining or Row 4.5 on the 9-step AA TCC Chro-matic Transference Scale.Grade 4—color transfer equivalent to Step 4 on the Gray Scale for Staining or Row 4 on the 9-step AATCC Chromatic Transference Scale.Grade 3.5—color transfer equivalent to Step 3-4 on the Gray Scale for Staining or Row 3.5 on the 9-step AA TCC Chro-matic Transference Scale.Grade 3—color transfer equivalent to Step 3 on the Gray Scale for Staining or Row 3 on the 9-step AATCC ChromaticTransference Scale.Grade 2.5—color transfer equivalent to Step 2-3 on the Gray Scale for Staining or Row 2.5 on the 9-step AATCC Chro-matic Transference Scale.Grade 2—color transfer equivalent to Step 2 on the Gray Scale for Staining or Row 2 on the 9-step AATCC Chromatic Transference Scale.Grade 1.5—color transfer equivalent to Step 1-2 on the Gray Scale for Staining or Row 1.5 on the 9-step AATCC Chro-matic Transference Scale.Grade 1—color transfer equivalent to Step 1 on the Gray Scale for Staining or Row 1 on the 9-step AATCC Chromatic Transference Scale.10.4 Average individual results to the nearest 0.1 grade when multiple speci-mens are tested or when a panel of evalu-ators rate color transfer.11. Report11.1 State whether dry or wet crocking test.11.2 Report the grade determined in 10.3.11.3 Report the grade determined in 10.4 to the nearest 0.1 grade.11.4 State whether Gray Scale for Staining or Chromatic Transference Scale was used for evaluating staining (see 13.5, 13.9).11.5 If any pretreatment or aftertreat-ment was given to any specimens (see 1.3) indicate method of treatment.12. Precision and Bias12.1 Precision. An interlaboratory test was conducted in 1986 to establish the precision of the test method. Testing was conducted under the normal atmospheric conditions of each laboratory and not necessarily under ASTM standard condi-tions. Two operators at each of 12 labora-tories evaluated 5 fabrics in 3 replications by both dry and wet test method. Each of 3 raters independently rated the stained crock squares using both the Gray Scale for Staining and the Chromatic Transfer-ence Scale. The original data is on file at the AATCC Technical Center.12.1.1 The components of variance as standard deviations of the Gray Scale for Staining or Chromatic Transference Scale rating units are given in Table I.12.1.2 Critical differences are given in Table II.Table I—Components of VarianceTest ScaleDryWetChromatic Gray ChromaticGray Single Operator/Rater Within Laboratory Between Laboratory0.200.200.100.200.190.170.240.310.380.250.340.54Copyright © 2007 American Association of Textile Chemists and ColoristsAATCC Technical Manual/2008TM 8-20071912.1.3 Example for determining be-tween laboratory differences using one observer and the chromatic scale are given in Table III.Interpretation: For the dry crock test,since the difference between labs is less than the critical differences in 12.1.2(0.82), the difference in results is not sig-nificant. For the wet crock test, since the difference between labs is greater than the critical difference (1.53), the differ-ence in results is significant.12.2 Bias. The true value of colorfast-ness to crocking can only be defined in terms of a test method. Within this limita-tion, this test method has no known bias.13. Notes13.1 For carpets, AATCC Method 165, Col-orfastness to Crocking: Carpets—AATCC Crockmeter Method, under the jurisdiction of Committee RA57, Floor Covering Test Meth-ods, should be used.13.2 The AATCC Crockmeter provides a reciprocating rubbing motion simulating the action of a human finger and forearm.13.3 The AATCC Crockmeter is so de-signed that the 16 ± 0.3 mm (0.625 ± 0.01 in.)diameter finger moves back and forth, with each complete turn of the crank, in a straight line along a 104 ± 3 mm track on the speci-men, with a downward force of 9 N ± 10%(2lb ± 10%). Two models, a manual and a motorized Crockmeter are available fromSDL Atlas L.L.C., 1813A Associate Lane,Charlotte NC 28217; tel: 704/329-0911; fax:704/329-0914; e-mail: info@.Comparable apparatus, such as the Crock-master, both manual and motorized, is available from James H. Heal & Co. Ltd.,Richmond Works, Halifax HX3 6EP, Eng-land; tel: 44 1422 366355; fax: 44 1422352440; e-mail: info@.13.4 Crockmeter Test Cloth is available from Testfabrics Inc., P.O. Box 26, 415 Dela-ware St., W. Pittston PA 18643; tel: 570/603-0432; fax: 570/603-0433; e-mail: testfabric@; or Textile Innovators Corp., div. of SDL Atlas L.L.C., 3934 Airway Drive, Rock Hill SC 29732; tel: 803/329-2110; fax: 803/329-2133; e-mail: info@.13.4.1 Crockmeter Test Cloth should meet the following specifications:Fiber100% 10.3-16.8 mm combed cotton staple, desized,bleached, with no optical brightener or finishing mate-rial presentYarn 15 tex (40/1 cotton count),5.9 turns/cm “z”Thread count 32 ± 3 warp ends/cm: 33 ± 3picks filling/cmWeave 1/1 plain pH 7 ± 0.5Mass/sq meter 113 ± 5 g greige: 100 ± 3 gfinishedWhiteness W = 80 ± 2 (Method 110)13.5 The Chromatic Transference Scale,Gray Scales for Staining and White AATCC Textile Blotting Paper are available from AATCC, P.O. Box 12215, Research Triangle Park NC 27709; tel: 919/549-8141; fax: 919/549-8933; e-mail: orders@.13.6 Accidental damage to the rubbing fin-ger, spiral clip or abrasive paper should be repaired as follows: neatly renew the abrasive paper; bend the clip further open or shut around a rod slightly smaller in diameter than the crock peg; resurface the finger by move-ment on an extra piece of fine emery cloth in amanner simulating regular use.13.7 The abrasive material currently sup-plied with the Crockmeter is “Wet or Dry Waterproof Silicon Carbide, W-320-A, Soft Back.” Replacement pieces are available from SDL Atlas L.L.C., 1813A Associate Lane,Charlotte NC 28217; tel: 704/329-0911; fax:704/329-0914; e-mail: info@.13.8 For more convenient crock testing of multiple strands of yarn or thread a dowel at-tachment is useful. This attachment was de-veloped to avoid the tendency of the standard finger to dig into and push aside the yarns, or slide off them and possibly give erroneous results. This attachment is 25 mm in diameter by 51 mm long. Positioned on its side and held in place by the standard finger, it provides a wider test area, and holds the white test square by two spring loaded clips. For additional in-formation on this development see the article by C. R. Trommer, “Modification of the AATCC Crockmeter for Yarn Testing,” Amer-ican Dyestuff Reporter , V ol. 45, No. 12, p357,June 4, 1956; also see articles by S. Korpanty and C. R. Trommer, “An Improved Crock-meter for Yarn Testing,” American Dyestuff Reporter , V ol. 48, No. 6, p40, March 23, 1959.A yarn testing finger kit for installation on the Crockmeter is available from SDL Atlas L.L.C., 1813A Associate Lane, Charlotte NC 28217; tel: 704/329-0911; fax: 704/329-0914;e-mail: info@.13.9 It has been noted that different grades may result depending upon whether the Gray Scale for Staining or Chromatic Trans-ference Scale is used for the evaluation. It is,therefore, important to report which scale was used.13.10 Experienced operators do not have to repeat this weighing procedure during a test session once the technique is established.13.11 For very critical evaluations and in cases of arbitration, grades must be based on the Gray Scale for Staining.13.12 For a discussion of crock testing, see the article by J. Patton, “Crock Test Problems can be Prevented,” Textile Chemist and Color-ist , V ol. 21, No. 3, p13, March 1989; and “Test-ing for Crocking: Some Problems and Pitfalls”by Allan E. Gore, Textile Chemists and Color-ists , V ol. 21, No. 3, p17, March 1989.13.13 For prints where the singling out of areas too small to test with the standard AATCC Crockmeter is necessary, see AATCC Method 116, Rotary Vertical Crockmeter Method. Specimens tested by both test methods may show dissimilar results. There is no known correlation between the two methods.13.14 An automated electronic grading sys-tem may be used as long as the system has been demonstrated to provide results that are equal to and provide equal or better repeatabil-ity and reproducibility than an experienced grader performing visual evaluation.13.15 Crockmeter Verification Cloth is available from Textile Innovators Corp., div of SDL Atlas L.L.C., 3934 Airway Drive, Rock Hill SC 29732; tel: 803/329-2110; fax: 803/329-2133; e-mail: info@. Details on the performance of the current lot of Crockmeter Verification Cloth are available from the AATCC Technical Center.Table II—Critical DifferencesFor the components of variance in Tab le I, two averages of ob served values should b e considered significantly different at the 95% probability level if the difference equals or exceeds the following critical differences.Test ScaleNo. of ObservationsDryWetChromatic Gray ChromaticGray Single Operator/Rater 1350.550.320.240.540.310.240.680.390.300.700.400.31Within Laboratory 1350.770.600.600.750.610.57 1.080.930.90 1.171.021.00Between Laboratory1350.820.690.660.890.770.741.531.431.411.901.811.79The critical differences were calculated using t = 1.96 which is based on infinite degrees of freedom.Table III—Crock Test ResultsDryWet Lab A 4.5 3.5Lab B 4.0 1.5Difference0.52.0Copyright © 2007 American Association of Textile Chemists and Colorists。

Silicon Laboratories AN678 精确32 si32FlashUtility 命

Rev. 0.1 3/12Copyright © 2012 by Silicon LaboratoriesAN678P ROGRAMMER U SER ’S G UIDE1. IntroductionThe Precision32™ si32FlashUtility Command-Line Programmer is a simple program to enable productionprogramming capability using the Silicon Labs 32-bit USB Debug Adapter. This utility can also program and eraselock bytes.Figure 1 shows an invocation of the command-line utility.Figure 1.Precision32 si32FlashUtility Command-Line Programmer2. Relevant DocumentationPrecision32 Application Notes are listed on the following website: /32bit-appnotes.⏹ AN667: Getting Started with the Silicon Labs Precision32™ IDE⏹AN669: Integrating Silicon Labs SiM3xxxx Devices into the Keil µVision® IDEAN6783. Programming OptionsThe si32FlashUtlility has a command-line form of:si32FlashUtility [-options] [drive:][path]imageThese options consist of the following:⏹ -v: Verify the image after downloading to Flash.⏹ -i: Display additional information during the programming process (i.e., verbose mode).⏹ -e {0,1,2}: Erase Flash with three mode options.⏹ -p {0,1,2}: Debug port selection with three mode options.⏹ -r {0,1,2}: Reset during programming with three mode options.⏹ -l: List the available USB Debug Adapters (UDAs).⏹ -s SERIAL: Specify the USB Debug Adapter serial string.This section discusses each of these programming options in more detail.3.1. Download VerificationUsing the -v option flag causes the si32FlashUtility to verify the Flash contents after the download. The command-line utility will output a Download complete and verified message if the Flash contents match the HEX image. 3.2. Verbose FeedbackWith the -i option flag, the si32FlashUtility programmer will report feedback about each step of the programming process, as shown in Figure2.Figure2.Verbose Mode OutputAN6783.3. Flash EraseThe -e option flag has three modes: merge, sector, and full. The default option is sector (-e 1) if no option is specified.The merge option is selected with -e 0 and causes the programmer to read the current contents of the Flash page selected by the HEX file address, copy any contents that are not written in the HEX image, erase the page, and write the merged image back to Flash. This option allows developers to maintain any calibration or code constants in Flash when updating code.When using the -e 1 sector erase option, the programmer will first erase the page selected by the HEX image address before programming the contents of the HEX image.The final option, -e 2, causes the programmer to erase the entire Flash before programming the HEX image.3.4. Debug PortThis option selects the debug port of the device. The -p 0 selection is for any devices with JTAG debug pins. The -p 1 option is for devices with Serial Wire debug pins only (SW-DP). The -p 2 option uses the Serial Wire protocol and is for devices with both JTAG and Serial Wire debug pins (SWJ-DP), like the SiM3U1xx device family. The default option is -p 2 if no option is specified.The JTAG selection (-p 0) does not have provisions for JTAG chaining.3.5. Reset OptionsThe utility supports three different reset options: none, before, and during. The default option is none (-r 0) if no option is specified.The none option (-r 0) prevents the utility from toggling the reset pin at any point during the programming process. The before option (-r 1) allows the si32FlashUtility to toggle reset immediately before programming. This option is useful for SiM3U1xx or SiM3C1xx devices that may be unresponsive due to switching to a non-existent clock. Using this option along with the recommended reset delay in the startup code ensures the USB Debug Adapter will be able to communicate with the device.For the during option (-r 2), the utility asserts the reset pin while attempting to halt the core. Once the core is halted, the utility deasserts the reset pin and starts programming. This option ensures the Debug Adapter can always communicate with a device without the reset delay in the startup code for devices that support this feature.Note:The -r 2 option is unavailable for SiM3U1xx and SiM3C1xx devices.3.6. USB Debug Adapter OptionsThe -l option flag lists the available USB Debug Adapters connected to the PC or system. The -s SERIAL option flag can then specify the USB Debug Adapter the utility should use for programming.AN6784. Creating HEX Files with the Precision32 IDEThe si32FlashUtility programmer expects HEX files as its input, and the Precision32 IDE includes a utility that can convert the GCC AXF file output to HEX files. This objcopy utility can be found in the ..\Precision32_vx.y\IDE\precision32\Tools\arm-none-eabi\bin path after installing the Precision32 software package from /32bit-software.More information on the usage of this utility can be found on the CodeRed website: /CodeRedWiki/OutputFormats.4.1. Using the Objcopy Utility from the IDETo use the objcopy utility from the IDE:1. Hold the Ctrl button and left-click on the project name in the IDE footer as shown in Figure3. This willopen a command prompt in the project directory with the proper paths to use the utility.Figure3.Opening a Project Command Prompt2. Type cd build_directory, where build_directory is Debug by default.3. Invoke the utility: arm-none-eabi-objcopy -O ihex project_name.axf project_name.hex. In the case ofthis example, which uses the sim3u1xx_Blinky project: arm-none-eabi-objcopy -O ihexsim3u1xx_Blinky.axf sim3u1xx_Blinky.hex.Rev. 0.1AN678Rev. 0.1Figure 4.Invoking the Objcopy Utility4.2. Setting the IDE Project to Automatically Generate a HEX FileTo configure the Precision32 IDE project to automatically generate a HEX file after a build:1. Right-click on the project_name in the Project Explorer view.2. Select Properties .3. In the C/C++ Build →Settings →Build Steps tab, type the following in the Post-build steps →Commandbox: arm-none-eabi-objcopy -O ihex ${BuildArtifactFileName} ${BuildArtifactFileBaseName}.hexFigure 5.Automatically Generating a HEX File on Project BuildAN6785. Examples To verify the download of the sim3u1xx_Blinky.hex file:si32FlashUtility -v sim3u1xx_Blinky.hex This example is shown in Figure6.Figure 6.Example with Flash VerificationTo verify the download of the sim3u1xx_Blinky.hex file, use verbose mode, erase the device before the download,and reset before:si32FlashUtility -v -i -e 2 -r 1 sim3u1xx_Blinky.hexFigure 7 shows an example of this call to the si32FlashUtility programmer.Figure 7.Example with Flash Verification, Verbose Mode, Full Device Erase, and Reset BeforeOptions Silicon Laboratories Inc.400 West Cesar Chavez Austin, TX 78701USASimplicity StudioOne-click access to MCU andwireless tools, documentation,software, source code libraries &more. Available for Windows,Mac and Linux!IoT Portfolio /IoT SW/HW /simplicity Quality /quality Support and CommunityDisclaimer Silicon Labs intends to provide customers with the latest, accurate, and in-depth documentation of all peripherals and modules available for system and software implementers using or intending to use the Silicon Labs products. Characterization data, available modules and peripherals, memory sizes and memory addresses refer to each specific device, and "Typical" parameters provided can and do vary in different applications. Application examples described herein are for illustrative purposes only. Silicon Labs reserves the right to make changes without further notice and limitation to product information, specifications, and descriptions herein, and does not give warranties as to the accuracy or completeness of the included information. Silicon Labs shall have no liability for the consequences of use of the information supplied herein. This document does not imply or express copyright licenses granted hereunder to design or fabricate any integrated circuits. The products are not designed or authorized to be used within any Life Support System without the specific written consent of Silicon Labs. A "Life Support System" is any product or system intended to support or sustain life and/or health, which, if it fails, can be reasonably expected to result in significant personal injury or death. Silicon Labs products are not designed or authorized for military applications. Silicon Labs products shall under no circumstances be used in weapons of mass destruction including (but not limited to) nuclear, biological or chemical weapons, or missiles capable of delivering such weapons.Trademark Information Silicon Laboratories Inc.® , Silicon Laboratories®, Silicon Labs®, SiLabs® and the Silicon Labs logo®, Bluegiga®, Bluegiga Logo®, Clockbuilder®, CMEMS®, DSPLL®, EFM®, EFM32®, EFR, Ember®, Energy Micro, Energy Micro logo and combinations thereof, "the world’s most energy friendly microcontrollers", Ember®, EZLink®, EZRadio®, EZRadioPRO®, Gecko®, ISOmodem®, Precision32®, ProSLIC®, Simplicity Studio®, SiPHY®, Telegesis, the Telegesis Logo®, USBXpress® and others are trademarks or registered trademarks of Silicon Labs. ARM, CORTEX, Cortex-M3 and THUMB are trademarks or registered trademarks of ARM Holdings. Keil is a registered trademark of ARM Limited. All other products or brand names mentioned herein are trademarks of their respective holders.。

MICROMASTER 420变频器说明书

2.4.4 屏蔽的方法........................................................................................................... 2-10
3
调试 ................................................................................................................................................ 3-1
2.1 概述 ....................................................................................................................................... 2-2
2.2 变频器运行的环境条件 .......................................................................................................... 2-3
2.4.2 电源和电动机的连接 .............................................................................................. 2-8
2.4.3 电磁干扰（EMI）的防护 ....................................................................................... 2-9

2007 AMC 8 Problems - AoPSWiki

Search Wiki Go SearchPage ToolsPage Discussion View source HistoryPersonal toolsLog inNavigationMain pageCommunity portal Recent changes Random page HelpToolboxWhat links here Related changes Special pages Printable version Permanent linkArt of Problem Solving2007 AMC 8 ProblemsFrom AoPSWikiContents1 Problem 12 Problem 23 Problem 34 Problem 45 Problem 56 Problem 67 Problem 78 Problem 89 Problem 910 Problem 1011 Problem 1112 Problem 1213 Problem 1314 Problem 1415 Problem 1516 Problem 1617 Problem 1718 Problem 1819 Problem 1920 Problem 2021 Problem 2122 Problem 2223 Problem 2324 Problem 2425 Problem 2526 See AlsoProblem 1Theresa's parents have agreed to buy her tickets to see her favorite band if she spends an average ofhours per week helping around the house for weeks. For the first weeks she helps around the house for , , , and hours. How m any hours m ust she work for the final week to earn the tickets?SolutionProblem 2students were surveyed about their pasta preferences. The choices were lasagna, m anicotti, ravioli and spaghetti. The results of the survey are displayed in the bar graph. What is the ratio of the num ber of students who preferred spaghetti to the num ber of students who preferred m anicotti?SolutionProblem 3What is the sum of the two sm allest prim e factors of ?SolutionProblem 4A haunted house has six windows. In how m any ways can Georgie the Ghost enter the house by one window and leave by a different window?SolutionProblem 5Chandler wants to buy a m ountain bike. For his birthday, his grandparents send him, his auntsends him and his cousin gives him. He earns per week for his paper route. He will use all of hisbirthday m oney and all of the m oney he earns from his paper route. In how m any weeks will he be able to buy the m ountain bike?SolutionProblem 6The average cost of a long-distance call in the USA in was cents per m inute, and the average costof a long-distance call in the USA in was cents per m inute. Find the approxim ate percent decreasein the cost per m inute of a long- distance call.SolutionProblem 7The average age of people in a room is years. An -year-old person leaves the room. What is theaverage age of the four rem aining people?SolutionProblem 8In trapezoid , is perpendicular to , = =, and =. In addition, is on ,and is parallel to . Find the area of .SolutionProblem 9To com plete the grid below, each of the digits 1 through 4 m ust occur once in each row and once in each colum n. What num ber will occupy the lower right-hand square?cannot be determ inedSolutionProblem 10For any positive integer , define to be the sum of the positive factors of . For exam ple,. Find .SolutionProblem 11Tiles and are translated so one tile coincides with each of the rectangles and . In the final arrangem ent, the two num bers on any side com m on to two adjacent tiles m ust be the sam e. Which of the tiles is translated to Rectangle ?cannot be determ inedSolutionProblem 12A unit hexagram is com posed of a regular hexagon of side length and its equilateral triangularextensions, as shown in the diagram. What is the ratio of the area of the extensions to the area of the original hexagon?SolutionProblem 13Sets and , shown in the Venn diagram, have the sam e num ber of elem ents. Their union haselem ents and their intersection has elem ents. Find the num ber of elem ents in .SolutionProblem 14The base of isosceles is and its area is . What is the length of one of the congruent sides?SolutionProblem 15Let and be num bers with . Which of the following is im possible?SolutionProblem 16Am anda Reckonwith draws five circles with radii and . Then for each circle she plots the point, where is its circum ference and is its area. Which of the following could be her graph?SolutionProblem 17A m ixture of liters of paint is red tint, yellow tint and water. Five liters of yellow tint areadded to the original m ixture. What is the percent of yellow tint in the new m ixture?SolutionProblem 18The product of the two -digit num bersandhas thousands digit and units digit . What is the sum of and ?SolutionProblem 19Pick two consecutive positive integers whose sum is less than . Square both of those integers and then find the difference of the squares. Which of the following could be the difference?SolutionProblem 20Before district play, the Unicorns had won of their basketball gam es. During district play, they won six m ore gam es and lost two, to finish the season having won half their gam es. How m any gam es did the Unicorns play in all?SolutionProblem 21Two cards are dealt from a deck of four red cards labeled and four green cards labeled . A winning pair is two of the sam e color or two of the sam e letter. What is the probability of drawing a winning pair?SolutionProblem 22A lem m ing sits at a corner of a square with side length m eters. The lem m ing runs m eters along a diagonal toward the opposite corner. It stops, m akes a degree right turn and runs m ore m eters. A scientist m easures the shortest distance between the lem m ing and each side of the square. What is the average of these four distances in m eters?SolutionProblem 23What is the area of the shaded pinwheel shown in the x grid?SolutionProblem 24A bag contains four pieces of paper, each labeled with one of the digits "1, 2, 3" or "4", with no repeats. Three of these pieces are drawn, one at a tim e without replacem ent, to construct a three-digit num ber. What is the probability that the three-digit num ber is a m ultiple of 3?SolutionProblem 25On the dart board shown in the Figure, the outer circle has radius and the inner circle has radius . Threeradii divide each circle into three congruent regions, with point values shown. The probability that a dart will hit a given region is proportional to the area of the region. When two darts hit this board, the score is the sum of the point values in the regions. What is the probability that the score is odd?SolutionSee Also2007 AMC 8 (Problems • Resources)Preceded by 2006 AMC 8Followed by 2008 AMC 81 •2 •3 •4 •5 •6 •7 •8 •9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20• 21 • 22 • 23 • 24 • 25AMC 8AMC 8 Problem s and SolutionsMathem atics com petition resourcesRetrieved from "http://www.artofproblem /Wiki/index.php/2007_AMC_8_Problem s"This page was last m odified on 25 Decem ber 2012, at 15:08. This page has been accessed 96,140 tim es. Privacy policy About AoPSWiki Disclaim ers。

安迪玛克 Optima 8x00 系列 ICP 光谱仪说明书

Optima 8x00 SeriesICP Optical Emission SpectrometersENVIRONMENTALEasy to use and engineered for exceptional throughput and detection limits,the Optima™ 8x00 series helps maximize productivity and profitability.• D ual view capability allows measurement of high and low concentrationsin the same run for enhanced productivity• T orch cassette—low maintenance, simple operationGEOCHEMICALDesigned to deliver reproducible accuracy even with complex matrices, theOptima 8x00 series offers unsurpassed performance without compromisingsample throughput.• F lat Plate™ plasma technology lowers operating and maintenance costs• W inLab™ Multicomponent Spectral Fitting—superior interference correctionfor more accurate results• S imultaneous data acquisition for maximum sample throughputPHARMACEUTICAL/NUTRACEUTICALWith the lowest detection limits of any ICP-OES and a full suite of enhanceddata security features, the Optima 8x00 series makes it easy to comply withstringent regulatory requirements.• D etection of full list of elements for transition to USP 232/233• W inLab for ICP Enhanced Security™ for 21 CFR Part 11 complianceFOOD/PRODUCT SAFETYWith a range of revolutionary technologies, the Optima 8x00 series offersunsurpassed flexibility for handling a variety of sample types and matrices.• F lat Plate plasma technology improves robustness for many different matrices• P lasmaCam™ aids in method development and productivity• W inLab for ICP software designed to deliver rapid method development2With its groundbreaking features and expanded capabilities, the Optima 8x00 series is more than justan evolution of the world’s most popular ICP-OES… it’s a revolution.Continuing PerkinElmer’s long history of excellence and leadership in ICP technology, the Optima 8x00 series carries on a tradition of offering the best resolution and linear dynamic range. More significantly, the 8x00 series delivers a level of stability and detection limits never before seen in an ICP instrument.Built around the proven design of the Optima platform and controlled with our industry-leading, Windows 7-compatible WinLab software, the 8x00 series will change the way you look at ICP-OES. Optima’s breakthrough performance is the result of a series of cutting-edge technologies that increase productivity, enhance plasma stability, simplify method development, and dramatically reduce operating costs. Laboratories have very different definitions of what it means to get the most out of their ICP. But whether your priority is precision or reliability, flexibility or stability, speed or simplicity, you’ll find the ideal solutionOptima 8300Two SCD detectors —Deliver superior resolution across the entire wavelength range, reducing interferences and improving accuracy, offering truly simultaneous data acquisition (Optima 8300).8000Maximum Throughput Fastest Warm-Up XUniversal Data Acquisition Time-Resolved Data Acquisition Smallest Instrument FootprintXneeds and priorities of your laboratoryTo complement its many new hardware innovations, the Optima 8x00 series features an equally impressive array of software enhancements making it faster and easier than ever to go from The Windows 7-compatible industry-leading WinLab for ICP software simplifies every stepUse the software’s built-in methods for added speed and simplicity, or follow four easy steps to create your own. Either way, WinLab software makes method development effortless and ensures compliance even with today’s most stringent regulatory standards.Particularly effective when running complex matrices, this patented approach to interferenceMulticomponent Spectral Fitting allows the analytical signal to be isolatedfrom the measured spectra—without interferences—for superior accuracy,precision and detection limits.Get more out of your dataTransient signal handling expands sample-introduction capabilities to includespeciation and hydride analysis.Sample preparationThe S10 Autosampler can easily turnyour Optima ICP-OES into a fullyautomated analytical workstation.ICP-MSFor more information on our full suite of atomic spectroscopy products and services—including a wide array of mercury analyzers and sample preparation tools—please visit /atomicspectroscopy。

AMC2输入输出扩展板用户指南说明书

The AMC2 16I-16O-EXT, the AMC2 16I-EXT and/or the AMC2 8I‑8O-EXT extension boards can only be used with the AMC2 access controller and provides additional input and output contacts.The AMC2 controller has eight input and eight output signals. The AMC2 determines the door status (open or closed) via the analog input signals. The relay outputs can be used to activate locking mechanisms, for example.If there are not enough contacts available on the AMC2 to transfer the necessary signals, up to three AMC2 xI-xO-EXT units can be connected to provide additional inputs and outputs.NoteSystems with Access Personal EditionSoftware can only connect one I/O-Extension to an AMC2 Controller.The electronics are located in a plastic housing, similar to the one on the AMC2 controller.The AMC2 16I-16O-EXT has 16 analog inputs and 16 relay outputs. It receives door status signals via the inputs and can authorize door releases or send messages to external surveillance systems via the outputs.Reduced versions of the extension board are alsoobtainable to make full use of the available signals. The AMC2 8I-8O-EXT module has eight input and eight output signals. The AMC2 16I-EXT has 16 analog inputs.System OverviewThe AMC2 xxx-EXT is integrated into the system via the AMC2 controller.1 = Host computer2 = AMC23 = Card reader4 = Communication and power supply5 = AMC2 xxx-EXTIn the default configuration, the connection to the AMC2 is established via the RS485 interface.AMC2 - Input/Output Extension Boards▶RS485 connection to the AMC2 controller▶Three models available one with 8 inputs & 8 outputs,one with 16 inputs & 16 outputs, and one with 16 inputs ▶Status of inputs and outputs shows on AMC2 LCD display ▶Transfer rate to EXT interface (RS485): 9,6 kBit/sec ▶The AMC2 Extensionboards can be supplied with the PBC-60 power supply unit with integrated UPS.2Installation/Configuration NotesUp to three extension boards can be connected to one AMC2 controller; this provides a maximum of 56 input and output signals for configuration with the AMC2 signals.For a system configuration the AMC2 16I-16O-EXT, AMC216I-EXT, and AMC2 8I-8O-EXT can also be used incombination, e.g. two AMC2 16I-16O-EXTs and one AMC28I-8O-EXT – but the maximum number of modules that can be connected is also restricted to three per AMC2controller.NoteSystems with Access Personal EditionSoftware can only connect one I/O-Extension to an AMC2 Controller.An AMC2 16I-16O-EXT can only provide signals for theentrances of the AMC2 controller to which it is connected.It is not possible to transmit to another AMC2.Configuration examples:Solid lines: Power supply Dotted lines: Data lines1.AMC2 with power supply.2.Power and data are supplied to the AMC2 xxx-EXT viathe AMC2.3.The AMC2 xxx-EXT with its own power supply receivesdata from the AMC2.4.The first AMC2 xxx-EXT is supplied by the AMC2 - thesecond has its own power supply and a connection to the third. All AMC2 xxx-EXTs receive their data from the AMC2.Power supplyAn external power supply (10 to 30 V DC) for the AMC2 is connected to the first (positive) and third pin (negative).When using an uninterruptible power supply (UPS), the relevant UPS output relay is connected to the pins• 4 and 7 for alternating current (AC)• 5 and 7 for the battery•6 and7 for direct current (DC)Otherwise, these pins will short-circuit.Voltage equalization - grounding•Different grounds can be balanced via jumpers withprotective ground.• A line (shielding, potential equalization) with protectiveground must only be connected in one place.•For further instructions, please see the operatingmanual.3ContactsInputsThe analog inputs can be used as digital or analog contacts. For analog use, resistance values can be specified to check for cable breaks and short-circuits.Relay outputsThe relay outputs offer the following functions:•The outputs can operate with potential free contacts for external power supply (dry mode).•The outputs can operate using the internal voltage of power supply (wet mode).•Only ohm resistive loads can be connected to the relay.•Inductive loads must be bypassed via recovery diodes.These diodes (IN4004) are enclosed.General instructions•All access equipment should be mounted within a "secured area".•Detailed connection conditions are specified in the operating manual!•After purchase, primary AC power must be carried out by a licensed electrician.Technical SpecificationsHardware16 or 8 or null relay outputs - with ohm load:- max. switching voltage: 30 V DC- max. switching current: 1,25 A16 or 8 analog inputsTamper switchTemperature0°C to +45°C (32° F to 113° F)Power supply- 10 or 30 V DC, max. 60 VAAvailable for external devices: 55 VA- or via the AMC2ProtectionclassIP 30Housing Base: PPO (UL 94 V-0)Upper: Polycarbonate (UL 94 V-0)Color WhiteDimensions WxHxD: 232 x 90 x 46 mm (9.13 x 3.54 x 1.81 in.) Weight Approx. 0.4 kg (0.88 lb)Type Rail mounting Ordering InformationAMC2 8I-8O-EXT8 i nput/output e xtension b oard, u p t o t hree p erAMC, can be combined with the AMC2 16I-EXTand the AMC2 16I-16O-EXTAPI-AMC2-8IOEAMC2 16I-16O-EXT16 input/output extension board, up to threeper AMC, can be combined with the AMC2 16I-EXT and the AMC2 8I-8O-EXTAPI-AMC2-16IOEAMC2 16I-EXT16 input extension board, up to three per AMC,can be combined with the AMC2 16I-16O-EXTand the AMC2 8I-8O-EXTAPI-AMC2-16IE4Americas:Bosch Security Systems, Inc. 130 Perinton Parkway Fairport, New York, 14450, USA Phone: +1 800 289 0096 Fax: +1 585 223 9180***********************.com Europe, Middle East, Africa:Bosch Security Systems B.V.P.O. Box 800025600 JB Eindhoven, The NetherlandsPhone: + 31 40 2577 284Fax: +31 40 2577 330******************************Asia-Pacific:Robert Bosch (SEA) Pte Ltd, Security Systems11 Bishan Street 21Singapore 573943Phone: +65 6258 5511Fax: +65 6571 2698*****************************Represented by© Bosch Security Systems Inc. 2010 | Data subject to change without notice T3538176395 | Cur: en-US, V9, 4 Jul 2010 | Src: en-US, V1, 16 Aug 2006。

2000 AMC 8 Problems - AoPSWiki

Search Wiki Go SearchPage Tools Page Discussion View source HistoryPersonal tools Log inNavigation Main pageCommunity portal Recent changes Random page HelpToolboxWhat links here Related changes Special pages Printable version Permanent linkArt of Problem Solving2000 AMC 8 ProblemsFrom AoPSWikiContents1 Problem 12 Problem 23 Problem 34 Problem 45 Problem 56 Problem 67 Problem 78 Problem 89 Problem 910 Problem 1011 Problem 1112 Problem 1213 Problem 1314 Problem 1415 Problem 1516 Problem 1617 Problem 1718 Problem 1819 Problem 1920 Problem 2021 Problem 2122 Problem2223 Problem 2324 Problem2425 Problem 2526 See AlsoProblem 1Aunt Anna isyears old. Caitlin is years younger than Brianna, and Brianna is half as old as Aunt Anna. Howold is Caitlin?SolutionProblem 2Which of these num bers is less than its reciprocal?SolutionProblem 3How m any whole num bers lie in the interval betweenandSolutionProblem 4Inonly of the working adults in Carlin City worked at hom e. By the "at-hom e" work force increased to . In there were approxim ately working at hom e, and in there were . The graph that best illustrates this isSolutionProblem 5Each principal of Lincoln High School serves exactly one -year term. What is the m axim um num ber of principals this school could have during an -year period?SolutionProblem 6Figure is a square. Inside this square three sm aller squares are drawn with the side lengths as labeled. The area of the shaded L-shaped region isSolutionProblem 7What is the m inim um possible product of three different num bers of the set ?SolutionProblem 8Three dice with faces num bered 1 through 6 are stacked as shown. Seven of the eighteen faces are visible, leaving eleven faces hidden (back, bottom, between). The total num ber of dots NOT visible in this view isSolutionProblem 9Three-digit powers of 2 and 5 are used in this cross-number puzzle. What is the only possible digit for the outlined square?SolutionProblem 10Ara and Shea were once the sam e height. Since then Shea has grown 20% while Ara has grow half as m any inches as Shea. Shea is now 60 inches tall. How tall, in inches, is Ara now?SolutionProblem 11The num ber 64 has the property that it is divisible by its units digit. How m any whole num bers between 10 and 50 have this property?SolutionProblem 12A block wall 100 feet long and 7 feet high will be constructed using blocks that are 1 foot high and either 2 feet long or 1 foot long (no blocks m ay be cut). The vertical joins in the blocks m ust be staggered as shown, and the wall m ust be even on the ends. What is the sm allest num ber of blocks needed to build this wall?SolutionProblem 13In triangle , we have and . If bisects , thenSolutionProblem 14What is the units digit of ?SolutionProblem 15Triangles , , and are all equilateral. Points and are m idpoints of and ,respectively. If , what is the perim eter of figure ?SolutionProblem 16In order for Mateen to walk a kilom eter (1000m) in his rectangular backyard, he m ust walk the length 25 tim es or walk its perim eter 10 tim es. What is the area of Mateen's backyard in square m eters?SolutionProblem 17The operation is defined for all nonzero num bers by . Determ ine .SolutionProblem 18Consider these two geoboard quadrilaterals. Which of the following statem ents is true?SolutionProblem 19Three circular arcs of radius 5 units bound the region shown. Arcs and are quarter-circles, and arc is a sem icircle. What is the area, in square units, of the region?SolutionProblem 20You have nine coins: a collection of pennies, nickels, dim es, and quarters having a total value of $, with at least one coin of each type. How m any dim es m ust you have?SolutionProblem 21Keiko tosses one penny and Ephraim tosses two pennies. The probability that Ephraim gets the sam e num ber of heads that Keiko gets isSolutionProblem 22A cube has edge length 2. Suppose that we glue a cube of edge length 1 on top of the big cube so that one of its faces rests entirely on the top face of the larger cube. The percent increase in the surface area (sides, top, and bottom) from the original cube to the new solid form ed is closest toSolutionProblem 23There is a list of seven num bers. The average of the first four num bers is 5, and the average of the last four num bers is 8. If the average of all seven num bers is , then the num ber com m on to both sets of four num bersisSolutionProblem 24If and , thenSolutionProblem 25The area of rectangle is 72. If point and the m idpoints of and are joined to form a triangle,the area of that triangle isSolutionSee Also2000 AMC 8 (Problems • Resources)Preceded by Followed by1999 AMC 82001 AMC 81 •2 •3 •4 •5 •6 •7 •8 •9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 •21 • 22 • 23 • 24 • 25AMC 8AMC 8 Problem s and SolutionsMathem atics com petition resourcesRetrieved from "http://www.artofproblem /Wiki/index.php/2000_AMC_8_Problem s"This page was last m odified on 30 July 2011, at 20:15. This page has been accessed 20,224 tim es. Privacy policy About AoPSWiki Disclaim ers。

《财富》杂志推荐的75本商业必读书

2007-03-04 04:58:52添加 13. Thirteen Days
作者 : Robert F. Kennedy/Arthur Schlesinger Jr. 出版社 : W. W. Norton & Company 评语 : 罗伯特弗兰克林肯尼迪以第一人称叙述的这部令人著迷的书，读起来就像汤姆克兰西（Tom Clancy，美国著名侦探和悬念小说家）的小说。该书讲述了有关授权和做出正确判断的重要经验。
2007-03-04 04:57:08添加 12. The Killer Angels
作者 : Michael Shaara 出版社 : Ballantine Books 评语 : 这部获得普利策奖的历史小说，让你像葛底斯堡战役的参战官兵那样亲历战场。这些人中有试图垂死一拼的罗伯特李（Robert E. Lee）将军。这部小说曾被改编为电影《葛底斯堡》，该电影被誉为最真实、最雄伟地反映美国南北战争的影片，通译《戈底斯堡战役》
作手回忆录》（ Reminiscences of a Stock Operator ）虽然写于 1923 年，但该书仍然能够与《门口的野
蛮人》（Barbarians at the Gate ）摆在一起。这两本书都不是教人具体怎么做的书——总的来说，我们
没有选那些有意识教导人的书，而是选了那些寓教于乐的书。而且没有比一手的信息更有价值的了。既然
自有黄金屋，它们正等待你去发掘呢！
全部图书(75)
推荐 983 人
2007-03-04 04:38:39添加 1. 非同寻常的大众幻想与群众性癫狂
作者 : （英）麦基出版社 : 中国金融出版社
评语 : 这本有关 1634 年荷兰郁金香狂热和 1720 年“南海泡沫”事件（南海公司成立于 1711 年，主要从事奴隶贸易。该公司的股票曾经在市场上炙手可热，吸引了大批投资者。1720 年 1 月，该股票从 128.5 英镑飙升至 1,000 英镑，引起了空前的投机热潮。但同年 9 月，股市狂跌，该股票跌至 124 英镑，使许多投机者破产。——译注）等非

2007-2012 AMC8 中文试题和答案

卤味面起司肉燥面水饭意大利面人數 A3BCD E3 62007年美国AMC8 (2007年11月日时间40分钟)1. 如果希瑞莎能够持续6周，平均每周花10小时帮忙照顾房子，她的父母就帮她买她喜爱乐团的入场券。

在前五周她分别花了8、11、7、12及10小时照顾房子。

在最后一周，她必须要花多少小时去照顾房子才能获得入场券？(A) 9 (B) 10 (C) 11 (D) 12 (E) 13 。

2. 调查650位学生对面食种类的偏好。

选项包含：卤味面、起司肉燥面、水饺、意大利面，调查结果如长条图所示。

试问偏好意大利面的学生数与偏好起司肉燥面的学生数之比值为多少？ (A)52 (B) 21 (C) 45 (D) 35 (E) 25。

3. 250的最小两个质因子之和为多少？(A) 2 (B) 5 (C) 7 (D) 10 (E) 12 。

4. 某间鬼屋有六个窗子。

小精灵乔治从一个窗子进入屋内，而从不同的另一个窗子出来的方法共有多少种？(A) 12 (B) 15 (C) 18 (D) 30 (E) 36 。

5. 姜德想买一辆价值美金500元的越野脚踏车。

在他生日时，祖父母给他美金50元，姑姑给他美金35元，表哥给他美金15元。

他送报纸每周可赚美金16元。

若用他生日得到的所有礼金及送报纸所有赚得的钱去买越野脚踏车，他需要送几周的报纸才能有足够的钱？ (A) 24 (B) 25 (C) 26 (D) 27 (E) 28 。

6. 在1985年美国的长途电话费是每分钟41分钱，在2005年的长途电话费是每分钟7分钱。

试求每分钟长途电话费下降的百分率最接近下列哪一项？ (A) 7 (B) 17 (C) 34 (D) 41 (E) 80 。

7. 房间内5个人的平均年龄为30岁。

若其中一位18岁的人离开了房间，则剩下四个人的平均年龄是几岁？ (A) 25 (B) 26 (C) 29 (D) 33 (E) 36 。

2007年AMC8中文版答案

1. (E) 一个立方体有12条边、8个角和6个面。

和是26。

2. (C) 最小的素数是2，它是每个偶数的因数。

因为58是唯一的偶数，它的质因数最小。

3.(D) 因为120克中有30克是填充物，所以30／120 = 25%的汉堡是填充物。

所以100% - 25% = 75%的汉堡不是填充物。

或者有120 - 30 = 90克不是填料。

所以90／120 = 75%不是4. (C) 下表显示答案一定是5辆三轮车。

或者，设b等于自行车的数量，t等于三轮车的数量。

则车辆数量为b+t = 7，车轮数量为2b+3t = 19。

因为b = 7 - t，因此或者，如果每个孩子都有一辆自行车，就会有14个轮子。

由于有19个轮子，其中5辆必须是三轮车。

5. (B) 如果这个数字的20%是12，这个数字必须是60。

那么60的30%是0.30×60 = 18。

或因为这个数的20%是12，所以这个数的10%是6。

所以这个数的30%是18。

square units平方单位7. (A) 布莱克在四项测试中总共得了4×78 = 312分。

珍妮比布莱克多得10 - 10 + 20 + 20 = 40分，所以她的平均分是352／4 = 88，比布莱克高10分。

或Jenny和Blake的测试总分差为10 - 10 + 20 + 20 = 40分。

平均差值是40 ／4= 10分。

8.(A) 因为所有的饼干都有相同的厚度，只有表面的面积，需要考虑它们的形状。

阿特饼干的表面积梯形饼干是1／2·3·8 = 12平方英寸。

因为他做了12块饼干面团的面积是12×12 = 144平方英寸。

罗杰的饼干每个的表面积为2·4 = 8平方英寸;因此,他就能得到144÷8 = 18块饼干。

保罗的平行四边形饼干每个都有2·3 = 6 平方英寸的表面积。

他有144÷6 = 24块饼干特丽莎的三角形饼干每个都有1／2·4·3 = 6 平方英寸的表面积。