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聚磷菌AP7的筛选及除磷特性研究
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Schmalz SNG-AP needle grippers产品说明说明书
Needle GrippersNeedle Grippers SNG-APNeedle stroke max. 3 mm to max. 20 mm (variable)Needle grippers SNG-AP•Needle gripper for handling non-rigid and highly porous materials(primarily textiles)•Handling materials that are difficult to grip using vacuum such as composite textiles, fleece, filter materials, insulation and foam materials etc.•Flexible handling of materials with changing stacking height due to free selectable stroke adjustmentSystem design needle grippers SNG-AP•Driven by double-acting pneumatic cylinders •High-strength housing with lightweight design (1)•Three sizes with needle strokes of max. 3 mm, 10 mm or 20 mm •Adjustment wheel (2) with scale for continuous, simultaneous stroke adjustment•Ten needles (3) with diameters of 0.8 mm or 1.2 mm (depending on the model)•Insertion angle of 30° or 45° (depending on the model)•Optional sensors for monitoring the needle end positions•Can also be mounted with the Schmalz holder system HTSNeedle grippers SNG-AP being used for handling composite textiles•Intersecting needles and small gripping area>Safe handling, even of small and very unstable workpieces •Low weight and double-acting pneumatic cylinders >High acceleration for minimized cycle times •Tool-free simultaneousneedle stroke adjustment up to a maximum of 20 mm >Individual adaptation to different workpiece geometries; fast start of operations and set-up time •One central pneumatic drive>Synchronous extension and retraction of the needles; reduces the need for couplings and hoses •Blow off function for fast and reliable load release >High level of process reliability and exactpositioning; short cycle times •Quick and tool-free cleaning of the needles and replacing the needle modules>Low maintenanceNeedle GrippersNeedle Grippers SNG-APNeedle stroke max. 3 mm to max. 20 mm (variable)Needle gripper SNG-AP is delivered assembled. The product consists of:•Gripper of type SNG-AP – available with various needle diameters and strokesAvailable spare parts: needle modules, maintenance coverAvailable accessories: mounting plate, holder system, add-on kit sensor**Set of sensor and mounting element***Note: suitable screw in push fittings can be found under "Screw in push fittings" in section "Filters and Connections"**Set of two coveragesy o f C M A /F l o d y n e /H y d r a d y n e ŀ M o t i o n C o n t r o l ŀ H y d r a u l i c ŀ P n e u m a t i c ŀ E l e c t r i c a l ŀ M e c h a n i c a l ŀ (800) 426-5480 ŀ w w w .c m a f h .c o mNeedle GrippersNeedle Grippers SNG-APNeedle stroke max. 3 mm to max. 20 mm (variable)SNG-APNeedle GrippersNeedle Grippers SNG-APNeedle stroke max. 3 mm to max. 20 mm (variable)HTS-A2 AP SNGHTS-A3 AP SNGBEF-PLy o f C M A /F l o d y n e /H y d r a d y n e ŀ M o t i o n C o n t r o l ŀ H y d r a u l i c ŀ P n e u m a t i c ŀ E l e c t r i c a l ŀ M e c h a n i c a l ŀ (800) 426-5480 ŀ w w w .c m a f h .c o mNeedle GrippersNeedle Grippers SNG-VNeedle stroke 0 mm to 7 mm (variable)Needle grippers SNG-V•Needle gripper for handling non-rigid and highly porous materials(primarily textiles)•Handling materials that are difficult to grip using vacuum such as composite textiles, fleece, filter materials, insulation and foam materials etc.System design needle gripper SNG-V•Robust aluminum housing (1)•Drive via double-acting pneumatic cylinders (2)•10 needles with diameter 1.2 mm (3)•Insertion angle 30°•Continuously variable stroke adjustment (4)•Optional mounting with holder system HTSNeedle grippers SNG-V being used for handling composite textiles•Intersecting needles >High holding force, even for flexible, non-rigid workpieces •Minimized active contact surface>Handling of small workpieces possible•Double-acting pneumatic cylinders>Very short cycle times •Variable needle stroke>Individual adjustment for different workpiecethicknesses, sizes and shapes •One pneumatic connection point for both pneumatic cylinders>Saves pneumatic tubes and connectors; ensuressynchronous movement of needlesNeedle GrippersNeedle Grippers SNG-VNeedle stroke 0 mm to 7 mm (variable)Needle gripper SNG-V is delivered assembled.Available spare parts: needle module Available accessories: mounting plate**Including mounting screwsy o f C M A /F l o d y n e /H y d r a d y n e ŀ M o t i o n C o n t r o l ŀ H y d r a u l i c ŀ P n e u m a t i c ŀ E l e c t r i c a l ŀ M e c h a n i c a l ŀ (800) 426-5480 ŀ w w w .c m a f h .c o mNeedle GrippersNeedle Grippers SNG-VNeedle stroke 0 mm to 7 mm (variable)SNG-V 10 1.2 VBEF-PL SNGNeedle GrippersNeedle Grippers SNG-MNeedle Stroke 3 mmNeedle grippers SNG-M•Needle gripper for handling of flexible, non-rigid components •Handling of materials which are difficult to grip with vacuum, such as composite textiles, fleece, filters, woven fibreglass or carbon-fibre, woven aramide, foam materials, etc.System design needle grippers SNG-M•Robust aluminum housing •Four needles (2)•Activated by compressed air, needles retracted by springs on the right (1) or optional above (3)•Insertion angle 30°•The needle gripper can be optionally connected using a mounting plateNeedle grippers SNG-M being used for handling structured foam materials•Very small size>Optimal for installation in restricted spaces •Needles retracted by springs >Only one control signal •Synchronised extension of the needles>Safe handling of the work-pieces•Optionally available with adapter flange plate>Perfect adaptation to other mounting componentsy o f C M A /F l o d y n e /H y d r a d y n e ŀ M o t i o n C o n t r o l ŀ H y d r a u l i c ŀ P n e u m a t i c ŀ E l e c t r i c a l ŀ M e c h a n i c a l ŀ (800) 426-5480 ŀ w w w .c m a f h .c o mNeedle GrippersNeedle Grippers SNG-MNeedle Stroke 3 mmNeedle gripper SNG-M is delivered assembled. The assembly consists of:•Gripper of type SNG-MAvailable spare parts: needle piston Available accessories: mounting plate**Note: suitable screw in push fittings can be found under "Screw in push fittings" in section "Filters and Connections"Needle GrippersNeedle Grippers SNG-MNeedle Stroke 3 mmSNG-M 4 0.8BEF-PL SNGy o f C M A /F l o d y n e /H y d r a d y n e ŀ M o t i o n C o n t r o l ŀ H y d r a u l i c ŀ P n e u m a t i c ŀ E l e c t r i c a l ŀ M e c h a n i c a l ŀ (800) 426-5480 ŀ w w w .c m a f h .c o m。
不同助跑速度急停起跳对排球运动员膝关节生物力学特征的影响
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摘-要目的本文旨在探究改变急停起跳动作的助跑速度对排球运动员膝关节生物力学特征的影响为 排球项目中的下肢损伤机制以及损伤预防和康复工作提供科学依据 方法使用 # 镜头 =>A4:9D9+"" 万像 素的三维红外运动捕捉系统和两块 _:984;7三维测力台同步采集受试者在不同助跑速度下完成急停起跳动 作时膝关节的运动学和 动 力 学 信 号采 样 频 率 分 别 为 $""dQ和 %"""dQ 通 过 =>A4:9D9'7A1R ^A<AM;7 $"%*E$和 `:9>A4
N-CHANNEL ENHANCEMENT MODE Electronics Corp.POWER MOSFET▼Simple Drive Requirement BV DSS 30V ▼ Low Gate Charge R DS(ON)9m Ω▼ Fast Switching I D60A▼ RoHS CompliantDescriptionAbsolute Maximum RatingsSymbol Units V DS V V GSV I D @T A =25℃A I D @T A =100℃A I DMA P D @T A =25℃W W/℃T STG ℃T J℃Symbol Value Units Rthj-c Thermal Resistance Junction-case Max. 2.8℃/W Rthj-aThermal Resistance Junction-ambientMax.110℃/WData and specifications subject to change without notice200823053-1/4AP70T03GH/JPb Free Plating ProductParameterRating Drain-Source Voltage 30Gate-Source Voltage±20Continuous Drain Current, V GS @ 10V 60Continuous Drain Current, V GS @ 10V 43Pulsed Drain Current 1195Total Power Dissipation 53-55 to 175Operating Junction Temperature Range-55 to 175Linear Derating Factor 0.36Thermal DataParameterStorage Temperature RangeThe Advanced Power MOSFETs from APEC provide the designer with the best combination of fast switching,ruggedized device design, low on-resistance and cost-effectiveness.The TO-252 package is universally preferred for all commercial-industrial surface mount applications and suited for low voltage applications such as DC/DC converters. The through-hole version (AP70T03GJ) are available for low-profile applications.G DSTO-252(H)GDSTO-251(J)Electrical Characteristics@T j=25o C(unless otherwise specified) Symbol Parameter Test Conditions Min.Typ.Max.UnitsBV DSS Drain-Source Breakdown Voltage V GS=0V, I D=250uA30--V ΔB V DSS/ΔT j Breakdown Voltage Temperature Coefficient Reference to 25℃, I D=1mA-0.03-V/℃R DS(ON)Static Drain-Source On-Resistance V GS=10V, I D=33A--9mΩV GS=4.5V, I D=20A--18mΩV GS(th)Gate Threshold Voltage V DS=V GS, I D=250uA1-3V g fs V DS=10V, I D=33A-35-S I DSS Drain-Source Leakage Current (Tj=25o C)V DS=30V, V GS=0V--1uA Drain-Source Leakage Current (T j=175o C)V DS=24V ,V GS=0V--250uAI GSS Gate-Source Leakage VGS= ±20V--±100nA Q g Total Gate Charge2I D=33A-1727nC Q gs Gate-Source Charge V DS=20V-5-nC Q gd Gate-Drain ("Miller") Charge V GS=4.5V-10-nC Q oss Output Charge V DD=15V,V GS=0V-13.522nC t d(on)Turn-on Delay Time2V DS=15V-8-ns t r Rise Time I D=33A-105-ns t d(off)Turn-off Delay Time R G=3.3Ω,V GS=10V-22-ns t f Fall Time R D=0.45Ω-9-ns C iss Input Capacitance V GS=0V-14852400pF C oss Output Capacitance V DS=25V-245-pF C rss Reverse Transfer Capacitance f=1.0MHz-170-pF Source-Drain DiodeSymbol Parameter Test Conditions Min.Typ.Max.Units V SD Forward On Voltage2I S=33A, V GS=0V-- 1.3V t rr Reverse Recovery Time I S=20A, V GS=0V,-27-ns Q rr Reverse Recovery Charge dI/dt=100A/µs-20-nCNotes:1.Pulse width limited by safe operating area.2.Pulse width <300us , duty cycle <2%.2/4 AP70T0G3H/JAP70T03GH/JFig 3. On-Resistance v.s. Gate VoltageFig 4. Normalized On-Resistancev.s. Junction TemperatureReverse DiodeJunction TemperatureFig 8. Typical Capacitance CharacteristicsFig10. Effective Transient Thermal ImpedanceFig 11. Switching Time Waveform Fig 12. Gate Charge WaveformAP70T03GH/J。
W78C438CF-40资料
8-BIT MICROCONTROLLERPublication Release Date: July 1998GENERAL DESCRIPTIONThe W78C438C is a high-performance single-chip CMOS 8-bit microcontroller that is a derivative of the W78C58 microcontroller family. The W78C438C is functionally compatible with the W78C32,except that it provides either a 64 KB program/1 MB data memory address or memory-mapped chip select logic, five general I/O ports, and four external interrupts.In the W78C32, two I/O ports, Port 1 and Port 3, are available for general-purpose use (Port 3 also supports alternative functions), and Port 2 and Port 0 are used as the address bus and data bus,respectively. To enable Port 0 and Port 2 to also be used as general purpose I/O ports, the W78C438C provides two dedicated address ports (AP5 and AP6) that serve as address output for 64KB of memory and one address/data port (DP4) that serves as ROM code input and external RAM data input/output. Unlike the W78C32, this product does not require an external latch device for multiplexing low byte addresses. The W78C438C also provides four pins (AP7.0−AP7.3) to support either 64 KB program/1 MB data memory space or memory-mapped chip select logic, one parallel I/O port (Port 8) without bit addressing mode, and two additional external interrupts (INT2, INT3) .The W78C438C is programmed in a manner fully compatible with that used to program the W78C32,except that the external data RAM is accessed by the "MOVX @Ri" instruction. Address paging is performed by loading page addresses into the HB (high byte) register, which is not a standard register in the W78C32, before execution of the "MOVX @Ri" instruction.FEATURES•8-bit CMOS microcontroller •Fully static design •DC to 40 MHz operation •ROM-less operation•256-byte on-chip scratchpad RAM•Either 64 KB program/1 MB data memory address space or 4 memory-mapped chip select pins •One 8-bit data/address port•Two 8-bit and one 4-bit (optional) address ports •Five 8-bit bidirectional I/O ports −Four 8-bit bit-addressable I/O ports and one 8-bit parallel I/O port •Eight-source, two-level interrupt capability •Three 16-bit timer/counters •Four external interrupts•One full-duplex serial channel •Built-in power management −Idle mode−Power-down mode •Packages:− 84-pin PLCC: W78C438CP-24/40− 100-pin PQFP: W78C438CF-24/40PIN CONFIGURATIONSPublication Release Date: July 1998Pin Configurations, continuedPIN DESCRIPTIONP0.0−P0.7 I/O Port 0These pins function the same as those in the W78C32, except that a multiplexed address/data bus is not provided during accesses to external memory.P1.0−P1.7 I/O Port 1Functions are the same as in the W78C32.P2.0−P2.7 I/O Port 2Functions are the same as in the W78C32, except that an upper address bus is not provided during accesses to external memory.P3.0−P3.7 I/O Port 3Functions are the same as in the W78C32.DP4.0−DP4.7 Data/Address BusDP4 provides multiplexed low-byte address/data during access to external memory.AP5.0−AP5.7 Address BusAP5 outputs the <7:0> address of the external ROM multiplexed with the <7:0> address of the external data RAM.AP6.0−AP6.7 Address BusAP6 outputs the <15:8> address of the external ROM multiplexed with the <15:8> address of the external data RAM. During the execution of "MOVX @Ri," the output of AP6 comes from the HB register, which is the page register for the high byte address, and its address is 0A1H.AP7.0−AP7.3 Address Bus/Chip Select PinsSet bit 7 of the EPMA (Extended Program Memory Address) register to determine the functions of port 7. When this bit is "0" (default value), AP7 allows the external memory data to be accessed by outputting the <19:16> address of the external memory from bits<3:0> of the EPMA register during the execution of "MOVC A, @A+DPTR" or "MOVX dest, src." At all other times, AP7<3:0> will output 0H.When this bit is "1," AP7<3:0> (CS3−0) are the chip select pins, which support memory-mapped peripheral device select, and only one pin is active low at any one time. These pins are decoded by AP6<7:6>. For details, see the table below.AP6.7AP6.6DESCRIPTION00AP70: low; others: high01AP71: low; others: high10AP72: low; others: high11AP73: low; others: highPublication Release Date: July 1998P8.0−P8.7 I/O PortFunctions are the same as those of Port 1 in the W78C31, except that they are mapped by the P8register and not bit-addressable. The P8 register is not a standard register in the W78C32. Its address is at 0A6H.INT2, INT3 External Interrupt, InputFunctions are similar to those of external INT0, INT1 in the W78C32, except that the functions/status of these interrupts are determined/shown by the bits in the XICON (External Interrupt Control)register. The XICON register is bit-addressable but is not a standard register in the W78C32. Its address is at 0C0H. For details, see the Functional Description below.EA External Address, InputFunctions same as W78C32.RST, XTAL1, XTAL2, PSEN , ALEFunctions same as W78C32.BLOCK DIAGRAMFUNCTIONAL DESCRIPTIONThe W78C438C is a functional extension of the W78C58 microcontroller. It contains a 256 × 8 RAM, 64 KB program/1 MB data memory address or memory-mapped chip select logic, two 8-bit address ports, one 8-bit data port, five general I/O ports, four external interrupts, three timers/counters, and one serial port.Dedicated Data and Address PortThe W78C438C provides four general-purpose I/O ports for W78C32 applications; the address and data bus are separated from Port 0 and Port 2 so that these ports can be used as general-purpose I/O ports. In this product, DP4 is the data bus for external ROM and RAM, AP5<7:0> are the low byte address, AP6<7:0> are the high byte address, PSEN enables the external ROM to DP4, and P3.6 (WR) and P3.7 (RD) are the write/read control signals for the external RAM. The external latch for multiplexing the low byte address is no longer needed in this product. The W78C438C uses AP5 and AP6 to support 64 KB external program memory and 64 KB external data memory, just as a standard W78C32 does.The W78C438C provides four pins, AP7.3−AP7.0 (CS3−CS0), to support either 64 KB program/1 MB data memory space or memory-mapped chip select logic. Bit 7 of the EPMA (Extended Program Memory Address) register, which is described in Table 1 below, determines the functions of these pins.When this bit is "0" (the default value), AP7<3:0> support external program/data memory addresses up to 64 KB/1 MB for applications which need additional external memory to store large amounts of data.Although there is 1M bytes memory space, instructions stored here can not be run at full range of this area except the first 64 Kbytes. It is owing to the fact that during the instruction fetch cycle, AP7<3:0> always output 0s to address lines A19−A16. This limits the program code to store at address 0−0FFFFH (64K). The rest of the area (10000H−FFFFFH) can be treated as ROM data storage which can be read by "MOVC A, @A+DPTR" instruction.When "MOVC A, @A+DPTR" is executed to read the external ROM data or "MOVX dest, src" is executed to access the external RAM data, AP7<3:0> output address <19:16> from bits <3:0> of the EPMA (Extended Program Memory Address) register. At other times, AP7<3:0> always output 0H to ensure the instruction fetch is within the 64K program memory address. Different banks can be selected by modifying the content of the EPMA register before the execution of "MOVC A, @A+DPTR" or "MOVX dest, src."[Example]. Access the external ROM/RAM data from external memory space.CLR A; Clear Accumulator.MOV DPTR, #0H; Clear DPTR.MOV0A2H, #02; Initialize EPMA(0A2H). EPMA.7 = 0: extended memory space; EPMA.<3:0> = 0010B, the address range: 20000−2FFFFH.MOVC A, @A+DPTR; Read the external ROM data from location 20000H.MOVX A, @DPTR; Read the external RAM data from location 20000H.CLR AMOV0A2H, #03H; EPMA.<3:0> = 0011B, the address range: 30000H−3FFFFH.MOVC A, @A+DPTR ; Read the external ROM data from location 30000H.MOVX@DPTR, A; Write the contents of Accumulator to external RAM data.; location 30000H.Publication Release Date: July 1998(A) EPMA.7 = 0chip select logic, which eliminates the need for glue logic. These pins are decoded by AP6<7:6>.Only one pin is active low at any time. That is, they are active individually with 16K address resolution. For example, CS0 is active low in the address range from 0000H to 3FFFH, CS1 is active low in the address range from 4000H to 7FFFH, and so forth.(B) EPMA.7 = 1The EPMA register is a nonstandard 8-bit SFR at address 0A2H in the standard W78C32. To read/write the EPMA register, one can use the "MOV direct" instruction or "read-modify-write" instructions. Bits <6:4> of the EPMA register are reserved bits, and their output values are 111B if they are read. The content of EPMA is 70H after a reset. The EPMA register does not support bit-addressable instructions.BIT NAME FUNCTION7EPMA7EPMA7 = 0: 64 KB program/1 MB data memory space modeEPMA7 = 1: memory-mapped chip select mode6EPMA6Reserved5EPMA5Reserved4EPMA4Reserved3EPMA3Value of AP7.32EPMA2Value of AP7.21EPMA1Value of AP7.10EPMA0Value of AP7.0Table 1. Functional Description of EPMA RegisterAdditional I/O PortThe W78C438C provides one parallel I/O port, Port 8. Its function is the same as that of Port 1 in the W78C31, except that it is mapped by the P8 register and is not bit-addressable. The P8 register is not a standard register in the standard W78C32. Its address is at 0A6H. To read/write the P8 register, one can use the "MOV direct" instruction or "read-modify-write" instructions.[Example]: MOV 0A6H, A; Output data via Port 8.MOV A, 0A6H; Input data via Port 8.Additional External InterruptThe W78C438C provides two additional external interrupts, INT2 and INT3, whose functions are similar to those of external interrupts 0 and 1 in the W78C32. The functions (or the status) of these interrupts are determined by (or shown by) the bits in the XICON (External Interrupt Control) register. For details, see Table 2. The XICON register is bit-addressable but is not a standard register in the standard 80C32. Its address is at 0C0H. To set/clear the bit of the XICON register, one can use the vector addresses and the priority polling sequence within the same level are shown in Table 3. [Example].SETB0C0H; INT2 is falling-edge triggered.SETB0C3H; INT2 is high-priority.SETB0C2H; Enable INT2.CLR0C4H; INT3 is low-level triggered.Publication Release Date: July 1998Table 2. Functions of XICON RegisterINTERRUPT SOURCE VECTOR ADDRESSPRIORITY SEQUENCEExternal Interrupt 003H 0 (Highest)Timer/Counter 00BH 1External Interrupt 113H 2Timer/Counter 11BH 3Serial Port 23H 4Timer/Counter 22BH 5External Interrupt 233H 6External Interrupt 33BH7 (Lowest)Table 3. Priority of InterruptsNewly Added Special Function RegistersThe W78C438C uses four newly defined special function registers, which are described in Table 4. Toread/write these registers, use the "MOV direct" or "read-modify-write" instructions.Table 4. Newly Added Special Function Registers of the W78C438CNotes:1. The instructions used to access these nonstandard registers may cause assembling errors with respect to the 2500 A. D.assembler, but these errors can be ignored by adding directive ".RAMCHK OFF" ahead these instructions.2. In the newly added SFR of W78C438C, only XICON register is bit-addressable.Power Reduction FunctionThe W78C438C supports power reduction just as the W78C32 does. The following table shows the status of the external pins during the idle and power-down modes.Note: AP7 is either 0 or a value decoded by AP6<7:6>, depending on the value of EPMA.7.Programming DifferenceThe W78C438C is programmed in the same way as the W78C32, except that the external data RAM is accessed by a "MOVX @Ri" instruction. To support address paging, there is an additional 8-bit SFR "HB" (high byte), which is a nonstandard register, at address 0A1H. During execution of the "MOVX @Ri" instruction, the contents of HB are output to AP6. The page address is modified by loading the HB register with a new value before execution of the "MOVX @Ri" instruction. To read/write the HB register, one can use the "MOV direct" instruction or "read-modify-write" instructions. The HB register does not support bit-addressable instructions.[Example].MOV R1, #0H; R1 = 0.MOV0A1H, #0FFH; HB contents FFH.MOVX A, @R1; Read the contents of external RAM location FF00H into; Accumulator.MOV0A1H, #12H; HB contents 12H.MOVX@R1, A; Copies the contents of Accumulator into external RAM; location 1200H.ABSOLUTE MAXIMUM RATINGSPARAMETER SYMBOL MIN.MAX.UNIT DC Power Supply V DD−V SS-0.3+7.0V Input Voltage V IN V SS -0.3V DD +0.3V Operating Temperature T OPR070°C Storage Temperature T STG-55+150°C Note: Exposure to conditions beyond those listed under Absolute Maximum Ratings may adversely affect the life and reliability of the device.Publication Release Date: July 1998DC CHARACTERISTICSDD −SS A OSC Notes:1. 0 < V IN < V DD , for INT2, INT3, RESET, EA , Port 0, DP4, P1, P2, P3 and P8 inputs in leakage.2. Using an internal pull low/high resistor (approx. 30K).3. ALE, PSEN , P0 and DP4 in external program or data access mode.4. The maximum input voltage is V DD +0.2V.5. XTAL1 is a CMOS input and RESET is a Schmitt trigger input.AC CHARACTERISTICSAC specifications are a function of the particular process used to manufacture the product, the ratings of the I/O buffers, the capacitive load, and the internal routing capacitance. Most of the specifications can be expressed in terms of multiple input clock periods (T CP), and actual parts will usually experience less than a ±20 nS variation.Clock Input WaveformPARAMETER SYMBOL MIN.TYP.MAX.UNIT NOTES Operating Speed F OP0-40MHz1 Clock Period T CP25--nS2 Clock High T CH10--nS3 Clock Low T CL10--nS3Notes:1. The clock may be stopped indefinitely in either state.2. The T CP specification is used as a reference in other specifications.3. There are no duty cycle requirements on the XTAL1 input.Program Fetch CycleData Memory Read/Write CycleNote: "∆" (due to buffer driving delay and wire loading) is 20 nS.Publication Release Date: July 1998TIMING WAVEFORMSProgram Fetch CycleData Memory Read/Write CycleTYPICAL APPLICATION CIRCUITSUsing 128K × 8 bit External EPROM (W27E010)Figure APublication Release Date: July 1998CRYSTAL C1C2R 16 MHz 30P 30P −24 MHz 15P 15P −33 MHz 10P 10P 6.8K 40 MHz5P5P6.8KAbove table shows the reference values for crystal applications.Notes:1. For C1, C2, R components refer to Figure A.2. It is recommended that the crystals be replaced with oscillators for applications above 35 MHz.PACKAGE DIMENSIONS84-pin PLCCPackage Dimensions, continued100-pin QFPHeadquarters No. 4, Creation Rd. III,Science-Based Industrial Park,Hsinchu, Taiwan TEL: 886-3-5770066FAX: 886-3-5792766/Voice & Fax-on-demand: 886-2-27197006Taipei Office11F, No. 115, Sec. 3, Min-Sheng East Rd.,Taipei, TaiwanTEL: 886-2-27190505FAX: 886-2-27197502Winbond Electronics (H.K.) Ltd.Rm. 803, World Trade Square, Tower II,123 Hoi Bun Rd., Kwun Tong,Kowloon, Hong Kong TEL: 852-********FAX: 852-********Winbond Electronics North America Corp.Winbond Memory Lab.Winbond Microelectronics Corp.Winbond Systems Lab.2727 N. First Street, San Jose,CA 95134, U.S.A.TEL: 408-9436666FAX: 408-5441798Note: All data and specifications are subject to change without notice.。
AP环境科学教材配套练习题答案
Environmental Science Answers for Chapter ExerciseThe first edition by Mony SuTopic 1 Earth Systems and Resources (10-15%)Chapter 02 Principles of Science and SystemsMultiple Choice Questions1 2 3 4 5 6 7 8 9 10B D D B E A AC A B11 12 13 14 15 16 17 18 19 20A C C A A A C D A A21 22 23A A DTrue / False Questions24 25 26F F FChapter 14 Geology and Earth ResourcesMultiple Choice Questions1 2 3 4 5 6 7 8 9 10C D E D A D B B B C11 12 13 14 15 16 17 18 19 20C B A C A E B AD B21 22 23 24 25 26 27 28 29 30E C D C B C A A D A31 32 33 34 35 36 37 38 39 40B A B EC C C A A B41ATrue / False Questions42 43 44 45 46T T T T FEssay Questions47.The diagram should look similar to Figure 14.8 on p. 307 in the textbook. Arrows should indicate that each rock type can be transformed into the other types, depending on the conditions.Chapter 15 Climate ChangeMultiple Choice Questions1 2 3 4 5 6 7 8 9 10A A C C DB B A B D11 12 13 14 15 16 17 18 19 20B A DC A BD C C D21 22 23 24 25 26 27 28 29 30B A BC A E A B B E31 32 33 34 35 36 37 38 39 40B A ACD A D C A A41 42 43 44 45 46 47 48 49 50A D D C C CB EC C51 52 53 54 55C A BD DTrue / False Questions56 57 58 59 60 61T T F F F FEssay Questions62.ENSO = El Nino Southern Oscillation. El Nino years typically bring intense storms and heavy rain from California across the Midwestern states. In general, the U.S. sees an increased amount of rainfall during El Nino years. La Nina years normally bring hot, dry weather to most of the U.S. The Pacific northwest (Washington, Oregon) usually has the reverse weather patterns. (Drier during El Nino and wetter during La Nina).63.The Kyoto Protocol is a treaty that was established in Kyoto, Japan in 1997. About 160 nations agreed to cut back on emissions of the main greenhouse gases to help with the problems associated with worldwide climate change. Even though the U.S. played an important role in leading the negotiations at Kyoto, it has never been ratified by the U.S. government. President Bush claims that it would be detrimental to our economy to doso. Several big businesses in the U.S. have joined with four of the largest environmental groups to call for strong national legislation to ultimately achieve significant reductions of greenhouse gases. These are huge companies that can make a major impact (GE, Alcoa, BP Gas, etc.) if they are successful. On an individual level, there are many things that can be done including: driving less, driving a fuel-efficient vehicle, planting trees, producing less waste (recycle or compost when possible), adjusting thermostats-especially when not at home, insulating your home, purchasing energy-efficient appliances, turning off lights, computers and other energy-consuming items when not in use, etc.Chapter 17 Water Use and ManagementMultiple Choice Questions1 2 3 4 5 6 7 8 9 10C A B A B C A C A A11 12 13 14 15 16 17 18 19 20D C A C C D B AE E21 22 23 24 25 26 27 28 29 30B D DC E B A C A A31 32 33 34 35 36D C D C B ATrue / False Questions37 38 39 40T F T FEssay Questions41.By comparison, both projects have the same purpose. That is to divert or transfer water from one region to another. In California, there is plentiful rainfall in the north, so excess water is pumped to the south. In China, it is the reverse. Southern China has plentiful water and will be pumping it to the north where it is scarcer. In California, much of the original project was done rather underhandedly. In the early 1900s, land in northern California was quietly purchased by persons in power in Los Angeles. Eventually, they controlled over 90% of the water rights in the Owens Valley area of northern California. They built a huge aqueduct and transported the water to the south. So much water was transferred that the Owens River became dry for much of its course and Owens Lake, which was fed by the river, completely disappeared. In the 1940s, even more water was needed, so sources even further north were tapped to increase the supply. Another lake in this area lost half of its volume. This had serious environmental effects by decimating the population of brine shrimp that lived in the lake. This in turn decreased the number of waterbirds that relied on the shrimp as a food source. After many years of legal issues, the California Water Resources Board ruled in 1994 that LA must allow some water to replenish Lake Mono (the second lake affected). By 2014, the lake must be returned to its 1964 level. Some increase has been seen so far. The ecology also seems to be recovering slowly in this area. In China, a huge multi-year, multi-billion dollar project is now underway to transfer water from southern to northern China. This will involve not one, but three separate routes to transfer the water to the needed regions. There are many problems and issues that will need to be dealt with. One issue is that water polluted by sewage and industrial waste is being transferred. Even though some areas are extremely dry, they are reluctant to accept this water. One of the routes will be extremely expensive and probably will not reach completion until at least 2050. This route will tunnel through mountains and over deep canyons. In addition, if global warming melts all of Tibet's glaciers, it may not be feasible in the long run. Environmental scientists worry that drawing from the Yangtze River will only worsen its pollution problems. Drawing water away from rivers on which millions rely only makes pollution problems worse. Downstream wetlands may also dry up, and ocean circulation may even be affected.42.Should include at least some of the following, but may include others as well. ▪ don't flush every time you use the toilet ▪ don't let the faucet run when washing hands, dishes, or brushing teeth ▪ take shorter showers ▪ use water-efficient plumbing fixtures ▪ check for leaky plumbing ▪ xeriscaping ▪ use recycled (gray) water for outside uses (if possible)—watering lawn, washing car, etc. ▪ run dishwasher only when fullTopic 2 The Living World (10-15%)Chapter 03 Matter, Energy, and LifeMultiple Choice Questions1 2 3 4 5 6 7 8 9 10E A B D E C C D E C11 12 13 14 15 16 17 18 19 20B E DC E A B E C A21 22 23 24 25 26 27 28 29 30B A B DC B C E A C31 32 33 34 35 36 37 38 39 40B DC AD A C B B E41 42 43 44 45 46 47 48 49 50E D D E A D E D A C51 52 53B E ATrue / False Questions54 55 56 57T T T FEssay Questions58.IV is false. There are many types of biogeochemical cycles, including carbon, nitrogen, phosphorus, and sulfur.59.Points awarded on depth and accuracy of answer. Answer should mention sunlight as the starting point for all energy and transfer of energy through living things in the foodchain/web (including energy lost as heat along each step of the pathway).60.Should include the following: carbon dioxide in the atmosphere, taken up by photosynthesis and released by cellular respiration (same in the oceans); carbon stored in the oceans; carbon deposits (dead organisms) forming calcium carbonate (limestone) on the ocean floor; carbon deposition from dead plants and animals millions of years ago formed today's fossil fuels.Chapter 04 Evolution, Biological Communities, and Species InteractionsMultiple Choice Questions1 2 3 4 5 6 7 8 9 10D C B B B A D DE A11 12 13 14 15 16 17 18 19 20B D BC BD C A A B21 22 23 24 25 26 27 28 29 30D A B D B B D D A D31 32 33 34 35 36 37 38 39 40A ABCD A A C A D41 42 43 44 45 46 47 48E C A E A E B BChapter 05 BiomesMultiple Choice Questions1 2 3 4 5 6 7 8 9 10B C A B C D B B D D11 12 13 14 15 16 17 18 19 20D C D C B BE B A C21 22 23 24 25 26 27 28 29 30D A B D C CE E D D31 32 33 34 35 36 37 38 39 40C B B BD B A A B A41 42 43 44 45 46 47 48 49 50C E E B C B B C C C51DTrue / False Questions52 53 54 55 56F T F T TChapter 11 BiodiversityMultiple Choice Questions1 2 3 4 5 6 7 8 9 10C CD AE C A A C D11 12 13 14 15 16 17 18 19 20D C D A B C C BE B21 22 23 24 25 26 27 28 29 30A D C CBC AD D B31 32 33 34 35 36 37 38 39 40A D D D A DB BC D41 42 43 44 45 46 47 48D B A B CE B ATrue / False Questions49 50 51 52 53T F T T FEssay Questions54.Should include some of the following, but may include others as well. 1) We have a large variety of food sources to choose from—all types of grains, starches, fruits, vegetables, seafood, and meat. 2) Pollinators provide us with many of our food sources, so they are also extremely important. They include birds, insects, and bats. 3) Bacteria and fungi provide us with many antibiotics. 4) Bacteria and fungi are also very beneficial as decomposers—cycling of nutrients. 5) Many plants have provided us with numerous drugs used to treat all types of diseases and illnesses. There are many discovered and undiscovered plants that may have medicinal potential. 6) Organisms provide us with ecological services that are invaluable to us—things like soil formation, water purification, production of oxygen, etc. 7) Organisms provide us with the opportunity for recreation—camping in a forest, fishing, horseback riding, etc. 8) Biodiversity can be economically beneficial. Many countries are now turning to ecotourism—making income by maintaining the natural environment for visitors to enjoy.55.Will vary depending upon the region you live in.Topic 3 Population (10-15%)Chapter 06 Population BiologyMultiple Choice Questions1 2 3 4 5 6 7 8 9 10A D CB A B ECD B11 12 13 14 15 16 17 18 19 20A EBC B A E E C E21 22 23 24 25 26 27 28 29 30A C ABCDE C E D31 32 33 34 35 36D B A C D ATrue / False Questions37 38 39 40T F F TChapter 07 Human PopulationsMultiple Choice Questions1 2 3 4 5 6 7 8 9 10C E E E E E A B A C11 12 13 14 15 16 17 18 19 20C A B A B E CD C A21 22 23 24 25 26 27 28 29 30C E B A A E E B B C31 32 33 34 35 36 37 38 39 40A B D B D C A B A E41 42 43 44 45 46 47 48 49 50B E DC E A B A A CD E B E C A D D E BTrue / False Questions61 62 63 64F T T TEssay Questions65.General trends, not numbers, should be included. There are three basic trends: 1) Rapidly growing countries - characterized by high birth and death rates, high fertility rates, and typically, high emigration rates 2) Stable populations - characterized by low birth and death rates, low fertility rates, and low emigration rates 3) Negative growth countries - characterized by death rates higher than birth rates, (however, both are low), extremely low fertility rates, (typically less than the 2.1 replacement rate) and low emigration rates66.x-axis should be labeled with increasing years of education, y-axis should be labeled with increasing rates of infant mortality. Graph should show a decline in infant mortality rates as years of education increase. Please include X and Y axis label, appropriate scales on the axes, and a legend.Topic 4 Land and Water Use (10-15%)Chapter 09 Food and HungerMultiple Choice Questions1 2 3 4 5 6 7 8 9 10C CD B D DE A C AE E B D A C C D D A21 22 23 24 25 26 27 28D C D B AE A DTrue / False Questions29 30 31 32 33 34T F F T T FEssay Questions35.Genetic recombination involves removing specific genes from one organisms and inserting them into another. This type of technology allows for many advantages. Someone who sees the positive benefits of this technology would be a technological optimist. Scientists working in this field would obviously see the benefits; opponents would most likely not be those in the field of genetic engineering. There are many benefits including: improved crops (yield, pest and disease resistance, salt tolerance, etc.), vaccines could be placed in foods like bananas and potatoes, insulin and other hormones can be mass-produced relatively cheaply.Chapter 10 Farming: Conventional and Sustainable PracticesMultiple Choice Questions1 2 3 4 5 6 7 8 9 10A B B E C D C E E A11 12 13 14 15 16 17 18 19 20B B EC C B E B C B21 22 23 24 25 26 27 28 29 30B E D D BC E B E B31 32 33 34 35 36 37 38 39 40A D AB B BC C B E41 42 43 44 45 46 47 48 49 50B D BC B A C B A AD B CE E D B A E A61 62 63 64 65 66 67 68 69 70B AC E C A E C E B71 72 73 74C D E BTrue / False Questions75 76 77 78 79 80T T T F F TEssay Questions81.Industrial farming produces very large amount of foods—in fact more than enough to feed the world's population (if distributed evenly).However, a large amount of this food goes to waste. The use of pesticides in industrial farming is very high and this results in many environmental problems—Poisoning nontarget species, including beneficial predators, pesticide resistance, reproductive problems in nontarget species, persistence and mobility—all can affect humans and animals thousands of miles away. Pesticides are also responsible for a myriad of human health problems. Organic farming does not result in as great a yield as industrial.However, it is much more eco-friendly. It leaves the soil in much better condition and since prices paid for organic products are higher than conventional, net returns are typically higher with organic crops. Since no pesticides are used, there are no negative health effects or other negative impacts associated with this type of farming.82.Should include at least some of the following, but may include others. ▪ buy organic—should contain no pesticides ▪ wash and scrub all fresh fruits and vegetables to remove residues ▪ peel fruits and vegetables when possible to remove all traces of pesticides ▪ throw away the outer leaves of leafy vegetables to remove highest concentration of pesticides ▪ store food carefully to avoid mold or bacterial growth—these organisms can produce their own toxins ▪ cook foods that you suspect have pesticides to break down residues ▪ trim the fat from meat, chicken, and fish—fat contains the highest concentrations of pesticides ▪ reduce the amount of meat in your diet to reduce your pesticide intake ▪ don't pick and eat wild berries that may have been sprayed—it's better to be safe—wash them first ▪ grow your own fruits and vegetables—then you know exactly where the food came from! Chapter 12 Biodiversity: Preserving LandscapesMultiple Choice Questions1 2 3 4 5 6 7 8 9 10D B C D D B A A C A11 12 13 14 15 16 17 18 19 20A B C B C A C D A B21 22 23 24 25 26 27 28 29 30D E B C C C B C C B31 32 33 34 35 36 37 38 39 40B A E B B D D EC B41 42 43 44C D C BTrue / False Questions45 46 47T T TEssay Questions48.Old growth forests have the following characteristics: very high levels of biodiversity, many unique species live only in old-growth forests, they accumulate more total biomass in standing vegetation per unit area than any other ecosystem, little or no erosion, nutrient-rich soil, only a small percentage remains and large percentages of that are scheduled to be harvested, the most valuable of these forests are protected (at least for now). Tree farms have the following characteristics: the types and sizes of trees can vary depending upon the cutting technique that is used; however, most are made up of one type of tree, most of which are about the same age and size (clear-cutting), typically soil erosion is prevalent due to lack of undergrowth, rotting logs, and other vegetation, soil is also typically nutrient-poor (no vegetation to be recycled—everything is removed), very little biodiversity due to little variation in habitat, alternative methods of cutting such as selective cutting are much better environmentally—decreases erosion, improves soil quality, increases biodiversity among other benefits.49.Brazil has the largest amount of land in protected status as of now. The majority of this protected land is in the Amazon basin. Nine new protected areas in the northern Amazon basin were established in 2006 (along the borders of Suriname and Guyana). About half of this newly protected land will be strictly protected and will create the largest tropical forest reserve in the world. In contrast to this is the Pantanal. This is the world's largestwetland/savanna complex (somewhat similar to the Florida everglades). Some of the regions of the Pantanal have even greater amounts of biodiversity than the Amazon basin. However, most of this region is privately owned and so far, very little of it has any protected status.Chapter 13 Restoration EcologyMultiple Choice Questions1 2 3 4 5 6 7 8 9 10D C AE E A E D A B11 12 13 14 15 16 17 18 19 20C A E E B BD C A A21 22 23 24 25 26 27 28 29 30A C D E A A C E A A31 32 33 34D D B ATrue / False Questions35 36 37 38 39T F F T TEssay Questions40.The intent of both is obviously to preserve the prairie. However, it is being approached in two completely different ways. The Nature Conservancy (TNC) is cooperating with local ranchers and allowing them to continue grazing cattle on most of the land (which TNC owns) in exchange for specific conservation measures including protection of prairie dog colonies and sage grouse nests. They must also control weed growth. TNC's approach is that by keeping ranch families working on the land, it preserves their lifestyle and at the same time, preserves the biodiversity of the Great Plains. Close by, the American Prairie Foundation (APF) is going about preservation by a completely different route. They have purchased approximately the same amount of land as TNC (close to 60,000 acres). Instead of continuing to allow cattle ranching, they will remove all fences and buildings and return the area to wilderness. They also plan to return wildlife including elk, bison, wolves and grizzly bears to the land. Nearby ranchers are not thrilled with the prospect of the predators being returned, as they feel their livestock will be threatened. Many also are not happy that the funding is coming mainly from Wall Street or Silicon Valley in California. They are upset that people with money from the outside are forcing changes upon them. They worry about restrictions that may be placed on the land. The APF defends its side by saying that tourism, bird-watching, and hunting will be allowed on nearly all of its lands and that this will bring in more income than raising cattle.41.Should include some of the following: 1) To reduce sediment influx (erosion from stream banks or other areas), several different methods may be employed including planting ground cover on banks or uplands; gullies that empty into the stream may be filled with rocks or brush; barriers can be used to deflect the current away from the stream banks or to trap sediment (these may include weirs, vanes, dams, logs, bundled brush, root wads, etc.)—these can actually be beneficial in carving out deep pools in the stream bottom, which provide excellent habitat for fish and other organisms; stabilizing stream banks—should be no more than 45 degrees to minimize erosion; soil can be held in place by plants, rocks, or other ground cover; if there is not enough space to recontour, steep banks will need to be supported by rock walls, riprap, or embedded tree trunks.Chapter 22 Urbanization and Sustainable CitiesMultiple Choice Questions1 2 3 4 5 6 7 8 9 10D D AE E B C B E A11 12 13 14 15 16 17 18 19 20C B CD C A B A B C21 22 23 24 25 26 27 28 29 30C A B A B A A C E E31 32 33 34C C B DTrue / False Questions35 36 37 38 39T T F F TEssay Questions40.Push factors: no jobs, lack of food, inadequate housing, political conflicts, racial conflicts, religious conflicts Pull factors: opportunity for education, variety of jobs, entertainment, freedom, social mobility, prestige, power41.Should contain some of the following information and may include others as well. Compare: Both are communities of living things along with the physical environment; both are affected by the abiotic conditions; both have a constant flow of matter and energy cycling through both living and non-living; both involve niches; both have fairly distinctboundaries. Contrast: Cities involve only humans—other species may live there, but are not an integral part of the functioning city; people not affected so much by abiotic factors (e.g., temp. is regulated by A/C and heating, go to work whether it is raining or snowing); many human activities and inputs are part of a city, but not an ecosystem (city foundation, drainage, sewage, pollution, garbage, etc.); infrastructure completely different—man-made in cities, natural in ecosystems.Chapter 23 Ecological EconomicsMultiple Choice Questions1 2 3 4 5 6 7 8 9 10E C E A C B B C C D11 12 13 14 15 16 17 18 19 20C A CD D A BE B E21 22 23 24 25 26 27 28 29 30D A D C A B BE B D31 32 33 34 35 36 37 38 39 40C E B C A ADE A E41 42 43 44 45 46 47 48A AB E D A B ATrue / False Questions49 50 51 52 53T T T F FEssay Questions54.Should look like Fig. 23.7 on p. 521 in textbook.55.Should include some of the following answers: Economist: focus on human resources (buildings, roads, labor); natural systems essential but externalized; manufactured capital is regarded as scarce and valuable; natural capital is regarded as plentiful and cheap; as one natural resource becomes scarce, a substitute will easily be found; based on supply and demand. Ecologist: focus on value of natural services; natural services are internalized; manufactured capital is very large (not really valuable) and puts stresses on natural resources; recycling is important; limited supplies of natural capital, which is valuable and often fragile.Topic 5 Energy Resources and Consumption (10–15%)Chapter 19 Conventional EnergyMultiple Choice Questions1 2 3 4 5 6 7 8 9 10A C EB D D E A D E11 12 13 14 15 16 17 18 19 20A A CB D A D A B B21 22 23 24 25 26 27 28 29 30D C A D AE A E E B31 32 33 34 35 36 37 38 39 40C A BD A B D B D C41 42 43 44 45A B C E BTrue / False Questions46 47 48 49 50 51F F T T F FEssay Questions52.In your evaluation, provide the pros and cons and the context in which each energy source would work best.53.Answers should contain at least some of the following but may contain others.Chapter 20 Sustainable EnergyMultiple Choice Questions1 2 3 4 5 6 7 8 9 10B BC AD C C B A B11 12 13 14 15 16 17 18 19 20E B D E C C C D C C21 22 23 24 25 26 27 28 29 30E E B E A C E A C B31 32 33 34 35A A C A BTrue / False Questions36 37 38 39 40 41F T T F F FEssay Questions42.Solar energy would be the best option for this situation. The new amorphous silicon collectors can be made into lightweight, paper-thin sheets that can be layered right on to roof tiles. A tropical country implies that it is warm and sunny year-round, providing the optimalconditions for solar collection. These collectors are already currently being used in remote places without access to conventional power, so this would be a perfect place for this technology. Homes and offices can be built without power plants and power lines; no fuels would need to be purchased; and you would have no monthly energy bills. Prices of solar electricity are dropping each year and will be competitive with conventional power (fossil fuels) by 2020. Even though the start-up cost may be more currently, in the long run the solar power will more than pay for itself.43.Should contain some of the items listed in the table below.Topic 6 Pollution (25-30%)Chapter 08 Environmental Health and ToxicologyMultiple Choice Questions1 2 3 4 5 6 7 8 9 10D E D A C A B D A A11 12 13 14 15 16 17 18 19 20B ACD B C B B A D21 22 23 24 25 26 27 28 29 30D E C D B A A E D A31 32 33 34 35 36 37 38 39 40D A B A B DE E C A41 42 43 44 45 46 47 48 49 50B C A B A E D C B C51 52 53 54 55C D E C ATrue / False Questions56 57 58 59 60T T T F TEssay Questions61.You would most likely be worried because: (should mention at least one from each category) 1) They may cause kidney and/or liver damage. 2) They may cause some types of cancer. 3) They can act as endocrine disrupters, affecting sex hormones; this can lead to reproductive abnormalities and decreased fertility as well as low sperm counts and decreased sperm motility.62.Should look like Fig. 8.16 in textbook (see explanation for the below figure).Chapter 16 Air PollutionMultiple Choice Questions1 2 3 4 5 6 7 8 9 10E A B C D A B C B A11 12 13 14 15 16 17 18 19 20E C C B A E A B D C21 22 23 24 25 26 27 28 29 30A A D C D D EB A D31 32 33 34 35 36 37 38 39 40C E E B AD CE A C41 42 43 44 45 46 47 48 49B BC BD B D B ATrue / False Questions50 51 52 53 54 55 56 57F F F F T F F FEssay Questions58.Both are formed by atmospheric oxygen (O2) combining with an atom of singlet oxygen (O). In the troposphere, ozone is a major component of smog. It is formed as a photochemical oxidant, resulting mainly from too many hydrocarbons in the air. It is a strong oxidizing agent and damages vegetation and buildings. It is also an irritant to the lungs and eyes. It can be very harmful to persons with underlying respiratory conditions, so itis considered a pollutant. Its role in the stratosphere is completely different. It acts as a UV filter, providing earth with a "natural" shield from incoming solar radiation. When it becomes depleted, due mainly to CFCs, excess UV makes it through the ozone layer. This results in increased incidence of skin cancer and eye damage in humans. It is also harmful to crops, which may show decreased productivity.Chapter 18 Water PollutionMultiple Choice Questions1 2 3 4 5 6 7 8 9 10C ED C A B A A C C11 12 13 14 15 16 17 18 19 20C B A B CD B C A B21 22 23 24 25 26 27 28 29 30D CE E D A E E E A31 32 33 34 35 36 37 38 39 40B C A E D A A C A B41 42D ETrue / False Questions43 44 45 46F F F TEssay Questions47.Point ▪ Examples include factories, power plants, sewage treatment plants, underground coal mines, and oil wells ▪ Pollution is discharged from specific locations (e.g., drain pipes, smoke stacks, ditches, sewer outfalls) ▪ Discrete and identifiable, so are relatively easy to monitor and regulate ▪ Generally feasible to divert effluent from the waste stream and treat it before it is released into the environment Nonpoint ▪ Examples include runoff from farm fields and feedlots, golf courses, lawns and gardens, construction sites, logging areas, roads, streets, and parking lots ▪ There is no specific location where they discharge, so it can end up in water anywhere ▪ Typically are scattered or diffuse ▪ Amount of runoff is seasonal (varies with times and amounts of precipitation); heavy rainfalls may flush or carry a lot of pollutants into lakes, rivers, and other bodies of water at one time ▪ Much more difficult to monitor, regulate, and treat48.BOD is one way to measure the amount of bacteria in a water sample. Organic wastes, including sewage, paper pulp, or food, are very rich in certain nutrients—especially nitrogen and phosphorus. Once in aquatic ecosystems, these nutrients stem the growth of decomposing bacteria. These bacteria consume large amounts of oxygen. The BOD can give us an approximation of the amount of organic waste in the water based on the oxygen content. The effects of oxygen-demanding wastes on bodies of water depend on the volume, flow, and temperature of the water. In general, a characteristic decline in oxygen is seen downstream from a point source (e.g., discharge pipe). This is called the oxygen sag. Farther downstream, levels of oxygen will eventually return to normal. A diagram similar to Fig. 18.7 on p. 402 in the text (showing the relationship between BOD and oxygen sag) should be drawn with appropriate labels. Zones, oxygen levels, and types of organisms may be included in this diagram.。
AP75T10GP
N-CHANNEL ENHANCEMENT MODE Electronics Corp.POWER MOSFET▼Simple Drive Requirement BV DSS 100V ▼ Lower On-resistanceR DS(ON)15m Ω▼ Fast Switching CharacteristicI D72ADescriptionAbsolute Maximum RatingsSymbol Units V DS V V GSV I D @T C =25℃A I D @T C =100℃A I DMA P D @T C =25℃W W/℃T STG ℃T J℃Symbol Value Units Rthj-c Thermal Resistance Junction-case Max.0.9℃/W Rthj-aThermal Resistance Junction-ambientMax.62℃/WAP75T10GS/PPb Free Plating ProductParameterRating Drain-Source Voltage 100Gate-Source Voltage±20Continuous Drain Current, V GS @ 10V 72Continuous Drain Current, V GS @ 10V 45Pulsed Drain Current 1260Total Power Dissipation 138-55 to 150Operating Junction Temperature Range-55 to 150Linear Derating Factor 1.11Thermal DataParameterStorage Temperature RangeThe Advanced Power MOSFETs from APEC provide the designer with the best combination of fast switching,ruggedized device design, low on-resistance and cost-effectiveness.The TO-263 package is universally preferred for all commercial-industrial surface mount applications and suited for low voltage applications such as DC/DC converters. The through-hole version (AP75T10GP) are available for low-profile applications.G DSTO-263(S)G DSTO-220(P)Electrical Characteristics@T j=25o C(unless otherwise specified) Symbol Parameter Test Conditions Min.Typ.Max.UnitsBV DSS Drain-Source Breakdown Voltage V GS=0V, I D=1mA100--V ΔB V DSS/ΔT j Breakdown Voltage Temperature Coefficient Reference to 25℃, I D=1mA-0.09-V/℃R DS(ON)Static Drain-Source On-Resistance2V GS=10V, I D=30A--15mΩV GS=4.5V, I D=16A--21mΩV GS(th)Gate Threshold Voltage V DS=V GS, I D=250uA1-3V g fs Forward Transconductance V DS=10V, I D=30A-52-S I DSS Drain-Source Leakage Current (Tj=25o C)V DS=100V, V GS=0V--10uA Drain-Source Leakage Current (T j=150o C)V DS=80V ,V GS=0V--100uAI GSS Gate-Source Leakage VGS= ±20V--±100nA Q g Total Gate Charge2I D=30A-69110.4nC Q gs Gate-Source Charge V DS=80V-12-nC Q gd Gate-Drain ("Miller") Charge V GS=4.5V-39-nC t d(on)Turn-on Delay Time2V DS=50V-12-ns t r Rise Time I D=30A-75-ns t d(off)Turn-off Delay Time R G=10Ω,V GS=10V-220-ns t f Fall Time R D=1.6Ω-250-ns C iss Input Capacitance V GS=0V-56909100pF C oss Output Capacitance V DS=25V-540-pF C rss Reverse Transfer Capacitance f=1.0MHz-310-pF R g Gate Resistance f=1.0MHz- 1.1-ΩSymbol Parameter Test Conditions Min.Typ.Max.Units V SD Forward On Voltage2I S=30A, V GS=0V-- 1.3V t rr Reverse Recovery Time2I S=30A, V GS=0V-51-ns Q rr Reverse Recovery Charge dI/dt=100A/µs-74-nCNotes:1.Pulse width limited by safe operating area.2.Pulse width <300us , duty cycle <2%.AP75T10GS/PAP75T10GS/PFig 1. Typical Output Characteristics Fig 2. Typical Output CharacteristicsFig 3. On-Resistance v.s. Gate VoltageFig 4. Normalized On-Resistancev.s. Junction TemperatureFig 5. Forward Characteristic ofReverse DiodeJunction TemperatureFig 7. Gate Charge Characteristics Fig 8. Typical Capacitance CharacteristicsFig 9. Maximum Safe Operating Area Fig 10. Effective Transient Thermal ImpedanceFig 11. Switching Time Waveform Fig 12. Gate Charge WaveformAP75T10GS/P。
WiFi7 综合讲解
WIFI7综合讲解目录●概述1.简介2.发展背景3.技术优点●技术讲解1.物理层提升1)320MHz带宽2)4096-QAM调制3)MIMO 16x162.多链路设备（MLD）3.OFDMA增强1)Multi-RU2)Preamble Puncturing4.多AP协同1)协同空间重用（CSR）2)联合传输（JXT）3)协同正交频分多址（C-OFDMA）4)协同波束赋形（CBF）●总结1.更高吞吐速率2.更低延时保障3.更强高密能力●缩略语●概述1.简介当前全球有近200亿的WIFI设备，在实际应用中，WiFi协议所传输无线流量已占到无线总流量的90%。
海量数据快速、安全传输受益于巨量WiFi设备高效、安全、可靠地工作，而WiFi设备高效安全工作的灵魂在于802.11协议的全面支持。
2.发展背景802.11协议发展历程：✓初版802.11协议速率仅为2Mbps；✓802.11b使用新的编码形式，将速率提升到11Mbps；✓802.11a利用新的5GHz频段，引入OFDM技术并采用64-QAM 调制将无线速率提升到54Mbps；✓802.11g将802.11a的技术同步推广到2.4GHz/54Mbps速率；✓802.11n，MIMO作为一项重大技术被引入WLAN协议，同时采用更宽的40MHz带宽，将WLAN速率提升到了600Mbps；✓802.11ac最大可用256-QAM调制，最大支持160MHz，将速率提升10余倍至6.9Gbps，同时为提升多用户体验，引入了MU-MIMO技术；✓802.11ax在前者基础上，引入OFDMA技术，同步采用1024-QAM 调制，传输速率达到9.6Gbps，相较于初始版本协议速率已提升近万倍。
✓伴随VR/AR、4K/8K视频、元宇宙、云游戏、云计算等应用的发展，对于网络有着更高速率、更低时延、更多并发、更安全、更可靠和更节能的需求，现有协议渐渐已无法满足需求。
为了应对新挑战，2019年5月，IEEE802.11be EHT工作组正式成立，从网络吞吐、干扰抑制、频谱效率和时延优化等多个维度对当前标准进行优化提升，制定了WiFi 7标准。
华为 AP6750-10T 无线访问点数据手册说明书
Huawei AP6750-10T Access Point DatasheetProduct OverviewHuawei AP6750-10T is an access point (AP) that supports 802.11ac Wave 2, has built-in adaptive array antennas, and provides triple radios: one 2.4 GHz radio and two 5 GHz radios. The 2.4 GHz radio supports 2x2 MIMO and two spatial streams, one 5 GHz radio supports 2x2 MIMO and two spatial streams, and the other 5 GHz radio supports 4x4 MIMO and four spatial streams. AP6750-10T complies with 802.11n, 802.11ac, and 802.11ac Wave 2, outperforms other APs in network compatibility, and provides optimal wireless network experience for users. With these features, AP6750-10T best adapts to high-density scenarios such as e-classrooms and supermarkets.AP6750-10T●Provides services simultaneously on one 2.4 GHz radio and two 5 GHz radios, at a rate of 3 Gbit/s for the entire device. The 2.4 GHz radio supports 2x2 MIMO, providing a maximum rate of 400 Mbit/s. One 5 GHz radio supports 2x2 MIMO, and the other 5 GHz radio supports 4x4 MIMO, providing a maximum rate of 867 Mbit/s and 1733 Mbit/s, respectively.●Uses adaptive array antenna technology to enable targeted signal coverage for mobile terminals and improve signal quality. Additionally, this technology implements switchover as STAs move.●Supports Bluetooth serial interface-based O&M through built-in Bluetooth and CloudCampus APP, and precise locating of Bluetooth terminals and tags by collaborating with the location server.●Provides a USB interface for external power supply and storage. An IoT module can also be installed on the USB interface to implement flexible IoT application extension.●Supports the Fat, Fit, and cloud modes and enables Huawei cloud management platform to manage and operate APs and services on the APs, reducing network O&M costs.Feature DescriptionsTriple-radio designThe AP has triple radios: one 2.4 GHz radio and two 5GHz radios. When all the triple radios work, the device rate can reach 3 Gbit/s.Adaptive array antennas (smart antennas)The AP integrates adaptive array antennas (smart antennas) and implicit beamforming to implement more precise user detection, suppress interference, and improve signal quality, bringing seamless and smooth wireless network experience at the users' fingertips.Cloud-based managementHuawei Cloud Managed Network (CMN) Solution consists of the cloud management platform and a full range of cloud managed network devices. The cloud management platform provides various functions including management of APs, tenants, applications, and licenses, network planning and optimization, device monitoring, network service configuration, and value- added services.High Density Boost technologyHuawei uses the following technologies to address challenges in high-density scenarios, including access problems, data congestion, and poor roaming experience:SmartRadio for air interface optimization●Load balancing during smart roaming: The load balancing algorithm can work during smart roaming, enabling load balancing detection between APs on the network after STA roaming to adjust the STA load on each AP, improving network stability.●Intelligent Dynamic Frequency Assignment (DFA) technology: The DFA algorithm is used to automatically detect adjacent-channel and co-channel interference, and identify any redundant 2.4 GHz radio. Through automatic inter-AP negotiation, a redundant radio is automatically switched to another mode (dual-5G AP models support 2.4G-to-5G switchover) or is disabled to reduce 2.4 GHz co-channel interference and increase the system capacity.●Intelligent conflict optimization technology: Dynamic enhanced distributed channel access (EDCA) and airtime scheduling algorithms are used to schedule the channel occupation time and service priority of each STA. This ensures that each STA is assigned a relatively equal amount of time for using channel resources and user services are scheduled in an orderly manner, improving service processing efficiency and user experience.Air interface performance optimization●In high-density scenarios where many STAs access the network, an increased number of low-rate STAs consume more resources on the air interface, reduce the AP capacity, and lower user experience. Therefore, Huawei APs will check the signal strength of STAs during access and reject access from weak-signal STAs. At the same time, the APs monitor the rate of online STAs in real time and forcibly disconnect low-rate STAs so that the STAs can reassociate with APs that have stronger signals. Terminal access control technology can increase air interface use efficiency and allow access of more STAs.5GHz-prior access●The AP supports both 2.4G and 5G frequency bands. The 5G-prior access function enables an AP to steer STAs to the 5 GHz frequency band first, which reduces load and interference on the 2.4 GHz frequency band, improving user experience.Automatic radio calibration●Automatic radio calibration allows an AP to collect signal strength and channel parameters of surrounding APs and generate AP topology according to the collected data. Based on interference from authorized APs, rogue APs, and non-Wi-Fi interference sources, each AP automatically adjusts its transmit power and working channel to make the network operate at the optimal performance. In this way, network reliability and user experience are improved.Wired and wireless dual security guaranteeTo ensure data security, Huawei APs integrate wired and wireless security measures and provide comprehensive security protection.Authentication and encryption for wireless access●Huawei APs support WEP, WPA/WPA2-PSK, WPA/WPA2-PPSK, WPA/WPA2-802.1X, and WAPI authentication/encryption modes to ensure security of a wireless network. The authentication mechanism is used to authenticate user identities so that only authorized users can access network resources. The encryption mechanism is used to encrypt data transmitted over wireless links to ensure that the data can only be received and parsed by expected users.Analysis on non-Wi-Fi interference sources●Huawei APs can analyze the spectrum of non-Wi Fi interference sources and identify them, including baby monitors, Bluetooth devices, digital cordless phones (on 2.4 GHz frequency band only), wireless audio transmitters (on both the 2.4 GHz and 5 GHz frequency bands), wireless game controllers, and microwave ovens. Coupled with Huawei eSight, the APs can accurately detect interference sources, and display the spectrum of them on eSight, enabling the administrator to remove the interference in a timely manner.Rogue device monitoring●Huawei APs support WIDS/WIPS, and can monitor, identify, defend against, counter, and perform refined management on rogue devices, providing security guarantees for air interface environment and wireless data transmission.Automatic application identificationHuawei APs support smart application control technology and can implement visualized management and control on Layer 4 to Layer 7 applications.Traffic identification●Coupled with Huawei ACs, the APs can identify over 6000 common applications in various office scenarios. Based on the identification results, policy control can be implemented on user services, including priority adjustment, scheduling, blocking, and rate limiting to ensure efficient bandwidth resource use and improve quality of key services.Traffic statistics collection●Traffic statistics of each application can be collected globally, by SSID, or by user, enabling the network administrator to know application use status on the network. The network administrator or operator can implement visualized control on service applications on smart terminals to enhance security and ensure effective bandwidth control.Basic SpecificationsFat/Fit AP modeWLAN features Compliance with IEEE 802.11a/b/g/n/ac/ac Wave 2Triple radios, eight spatial streams, providing a maximum rate of 3 Gbit/sMaximum ratio combining (MRC)Space-Time Block Coding (STBC)Cyclic Delay Diversity (CDD)/Cyclic Shift Diversity (CSD)BeamformingMU-MIMOLow Density Parity Check (LDPC)Maximum-Likelihood Detection (MLD)Frame aggregation, including A-MPDU (Tx/Rx) and A-MSDU (Tx/Rx)802.11 dynamic frequency selection (DFS)Short guard interval (GI) in 20 MHz, 40 MHz, and 80 MHz modesAutomatic and manual rate adjustmentWLAN channel management and channel rate adjustmentAutomatic channel scanning and interference avoidanceSeparate Service Set Identifier (SSID) hiding configuration for each AP, supporting Chinese SSIDsSignal Sustain Technology (SST)Unscheduled Automatic Power Save Delivery (U-APSD)Control and Provisioning of Wireless Access Points (CAPWAP) in Fit AP modeAutomatic login in Fit AP modeExtended Service Set (ESS) in Fit AP modeMesh networking in Fit AP modeMulti-user CACHotspot2.0Smart roaming based on 802.11k and 802.11v802.11r fast roaming (≤ 50 ms)WAN authentication escape between APs and WLAN ACs. In local forwarding mode, this featurekeeps existing STAs online and allows for the access of new STAs when APs are disconnectedfrom WLAN ACs, ensuring service continuity.Network features Compliance with IEEE 802.3abAuto-negotiation of the rate and duplex mode and automatic switchover between the MediaDependent Interface (MDI) and Media Dependent Interface Crossover (MDI-X)Compliance with IEEE 802.1QSSID-based VLAN assignmentVLAN trunk on uplink Ethernet portsManagement channel of the AP uplink port in tagged and untagged modeDHCP client, obtaining IP addresses through DHCPTunnel forwarding and direct forwarding of service dataSTA isolation in the same VLANAccess control list (ACL)Link Layer Discovery Protocol (LLDP)Uninterrupted service forwarding upon CAPWAP channel disconnection in Fit AP modeUnified authentication on the AC in Fit AP modeAC dual-link backup in Fit AP modeNetwork Address Translation (NAT) in Fat AP modeIPv6 in Fit AP modeIPv4/IPv6 ACLSoft Generic Routing Encapsulation (GRE)IPv6 Source Address Validation Improvements (SAVI)Multicast Domain Name Service (mDNS) gateway protocol: supports AirPlay and AirPrint servicesharing between users of different VLANsQoS features Priority mapping and packet scheduling that are compliant with Wi-Fi multimedia (WMM) toimplement priority-based data processing and forwardingWMM parameter management for each radioWMM power savingPriority mapping for upstream packets and flow-based mapping for downstream packetsQueue mapping and schedulingUser-based bandwidth limitingAdaptive bandwidth management (automatic bandwidth adjustment based on the user quantity andradio environment) to improve user experienceSmart Application Control (SAC) in Fit AP modeAirtime schedulingSupport for Microsoft Lync APIs and high voice call quality through Lync API identification andschedulingSecurity features Open system authenticationWEP authentication/encryption using a 64-bit, 128-bit, or 152-bit encryption keyWPA2-PSK authentication/encryption (WPA2-Personal edition)WPA2-802.1X authentication/encryption (WPA2-Enterprise edition)WPA-WPA2 hybrid authenticationWPA2-PPSK authentication/encryption802.1X authentication, MAC address authentication, and Portal authenticationDHCP snoopingDynamic ARP Inspection (DAI)IP Source Guard (IPSG)802.11w Protected Management Frames (PMFs)Application identificationMaintenance features Unified management and maintenance on the AC in Fit AP modeAutomatic login and configuration loading, and plug-and-play (PnP) in Fit AP modeBatch upgrade in Fit AP modeTelnetSTelnet using SSH v2SFTP using SSH v2Remote wireless O&M through Bluetooth console portsLocal AP management through the serial interfaceWeb NMS-based management in Fat AP mode upon login through HTTP or HTTPSReal-time configuration monitoring and fast fault locating using the NMSSNMP v1/v2/v3 in Fat AP modeSystem status alarmNetwork Time Protocol (NTP) in Fat AP modeBYOD NOTEThe AP supports bring your own device (BYOD) only in Fit AP mode.Identifies the device type according to the organizationally unique identifier (OUI) in the MACaddress.Identifies the device type according to the user agent (UA) information in an HTTP packet.Identifies the device type according to DHCP options.The RADIUS server delivers packet forwarding, security, and QoS policies according to the devicetype carried in the RADIUS authentication and accounting packets.Location service NOTEThe AP supports the locating service only in Fit AP mode.Locates tags in compliance with proprietary protocols of AeroScout and Ekahau.Locates Wi-Fi terminals.Works with the location server to locate rogue devices.Spectrum analysis NOTEThe AP supports spectrum analysis only in Fit AP mode.Identifies more than eight interference sources including Bluetooth devices, microwave ovens,cordless phones, ZigBee devices, game controllers, 2.4 GHz/5 GHz wireless video and audiodevices, and baby monitors.Works with the location server to locate and perform spectrum analysis on interference sources. Cloud-based management modeWLAN features Compliance with IEEE 802.11a/b/g/n/ac/ac Wave 2Triple radios, eight spatial streams, providing a maximum rate of 3 Gbit/sMaximum ratio combining (MRC)Space time block code (STBC)MU-MIMOMLDBeamformingLow-density parity-check (LDPC)Maximum-likelihood detection (MLD)Frame aggregation, including A-MPDU (Tx/Rx) and A-MSDU (Tx/Rx)802.11 dynamic frequency selection (DFS)Priority mapping and packet scheduling based on a Wi-Fi Multimedia (WMM) profile to implementpriority-based data processing and forwardingWLAN channel management and channel rate adjustmentNOTEFor detailed management channels, see the Country Code & Channel Compliance Table.Automatic channel scanning and interference avoidanceService set identifier (SSID) hidingSignal sustain technology (SST)Unscheduled automatic power save delivery (U-APSD)Automatic loginNetwork features Compliance with IEEE 802.3abAuto-negotiation of the rate and duplex mode and automatic switchover between the MediaDependent Interface (MDI) and Media Dependent Interface Crossover (MDI-X)Compliance with IEEE 802.1qSSID-based VLAN assignmentDHCP client, obtaining IP addresses through DHCPSTA isolation in the same VLANAccess control lists (ACLs)Unified authentication on the Agile ControllerNetwork Address Translation (NAT)QoS features Priority mapping and packet scheduling based on a Wi-Fi Multimedia (WMM) profile to implement priority-based data processing and forwardingWMM parameter management for each radioWMM power savingPriority mapping for upstream packets and flow-based mapping for downstream packetsQueue mapping and schedulingUser-based bandwidth limitingAirtime schedulingSecurity features Open system authenticationWEP authentication/encryption using a 64-bit, 128-bit, or 152-bit encryption keyWPA2-PSK authentication/encryption (WPA2-Personal edition)WPA2-802.1X authentication/encryption (WPA2-Enterprise edition)WPA-WPA2 hybrid authenticationWPA/WPA2-PPSK authentication/encryption802.1X authentication, MAC address authentication, and Portal authenticationDHCP snoopingDynamic ARP Inspection (DAI)IP Source Guard (IPSG)Maintenance features Unified management and maintenance on the Agile ControllerAutomatic login and configuration loading, and plug-and-play (PnP)Batch upgradeTelnetSTelnet using SSH v2SFTP using SSH v2Remote wireless O&M through Bluetooth console portWeb NMS-based management upon login through HTTP or HTTPSReal-time configuration monitoring and fast fault location using the NMSSystem status alarmNetwork Time Protocol (NTP)Technical SpecificationsTechnical specifications Dimensions (H x W x D) 47 mm x 220 mm x 220 mmWeight 1.2 kgInterface type 2 x 10/100/1000M adaptive Ethernet ports (RJ45)1 x USB portBuilt-in Bluetooth BLE5.0External IoT module Support for IoT modules expanded through the USB portLED indicator Indicates the power-on, startup, running, alarm, and fault states of thesystem.Power specifications Power input ●DC: 12 V ± 10%●PoE power supply: in compliance with 802.3at.Maximum power consumption 19.3 W (excluding output power consumption of the USB port)NOTEThe actual maximum power consumption depends on local laws and regulations.Environmental specifications Operating temperature -10°C to +50°CStorage temperature -40°C to +70°COperating humidity 5% to 95% (non-condensing) Dustproof andwaterproof gradeIP41Altitude -60 m to +5000 m Atmospheric pressure 53 kPa to 106 kPaRadio specifications Antenna type Built-in adaptive array antennas (smart antennas) Antenna gain 2.4 GHz: 3.5 dBi5 GHz-0: 5 dBi5 GHz-1: 5 dBiNOTE1. The gains above are the single-antenna peak gains.2. The equivalent antenna gain after all 2.4 GHz or 5 GHz antennas arecombined is 1 dBi in 2.4 GHz, 2 dBi in 5 GHz-0，3dBi in 5 GHz-1. Maximum number ofSSIDs for each radio≤ 16Maximum number of users ≤ 768NOTEThe actual number of users varies according to the environment.Maximum transmit power 2.4 GHz: 23 dBm (combined power)5 GHz-0: 24 dBm (combined power)5 GHz-1: 27 dBm (combined power)NOTEThe actual transmit power depends on local laws and regulations.Power increment 1 dBmMaximum number of non-overlapping channels 2.4 GHz (2.412 GHz~2.472 GHz)●802.11b/g−20 MHz: 3●802.11n−20 MHz: 3−40 MHz: 15 GHz (5.18 GHz~5.825 GHz)●802.11a−20 MHz: 13●802.11n−20 MHz: 13−40 MHz: 6●802.11ac−20 MHz: 13−40 MHz: 6−80 MHz: 3NOTEThe table uses the number of non-overlapping channels supported by China as an example. The number of non-overlapping channels varies in different countries. For details, see the Country Codes & Channels ComplianceStandards ComplianceSafety standards UL 62368-1EN 62368-1IEC 62368-1GB 4943EN 60950-1UL 60950-1CAN/CSA 22.2 No.60950-1IEC 60950-1Radio ETSI EN 300 328 RSS-210 AS/NZS 4268standardsETSI EN 301 893 FCC Part 15C: 15.247 EMCstandards EN 301 489-1 EN 301 489-17ETSI EN 60601-1-2FCC Part 15ICES-003YD/T 1312.2-2004 ITU k.20 GB 9254 GB 17625.1 AS/NZS CISPR22 EN 55022 EN 55024 CISPR 22 CISPR 24 IEC61000-4-6 IEC61000-4-2IEEEstandards IEEE 802.11a/b/g IEEE 802.11nIEEE 802.11ac IEEE 802.11h IEEE 802.11d IEEE 802.11eIEEE 802.11k IEEE 802.11u IEEE 802.11v IEEE 802.11w IEEE 802.11rSecuritystandards 802.11i, Wi-Fi Protected Access 2(WPA2), WPA 802.1XAdvanced Encryption Standards(AES), Temporal Key Integrity Protocol(TKIP)EAP Type(s)EMF CENELEC EN 62311CENELEC EN 50385 OET65 RSS-102 FCC Part1&2 FCC KDB SeriesRoHSDirective 2002/95/EC & 2011/65/EU ReachRegulation 1907/2006/EC WEEE Directive 2002/96/EC & 2012/19/EUAntennas Pattern2.4 GHz (Horizontal) 2.4 GHz (Vertical)5 GHz-0 (Horizontal) 5 GHz-0 (Vertical)5 GHz-1 (Horizontal) 5 GHz-1 (Vertical) Ordering Information Part NumberDescription 02352NAM AP6750-10T mainframe (11ac Wave 2, indoor, triple-radio, built-in antenna, 2*GE, USB, BLE) More InformationFor more information about Huawei WLAN products, visit or contact us in the following ways:●Global service hotline: /en/service-hotline ●Logging in to the Huawei Enterprise technical support web: /enterprise/ ● Sendinganemailtothecustomerservicemailbox:********************Copyright © Huawei Technologies Co., Ltd. 2019. All rights reserved.No part of this document may be reproduced or transmitted in any form or by any means without prior written consent of Huawei Technologies Co., Ltd.Trademarks and Permissionsand other Huawei trademarks are trademarks of Huawei Technologies Co., Ltd.All other trademarks and trade names mentioned in this document are the property of their respective holders.NoticeThe purchased products, services and features are stipulated by the contract made between Huawei and the customer. All or part of the products, services and features described in this document may not be within the purchase scope or the usage scope. Unless otherwise specified in the contract, all statements, information, and recommendations in this document are provided "AS IS" without warranties, guarantees or representations of any kind, either express or implied.The information in this document is subject to change without notice. Every effort has been made in the preparation of this document to ensure accuracy of the contents, but all statements, information, and recommendations in this document do not constitute a warranty of any kind, express or implied.Huawei Technologies Co., Ltd.Address:Huawei Industrial Base Bantian, Longgang Shenzhen 518129 People's Republic of ChinaWebsite:。
苏教版七年级上册数学压轴解答题（提升篇）（Word版含解析）
苏教版七年级上册数学压轴解答题（提升篇）（Word版含解析）苏教版七年级上册数学压轴解答题（提升篇）（Word 版含解析）⼀、压轴题1．如图：在数轴上点A 表⽰数a ，点B 表⽰数b ，点C 表⽰数c ，a 是多项式2241x x --+的⼀次项系数，b 是最⼩的正整数，单项式2412x y -的次数为.c()1a =________，b =________，c =________；()2若将数轴在点B 处折叠，则点A 与点C ________重合（填“能”或“不能”）；()3点A ，B ，C 开始在数轴上运动，若点C 以每秒1个单位长度的速度向右运动，同时，点A 和点B 分别以每秒3个单位长度和2个单位长度的速度向左运动，t 秒钟过后，若点A 与点B 之间的距离表⽰为AB ，点B 与点C 之间的距离表⽰为BC ，则AB =________，BC =________（⽤含t 的代数式表⽰）；()4请问：3AB BC -的值是否随着时间t 的变化⽽改变？若变化，请说明理由；若不变，请求其值.2．如图⼀，点C 在线段AB 上，图中有三条线段AB 、AC 和BC ，若其中⼀条线段的长度是另外⼀条线段长度的2倍，则称点C 是线段AB 的“巧点”．（1）填空：线段的中点这条线段的巧点（填“是”或“不是”或“不确定是”）（问题解决）（2）如图⼆，点A 和B 在数轴上表⽰的数分别是20-和40，点C 是线段AB 的巧点，求点C 在数轴上表⽰的数。
（应⽤拓展）（3）在（2）的条件下，动点P 从点A 处，以每秒2个单位的速度沿AB 向点B 匀速运动，同时动点Q 从点B 出发，以每秒4个单位的速度沿BA 向点A 匀速运动，当其中⼀点到达中点时，两个点运动同时停⽌，当A 、P 、Q 三点中，其中⼀点恰好是另外两点为端点的线段的巧点时，直接写出运动时间()t s 的所有可能值．3．某市两超市在元旦节期间分别推出如下促销⽅式：甲超市：全场均按⼋⼋折优惠；⼄超市：购物不超过200元，不给于优惠；超过了200元⽽不超过500元⼀律打九折；超过500元时，其中的500元优惠10%，超过500元的部分打⼋折；已知两家超市相同商品的标价都⼀样．（1）当⼀次性购物总额是400元时，甲、⼄两家超市实付款分别是多少？（2）当购物总额是多少时，甲、⼄两家超市实付款相同？（3）某顾客在⼄超市购物实际付款482元，试问该顾客的选择划算吗？试说明理由． 4．如图，数轴上A ，B 两点对应的数分别为4-，-1 （1）求线段AB 长度（2）若点D 在数轴上，且3DA DB =，求点D 对应的数（3）若点A 的速度为7个单位长度/秒，点B 的速度为2个单位长度/秒，点O 的速度为1个单位长度/秒，点A ，B ，O 同时向右运动，⼏秒后，3?OA OB =5．已知x ＝﹣3是关于x 的⽅程（k +3）x +2＝3x ﹣2k 的解．（1）求k 的值；（2）在（1）的条件下，已知线段AB ＝6cm ，点C 是线段AB 上⼀点，且BC ＝kAC ，若点D 是AC 的中点，求线段CD 的长．（3）在（2）的条件下，已知点A 所表⽰的数为﹣2，有⼀动点P 从点A 开始以2个单位长度每秒的速度沿数轴向左匀速运动，同时另⼀动点Q 从点B 开始以4个单位长度每秒的速度沿数轴向左匀速运动，当时间为多少秒时，有PD ＝2QD ？6．已知线段AB ＝m （m 为常数），点C 为直线AB 上⼀点，点P 、Q 分别在线段BC 、AC 上，且满⾜CQ ＝2AQ ，CP ＝2BP ．（1）如图，若AB ＝6，当点C 恰好在线段AB 中点时，则PQ ＝；（2）若点C 为直线AB 上任⼀点，则PQ 长度是否为常数？若是，请求出这个常数；若不是，请说明理由；（3）若点C 在点A 左侧，同时点P 在线段AB 上（不与端点重合），请判断2AP+CQ ﹣2PQ 与1的⼤⼩关系，并说明理由．7．（理解新知）如图①，已知AOB ∠，在AOB ∠内部画射线OC ，得到三个⾓，分别为AOC ∠，BOC ∠，AOB ∠，若这三个⾓中有⼀个⾓是另外⼀个⾓的两倍，则称射线OC 为AOB ∠的“⼆倍⾓线”．（1）⼀个⾓的⾓平分线______这个⾓的“⼆倍⾓线”（填“是”或“不是”）（2）若60AOB ∠=?，射线OC 为AOB ∠的“⼆倍⾓线”，则AOC ∠的⼤⼩是______；（解决问题）如图②，⼰知60AOB ∠=?，射线OP 从OA 出发，以20?/秒的速度绕O 点逆时针旋转；射线OQ 从OB 出发，以10?/秒的速度绕O 点顺时针旋转，射线OP ，OQ 同时出发，当其中⼀条射线回到出发位置的时候，整个运动随之停⽌，设运动的时间为t 秒．（3）当射线OP ，OQ 旋转到同⼀条直线上时，求t 的值；（4）若OA ，OP ，OQ 三条射线中，⼀条射线恰好是以另外两条射线为边组成的⾓的“⼆倍⾓线”，直接写出t 所有可能的值______． 8．已知线段AD ＝80，点B 、点C 都是线段AD 上的点．（1）如图1，若点M 为AB 的中点，点N 为BD 的中点，求线段MN 的长；（2）如图2，若BC ＝10，点E 是线段AC 的中点，点F 是线段BD 的中点，求EF 的长；（3）如图3，若AB ＝5，BC ＝10，点P 、Q 分别从B 、C 出发向点D 运动，运动速度分别为每秒移动1个单位和每秒移动4个单位，运动时间为t 秒，点E 为AQ 的中点，点F 为PD 的中点，若PE ＝QF ，求t 的值．9．如图1，在数轴上A 、B 两点对应的数分别是6，-6，∠DCE=90°（C 与O 重合，D 点在数轴的正半轴上）（1）如图1，若CF 平分∠ACE ，则∠AOF=_______;（2）如图2，将∠DCE 沿数轴的正半轴向右平移t （0②猜想∠BCE 和α的数量关系，并证明；（3）如图3，开始∠D 1C 1E 1与∠DCE 重合，将∠DCE 沿数轴正半轴向右平移t （010．已知AOB ∠是锐⾓，2AOC BOD ∠=∠.（1）如图，射线OC ，射线OD 在AOB ∠的内部（AOD AOC ∠>∠），AOB ∠与COD ∠互余；①若60AOB ?∠=，求BOD ∠的度数；②若OD 平分BOC ∠，求BOD ∠的度数.（2）若射线OD 在AOB ∠的内部，射线OC 在AOB ∠的外部，AOB ∠与COD ∠互补.⽅⽅同学说BOD ∠的度数是确定的；圆圆同学说：这个问题要分类讨论，⼀种情况下BOD ∠的度数是确定的，另⼀种情况下BOD ∠的度数不确定.你认为谁的说法正确?为什么?11．点O 为直线AB 上⼀点，在直线AB 同侧任作射线OC 、OD ，使得∠COD=90°（1）如图1，过点O 作射线OE ，当OE 恰好为∠AOC 的⾓平分线时，另作射线OF ，使得OF 平分∠BOD ，则∠EOF 的度数是__________度；（2）如图2，过点O 作射线OE ，当OE 恰好为∠AOD 的⾓平分线时，求出∠BOD 与∠COE 的数量关系；（3）过点O 作射线OE ，当OC 恰好为∠AOE 的⾓平分线时，另作射线OF ，使得OF 平分∠COD ，若∠EOC=3∠EOF ，直接写出∠AOE 的度数 12．观察下列各等式：第1个：22()()a b a b a b -+=-；第2个：2233()()a b a ab b a b -++=-；第3个：322344()()a b a a b ab b a b -+++=- ……（1）这些等式反映出多项式乘法的某种运算规律，请利⽤发现的规律猜想并填空：若n 为⼤于1的正整数，则1 2322321()( )n n n n n n a b aa b a b a b ab b -------++++++=______；（2）利⽤（1）的猜想计算：1233212222221n n n ---+++++++（n 为⼤于1的正整数）；（3）拓展与应⽤：计算1233213333331n n n ---+++++++（n 为⼤于1的正整数）．【参考答案】***试卷处理标记，请不要删除⼀、压轴题1．（1）4-，1，6；（2）能；（3）5t +，53t +；（4）3AB BC -的值不会随时间t 的变化⽽变化，值为10 【解析】【分析】（1）由⼀次项系数、最⼩的正整数、单项式次数的定义回答即可，（2）计算线段长度，若AB BC =则重叠，（3）线段长度就⽤两点表⽰的数相减，⽤较⼤的数减较⼩的数即可，（4）根据（3）的结果计算即可．【详解】（1）观察数轴可知，4a =-，1b =，6c =. 故答案为：4-；1；6.（2）()145AB =--=，615BC =-=，AB BC =，则若将数轴在点B 处折叠，点A 与点C 能重合. 故答案为：能.（3）经过t 秒后43a t =--，12b t =-，6c t =+，则5AB a b t =-=+，53BC b c t =-=+.故答案为：5t +；53t +. （4）5AB t =+，∴3153AB t =+. ⼜53BC t =+，∴()()315353AB BC t t -=+-+15353t t =+--10=.故3AB BC -的值不会随时间t 的变化⽽变化，值为10. 【点睛】本题考查列代数式求值，有理数的概念及分类，多项式的项与次数，单项式的系数与次数，在数轴上表⽰实数，解题的关键是⽤字母表⽰线段长度． 2．（1）是；（2）10或0或20；(3) 152t =；t=6；607t =；t=12；907t =；454t =．【解析】【分析】（1）根据新定义，结合中点把原线段分成两短段，满⾜原线段是短线段的2倍关系，进⾏判断即可；（2）由题意设C 点表⽰的数为x ，再根据新定义列出合适的⽅程即可；（3）根据题意先⽤t 的代数式表⽰出线段AP ，AQ ，PQ ，再根据新定义列出⽅程，得出合适的解即可求出t 的值．【详解】解：（1）因原线段是中点分成的短线段的2倍，所以线段的中点是这条线段的巧点，故答案为：是；（2）设C 点表⽰的数为x ，则AC=x+20，BC=40-x ，AB=40+20=60，根据“巧点”的定义可知：①当AB=2AC 时，有60=2（x+20），解得，x=10；②当BC=2AC 时，有40-x=2（x+20），解得，x=0；③当AC=2BC 时，有x+20=2（40-x ），解得，x=20．综上，C 点表⽰的数为10或0或20；（3）由题意得()()60601026046601015t t AP t AQ t PQ t t -≤≤??==-=?-≤??，，＜，（i ）、若0≤t ≤10时，点P 为AQ 的“巧点”，有①当AQ=2AP 时，60-4t=2×2t ，解得，152t =，②当PQ=2AP 时，60-6t=2×2t ，解得，t=6；③当AP=2PQ 时，2t=2（60-6t ），解得，607t =；综上，运动时间()t s 的所有可能值有152t =；t=6；607t =；（ii ）、若10＜t ≤15时，点Q 为AP 的“巧点”，有①当AP=2AQ 时，2t=2×（60-4t ），解得，t=12；②当PQ=2AQ 时，6t-60=2×（60-4t ），解得，907t =；③当AQ=2PQ 时，60-4t=2（6t-60），解得，454t =．综上，运动时间()t s 的所有可能值有：t=12；907t =；454t =．故，运动时间()t s 的所有可能值有：152t =；t=6；607t =；t=12；907t =；454t =．【点睛】本题是新定义题，是数轴的综合题，主要考查数轴上的点与数的关系，数轴上两点间的距离，⼀元⼀次⽅程的应⽤，解题的关键是根据新定义列出⽅程并进⾏求解．3．（1）甲超市实付款352元，⼄超市实付款 360元；（2）购物总额是625元时，甲、⼄两家超市实付款相同；（3）该顾客选择不划算. 【解析】【分析】（1）根据两超市的促销⽅案，即可分别求出：当⼀次性购物标价总额是400元时，甲、⼄两超市实付款；（2）设当标价总额是x 元时，甲、⼄超市实付款⼀样．根据两超市的促销⽅案结合两超市实付款相等，即可得出关于x 的⼀元⼀次⽅程，解之即可得出结论；（3）设购物总额是x 元，根据题意列⽅程求出购物总额，然后计算若在甲超市购物应付款，⽐较即可得出结论．【详解】（1）甲超市实付款：400×0.88=352元，⼄超市实付款：400×0.9=360元；（2）设购物总额是x 元，由题意知x >500，列⽅程： 0.88x =500×0.9+0.8(x -500) ∴x =625∴购物总额是625元时，甲、⼄两家超市实付款相同．（3）设购物总额是x 元，购物总额刚好500元时，在⼄超市应付款为：500×0.9=450(元)，482＞450，故购物总额超过500元．根据题意得： 500×0.9+0.8(x -500)=482 ∴x =540 ∴0.88x =475.2<482 ∴该顾客选择不划算．【点睛】本题考查了⼀元⼀次⽅程的应⽤，解题的关键是：（1）根据两超市的促销⽅案，列式计算；（2）找准等量关系，正确列出⼀元⼀次⽅程；（3）求出购物总额． 4．（1）3；（2）12或74-；（3）13秒或79秒【解析】【分析】（1）根据数轴上两点间距离即可求解；（2）设点D 对应的数为x ，可得⽅程314x x +=+，解之即可；（3）设t 秒后，OA=3OB ，根据题意可得47312t t t t -+-=-+-，解之即可．【详解】解：（1）∵A 、B 两点对应的数分别为-4，-1，∴线段AB 的长度为：-1-（-4）=3；（2）设点D 对应的数为x ，∵DA=3DB ，则314x x +=+，则()314x x +=+或()314x x +=--，解得：x=12或x=74-，∴点D 对应的数为12或74-；（3）设t 秒后，OA=3OB ，则有：47312t t t t -+-=-+-，则4631t t -+=-+，则()4631t t -+=-+或()4631t t -+=--+，解得：t=13或t=79，∴13秒或79秒后，OA=3OB ．【点睛】本题考查了⼀元⼀次⽅程的运⽤，数轴的运⽤和绝对值的运⽤，解题的关键是掌握数轴上两点之间距离的表⽰⽅法． 5．（1）2；（2）1cm ；（3）910秒或116秒【解析】【分析】（1）将x ＝﹣3代⼊原⽅程即可求解；（2）根据题意作出⽰意图，点C 为线段AB 上靠近A 点的三等分点，根据线段的和与差关系即可求解；（3）求出D 和B 表⽰的数，然后设经过x 秒后有PD ＝2QD ，⽤x 表⽰P 和Q 表⽰的数，然后分两种情况①当点D 在PQ 之间时，②当点Q 在PD 之间时讨论即可求解．【详解】（1）把x ＝﹣3代⼊⽅程（k +3）x +2＝3x ﹣2k 得：﹣3（k +3）+2＝﹣9﹣2k ，解得：k ＝2；故k ＝2；（2）当C 在线段AB 上时，如图，当k ＝2时，BC ＝2AC ，AB ＝6cm ，∴AC ＝2cm ，BC ＝4cm ，∵D 为AC 的中点，∴CD ＝12AC ＝1cm ．即线段CD 的长为1cm ；（3）在（2）的条件下，∵点A 所表⽰的数为﹣2，AD ＝CD ＝1，AB ＝6，∴D 点表⽰的数为﹣1，B 点表⽰的数为4．设经过x 秒时，有PD ＝2QD ，则此时P 与Q 在数轴上表⽰的数分别是﹣2﹣2x ，4﹣4x ．分两种情况：①当点D 在PQ 之间时，∵PD ＝2QD ，∴()()1222441x x ??---=---??，解得x ＝910②当点Q 在PD 之间时，∵PD ＝2QD ，∴()()1222144x x ??----=---??，解得x ＝116．答：当时间为910或116秒时，有PD ＝2QD ．【点睛】本题考查了⽅程的解，线段的和与差，数轴上的动点问题，⼀元⼀次⽅程与⼏何问题，分情况讨论是本题的关键．6．（1）4；（2）PQ 是⼀个常数，即是常数23m ；（3）2AP+CQ ﹣2PQ ＜1，见解析．【解析】【分析】（1）根据已知AB ＝6，CQ ＝2AQ ，CP ＝2BP ，以及线段的中点的定义解答；（2）由题意根据已知条件AB ＝m （m 为常数），CQ ＝2AQ ，CP ＝2BP 进⾏分析即可；（3）根据题意，画出图形，求得2AP+CQ ﹣2PQ ＝0，即可得出2AP+CQ ﹣2PQ 与1的⼤⼩关系．【详解】解：（1）∵CQ ＝2AQ ，CP ＝2BP ，∴CQ ＝23AC ，CP ＝23BC ，∵点C 恰好在线段AB 中点，∴AC ＝BC ＝12AB ，∵AB ＝6，∴PQ ＝CQ+CP ＝23AC+23BC ＝23×12AB+23×12AB ＝23×AB ＝23×6＝4；故答案为：4；（2）①点C 在线段AB 上：∵CQ ＝2AQ ，CP ＝2BP ，∴CQ＝23AC，CP＝2∵AB＝m（m为常数），∴PQ＝CQ+CP=23AC+23BC＝23×（AC+BC）＝23AB=23m；②点C在线段BA的延长线上：∵CQ＝2AQ，CP＝2BP，∴CQ＝23AC，CP＝23BC，∵AB＝m（m为常数），∴PQ＝CP﹣CQ＝23BC﹣23AC＝23×（BC﹣AC）＝223m；③点C在线段AB的延长线上：∵CQ＝2AQ，CP＝2BP，∴CQ＝23AC，CP＝23BC，∵AB＝m（m为常数），∴PQ＝CQ﹣CP＝23AC﹣23BC＝23×（AC﹣BC）＝23AB＝23m；故PQ是⼀个常数，即是常数2 3 m；（3）如图：∵CQ＝2AQ，∴2AP+CQ﹣2PQ＝2AP+CQ﹣2（AP+AQ）＝2AP+CQ﹣2AP﹣2AQ＝CQ﹣2AQ＝2AQ﹣2AQ＝0，∴2AP+CQ﹣2PQ＜1．【点睛】本题主要考查线段上两点间的距离，掌握线段的中点的性质、线段的和差运算是解题的关键．7．（1）是；（2）30?或40?或20?；（3）4t =或10t =或16t =；（4）2t =或12t =. 【解析】【分析】（1）若OC 为AOB ∠的⾓平分线，由⾓平分线的定义可得2AOB AOC ∠=∠，由⼆倍⾓线的定义可知结论；（2）根据⼆倍⾓线的定义分2,2,2AOB AOC AOC BOC BOC AOC ∠=∠∠=∠∠=∠三种情况求出AOC ∠的⼤⼩即可.（3）当射线OP ，OQ 旋转到同⼀条直线上时，180POQ ?∠=，即180POA AOB BOQ ?∠+∠+∠=或180BOQ BOP ?∠+∠=，或OP 和OQ 重合时，即360POA AOB BOQ ?∠+∠+∠=，⽤含t 的式⼦表⽰出OP 、OQ 旋转的⾓度代⼊以上三种情况求解即可；（4）结合“⼆倍⾓线”的定义，根据t 的取值范围分04t <<，410t ≤<，1012t <≤，1218t <≤4种情况讨论即可. 【详解】解：（1）若OC 为AOB ∠的⾓平分线，由⾓平分线的定义可得2AOB AOC ∠=∠，由⼆倍⾓线的定义可知⼀个⾓的⾓平分线是这个⾓的“⼆倍⾓线”；（2）当射线OC 为AOB ∠的“⼆倍⾓线”时，有3种情况，①2AOB AOC ∠=∠，60,30AOB AOC ??∠=∴∠=；②2AOC BOC ∠=∠，360AOB AOC BOC BOC ?∠=∠+∠=∠=，20BOC ?∴∠=，40AOC ?∴∠=；③2BOC AOC ∠=∠，360AOB AOC BOC AOC ?∠=∠+∠=∠=，20AOC ?∴∠=，综合上述，AOC ∠的⼤⼩为30?或40?或20?；（3）当射线OP ，OQ 旋转到同⼀条直线上时，有以下3种情况，①如图此时180POA AOB BOQ ?∠+∠+∠=，即206010180t t ++=，解得4t =；②如图此时点P 和点Q 重合，可得360POA AOB BOQ ?∠+∠+∠=，即206010360t t ++=，解得10t =；③如图此时180BOQ BOP ?∠+∠=，即1060(36020)180t t+--=，解得16t =，综合上述，4t =或10t =或16t =；（4）由题意运动停⽌时3602018t ??=÷=，所以018t <≤，①当04t <<时，如图，此时OA 为POQ ∠的“⼆倍⾓线”，2AOQ POA ∠=∠，即6010220t t +=?，解得2t =；②当410t ≤<时，如图，此时，180,180AOQ AOP ??∠>∠>，所以不存在；③当1012t <≤时，如图此时OP 为AOQ ∠的“⼆倍⾓线”，2AOP POQ ∠=∠，即360202(201060360)t t t ?-=?++- 解得 12t =；④当1218t <≤时，如图，此时180,180AOQ AOP ??∠>∠>，所以不存在；综上所述，当2t =或12t =时，OA ，OP ，OQ 三条射线中，⼀条射线恰好是以另外两条射线为边组成的⾓的“⼆倍⾓线”. 【点睛】本题考查了⼀元⼀次⽅程的应⽤，正确理解“⼆倍⾓线”的定义，找准题中⾓之间等量关系是解题的关键.8．（1）MN ＝40；（2）EF=35；（3）509=t 或t ＝12．【解析】【分析】（1）由MN ＝BM+BN ＝1122AB BD +即可求出答案；（2）根据EF ＝AD ﹣AE ﹣DF ，可求出答案；（3）可得PE ＝AE ﹣AB ﹣BP ＝52t +，DF ＝752t -，则QF ＝55722t -或75522t -，由PE ＝QF 可得⽅程，解⽅程即可得出答案．【详解】解：（1）∵M 为AB 的中点，N 为BD 的中点，∴12BM AB =，12BN BD =，∴MN ＝BM+BN ＝1122AB BD +＝11804022AD =?=；（2）∵E 为AC 的中点，F 为BD 的中点，∴12AE AC=，12DF BD=，()()1111352222EF AD AE DF AD AC BD AD AD BC AD BC =--=-+=-+=-=∴（3）运动t秒后，AQ＝AC+CQ＝15+4t，∵E为AQ的中点，∴115222AE AQ t==+，∴1552522PE AE AB BP t t t =--=+--=+，∵DP＝DB﹣BP＝75﹣t，F为DP的中点，∴175222t DF DP==-，⼜DQ＝DC﹣CQ＝65﹣4t，∴755576542222tQF DQ DF t t =-=--+=-，或75522 QF DF DQ t=-=-，由PE＝QF得：52t+=55722t-或52t+=55722t-解得：509=t或t＝12．【点睛】本题考查了⼀元⼀次⽅程的应⽤以及线段的中点，找准等量关系，正确列出⼀元⼀次⽅程是解题的关键．9．（1）45°；（2）①30°；②∠BCE=2α，证明见解析；（3）α=45-15t ，β=45+15t，3t2=【解析】【分析】（1）根据⾓平分线的定义即可得出答案；（2）①⾸先由旋转得到∠ACE=120°，再由⾓平分线的定义求出∠ACF，再减去旋转⾓度即可得到∠DCF；②先由补⾓的定义表⽰出∠BCE，再根据旋转和⾓平分线的定义表⽰出∠DCF，即可得出两者的数量关系；（3）根据α=∠FCA-∠DCA，β=∠AC1D1+∠AC1F1，可得到表达式，再根据|α-β|=45°建⽴⽅程求解.【详解】（1）∵∠ACE=90°，CF平分∠ACE∴∠AOF=12∠ACE=45° 故答案为：45°；（2）①当t=1时，旋转⾓度为30° ∴∠ACE=90°+30°=120° ∵CF 平分∠ACE∴∠ACF=60°，α=∠DCF=∠ACF-30°=30° 故答案为：30°；②∠BCE=2α，证明如下：旋转30t 度后，∠ACE=(90+30t)度∴∠BCE=180-(90+30t)=(90-30t)度∵CF 平分∠ACE ∴∠ACF=12∠ACE=(45+15t)度∠DCF=∠ACF-30t=(45-15t)度∴2∠DCF=2(45-15t)= 90-30t=∠BCE 即∠BCE=2α（3）α=∠FCA-∠DCA= 12(90+30t)-30t=45-15t β=∠AC 1D 1+∠AC 1F 1=30t+12(90-30t)=45+15t ||45βα-=?|30t|=45°∴3t 2=【点睛】本题考查了⾓平分线，⾓的旋转，⾓度的和差计算问题，熟练掌握⾓平分线的定义，找出图形中⾓度的关系是解题的关键. 10．（1）①10°，②18°；（2）圆圆的说法正确，理由见解析. 【解析】【分析】（1）①根据∠AOB 与∠COD 互余求出∠COD ，再利⽤⾓度的和差关系求出∠AOC+∠BOD=30°，最后根据∠AOC=2∠BOD 即可求出∠BOD ；②设∠BOD=x ，根据⾓平分线表⽰出∠COD 和∠BOC ，根据∠AOC=2∠BOD 表⽰出∠AOC ，最后根据∠AOB 与∠COD 互余建⽴⽅程求解即可；（2）分两种情况讨论：OC 靠近OA 时与OC 靠近OB 时，画出图形分类计算判断即可. 【详解】解：（1）①∵∠AOB 与∠COD 互余，且∠AOB=60°，∴∠COD=90°－∠AOB=30°，∴∠AOC+∠BOD=∠AOB－∠COD=60°－30°=30°，∵∠AOC=2∠BOD，∴2∠BOD+∠BOD=30°，∴∠BOD=10°；②设∠BOD=x，∵OD平分∠BOC，∴∠BOD=∠COD=x，∠BOC=2∠BOD=2x，∵∠AOC=2∠BOD，∴∠AOC=2x，∴∠AOB=∠AOC+∠COD +∠BOD=4x，∵∠AOB与∠COD互余，∴∠AOB+∠COD=90°，即4x+x=90°，∴x=18°，即∠BOD=18°；（2）圆圆的说法正确，理由如下：当OC靠近OB时，如图所⽰，∵∠AOB与∠COD互补，∴∠AOB+∠COD=180°，∵∠AOB=∠AOD+∠BOD，∠COD=∠BOC+∠BOD，∴∠AOD+∠BOD+∠BOC+∠BOD=180°，∵∠AOC=∠AOD+∠BOD+∠BOC，∴∠AOC+∠BOD=180°，∵∠AOC=2∠BOD，∴2∠BOD+∠BOD=180°，∴∠BOD=60°；当OC靠近OA时，如图所⽰，∵∠AOB与∠COD互补，∴∠AOB+∠COD=180°，∵∠AOB=∠AOD+∠BOD，∠COD=∠AOC+∠AOD，∴∠AOD+∠BOD+∠AOC+∠AOD=180°，∵∠AOC=2∠BOD，∴∠AOD+∠BOD+2∠BOD +∠AOD=180°，即3∠BOD+2∠AOD=180°，∵∠AOD不确定，∴∠BOD也不确定，综上所述，当OC靠近OB时，∠BOD的度数为60°，当OC靠近OA时，∠BOD的度数不确定，所以圆圆的说法正确.【点睛】本题考查⾓的计算，正确找出⾓之间的关系，分情况画出图形解答是解题的关键. 11．（1）135°；（2）∠BOD=2∠COE；（3）67.5°.【解析】【分析】（1）由∠COD=90°，则∠AOC+∠BOD=90°，由OE平分∠AOC，OF平分∠BOD，得∠COE+∠DOF=45°，即可求出∠EOF的度数；（2）由题意得出∠BOD+∠AOC=90°，∠BOD=180°-∠AOD，再由⾓平分线的定义进⾏计算，即可得出结果；（3）由⾓平分线定义得出∠AOC=∠COE，∠COF=∠DOF=45°，再由∠BOD+∠AOC=90°，设∠EOF=x，则∠EOC=3x，∠COF=4x，根据题意得出⽅程，解⽅程即可．【详解】解：（1）如图：∵∠COD=90°，∴∠AOC+∠BOD=90°，∵OE平分∠AOC，OF平分∠BOD，∴∠COE+∠DOF=11()904522AOC BOD∠+∠=??=?，∴∠EOF=∠COE+∠COD+∠DOF=45°+90°=135°；故答案为：135°；（2）∠BOD=2∠COE；理由如下：如图，∵∠COD=90°．∴∠BOD+∠AOC=90°，∵OE平分∠AOD，∴∠AOE=∠DOE=12∠AOD，⼜∵∠BOD=180°-∠AOD，∴∠COE=∠AOE-∠AOC=12∠AOD-（90°-∠BOD）=12（180°-∠BOD）-90°+∠BOD=12∠BOD，∴∠BOD=2∠COE；（3）如图，∵OC为∠AOE的⾓平分线，OF平分∠COD，∴∠AOC=∠COE，∠COF=∠DOF=45°，∵∠EOC=3∠EOF，设∠EOF=x，则∠EOC=3x，∴∠COF=4x，∴∠AOE=2∠COE=6x，∠DOF=4x，∵∠COD=90°，∴4x+4x=90°，解得：x=11.25°，∴∠AOE=6×11.25°=67.5°．【点睛】本题考查了⾓平分线定义、⾓的互余关系、邻补⾓定义以及⾓的计算；熟练掌握⾓平分线。
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１ ８ 、 ２． Ｖ 、 ２． Ｖ 、 ２． Ｖ 、 ３． Ｖ 、 ．Ｖ ０ ５ ８ ０
新型低压差线性稳压器
的 内置 Ｓ Ｉ 转 换 器 对 ３ ２ 输 入 电 有助 于降低所需的大 容量 电容 。此 外， ＥＰ Ｃ ～７Ｖ的
该 系列包括 ３ ０ ０ ｍＡ 、 １ ０ Ｖ压 降 源 进 行调节 ，以产 生５．Ｖ输 出。这 个 这 个双路 微型模块稳 压器含有一个 内置 ５ｍ ６
ＬＭ３ ５ 可 以在准确 调整输 出的同 ４０
下 ，提供 高达 ６ ｄＢ ５ 的额 定 电源 抑制 比 Ｌ ＧＡ封 装 中集 成 了 电感 器 、ＭＯ Ｆ Ｔ Ｎ 时 ，又可大 幅提 高输入端 的功 率因素 。 Ｓ Ｅ Ｓ
（ ＲＲ） 为 音 频 和 射 频 （ ） 用提 供 其他必需 的组 件。ＬＴＭ４ ２ 专 为将４ ５ 内 置的 相 位调 光 译 码 器 可 以解译 相位 ＰＳ ， ＲＦ 应 ６８ ． 低 噪 声 、高 质 量 的 电 源 。
，ｆ ： ｗｗｗ． ｎｅ ｒ ｍ ． ｎ ， ／ ／ １ ａ． ｉ ｃｏ ｃ
H3C无线胖AP设置
配置同段IP：登录默认的IP是192.168.0.50/24■ftb nr bjim 1 血匿⑴ p A 44* Vi 口 Q 三:VATS帐号：admin密码：h3capadmin修改设备管理IP：无线服务配置：桥接上行密码模式设置完后点击确定Hah-M rasH 八OOMrra^'D-N3VQS£frVWD£H■uEl m 口IFW・fs卜* -W泗LTM ff C：啊u叮◎ "■D-N?VOE£t7V/VOEH BSLW*：«ULMFK 口口rm Q■字■回口IF"科・斗・q*.pp厢L•理L壬I：；：EWP *MW-tEfHM MUCWVC] w-u 口wri VW it空MMIW呻M P A之后就可以看到发出来的信号了：.III HUAWEI-5505.ill|| ssidll| 匚huangmi - plug -v1 _mi io9cee这种设置的模式相当于共享交换机接口出来，也就是说DHCP是在交换机或上层设备分配的, 而不是像家用路由器一样自己分配IP。
如果需要类似家用路由器那种模式请按照下面配置:AP自己分配IP并做NAT 如果手动配置需要配置网关：新建一个vlan：A H -wm| fUM1 - . El - 3J-l|■ —・h■ D*1M |«IMET-JIAH UI □ I M.U WH3比町E> LOH W<*C&E3DV^XFfKi□ i MJMdteO?Bit配置vlanIP：：：）£H3C：H3CWA4S2O-ACN-CH1IJJ2»2»2!4Pni-wSit*. ig * ■ l ：H ■ WH. |--!'：*I配置 DHCP ：配置无线服务，其他和上面的配置一样：H3<ZwnBr«1IFn-H4□星却a ：回■E«H3CWA4J2O-ACN-C■CH*illU: *0：>•^4 ■S«M 3L*SB ™Mt3|-:C«> J U£业■鼻・'Mil**W1 ■sma创建ACL："MJB*fLWinto-wiiF>t*Me 十 Q cHrITi 口芷1 -=：曰 BAittAKJE ：*»T9H3C N3CWA4^20-ACN-Cwq —El 片用™7-nw■WJ口■n■BfiKX JMJI gHb配置 NAT ： HX. ME 他”凶OMUiwrvJzN3CWA4S20-ACN-C■-右 Q. EM-:VfKTI1 - Wf Rffl | 1I Pg*]-ir-WL"# ftuBW MiiiaRfflwi\1a<iivtKa v□ KR OH ■*PS54cwrtVKi。
DrayTek VigorAP 1060C 11ax 天花板 AP 快速引导版本 1.0 固件版本
VigorAP 1060C 11ax Ceiling AP Quick Start GuideVersion: 1.0Firmware Version: V1.4.0(For future update, please visit DrayTek web site)Date: March 31, 2021Intellectual Property Rights (IPR) InformationCopyrights © All rights reserved. This publication contains information that is protected by copyright. No part may be reproduced, transmitted, transcribed, stored ina retrieval system, or translated into any language without written permissionfrom the copyright holders.Trademarks The following trademarks are used in this document:●Microsoft is a registered trademark of Microsoft Corp.●Windows, Windows 8, 10 and Explorer are trademarks of Microsoft Corp.●Apple and Mac OS are registered trademarks of Apple Inc.●Other products may be trademarks or registered trademarks of theirrespective manufacturers.Safety Instructions and ApprovalSafety Instructions ●Read the installation guide thoroughly before you set up the device.●The device is a complicated electronic unit that may be repaired only beauthorized and qualified personnel. Do not try to open or repair thedevice yourself.●Do not place the device in a damp or humid place, e.g. a bathroom.●Do not stack the devices.●The device should be used in a sheltered area, within a temperaturerange of 0 to +40 Celsius.●Do not expose the device to direct sunlight or other heat sources. Thehousing and electronic components may be damaged by direct sunlight or heat sources.●Do not deploy the cable for LAN connection outdoor to preventelectronic shock hazards.●Keep the package out of reach of children.●When you want to dispose of the device, please follow local regulationson conservation of the environment.Warranty We warrant to the original end user (purchaser) that the device will be free from any defects in workmanship or materials for a period of two (2) yearsfrom the date of purchase from the dealer. Please keep your purchase receiptin a safe place as it serves as proof of date of purchase. During the warrantyperiod, and upon proof of purchase, should the product have indications offailure due to faulty workmanship and/or materials, we will, at our discretion,repair or replace the defective products or components, without charge foreither parts or labor, to whatever extent we deem necessary tore-store theproduct to proper operating condition. Any replacement will consist of a newor re-manufactured functionally equivalent product of equal value, and willbe offered solely at our discretion. This warranty will not apply if the productis modified, misused, tampered with, damaged by an act of God, or subjectedto abnormal working conditions. The warranty does not cover the bundled orlicensed software of other vendors. Defects which do not significantly affectthe usability of the product will not be covered by the warranty. We reservethe right to revise the manual and online documentation and to make changesfrom time to time in the contents hereof without obligation to notify anyperson of such revision or changes.Declaration of ConformityHereby, DrayTek Corporation declares that the radio equipment type VigorAP 1060C is in compliance with Directive 2014/53/EU.The full text of the EU declaration of conformity is available at the following internet address: https:///ftp/VigorAP 1060C/Document/CE/Manufacturer: DrayTek Corp.Address: No. 26, Fushing Rd, HuKou, Hsinchu Industrial Park, Hsin-Chu County, Taiwan 303 Product: VigorAP 1060CFrequency Information for Europe area:2.4G WLAN 2412MHz - 2472 MHz, max. TX power: 19.86 dBm *15G WLAN 5150MHz - 5250 MHz, max. TX power: 22.85 dBm;5250MHz - 5350 MHz, max. TX power: 22.85 dBm;5470MHz - 5725 MHz, max. TX power: 28.84 dBm *2(*1: for 2.4G WLAN model; *2: for 5G WLAN model)This product is designed for 2.4GHz and 5GHz WLAN network throughout the EC region.Regulatory InformationFederal Communication Commission Interference StatementThis equipment has been tested and found to comply with the limits for a Class B digital device, pursuant to Part 15 of the FCC Rules. These limits are designed to provide reasonable protection against harmful interference in a residential installation. This equipment generates, uses and can radiate radio frequency energy and, if not installed and used in accordance with the instructions, may cause harmful interference to radio communications. However, there is no guarantee that interference will not occur in a particular installation. If this equipment does cause harmful interference to radio or television reception, which can be determined by turning the equipment off and on, the user is encouraged to try to correct the interference by one of the following measures:●Reorient or relocate the receiving antenna.●Increase the separation between the equipment and receiver.●Connect the equipment into an outlet on a circuit different from that to which the receiveris connected.●Consult the dealer or an experienced radio/TV technician for help.This device complies with Part 15 of the FCC Rules. Operation is subject to the following two conditions:(1) This device may not cause harmful interference, and(2) This device may accept any interference received, including interference that may cause undesired operation.Radiation Exposure Statement: This equipment complies with FCC radiation exposure limits set forth for an uncontrolled environment. This equipment should be installed and operated with minimum distance 20cm between the radiator & your body.Company nameABP International Inc.Address 13988 Diplomat Drive Suite 180 Dallas TX 75234 ZIP Code 75234E-mail*******************USA Local Representative Contact PersonMr. Robert MesserTel. 19728311600Caution● Any changes or modifications not expressly approved by the grantee of this device could void theuser's authority to operate the equipment.● Any changes or modifications not expressly approved by the party responsible for compliancecould void the user's authority to operate this equipment.● This equipment complies with CE RF radiation exposure limits set forth for an uncontrolled environment. This equipment should be installed and operated with minimum distance 20cm between the radiator & your body.● Operations in the 5.15-5.35GHz band are restricted to indoor usage only.T a b l e o f C o n t e n t s1. Package Content (1)2. Panel Explanation (2)3. Installation (3)3.1 Ceiling-mount Installation (Wooden Ceiling) (3)3.2 Ceiling-mount Installation (Plasterboard Ceiling) (4)3.3 Suspended Ceiling (Lightweight Steel Frame) Installation (5)3.4 Wall-Mounted Installation (6)4. Connection and Configuration (7)4.1 Connect to a Vigor Router using AP Management (7)4.2 Web Configurations (8)Connected As a Mesh Node (in Mesh Network) (8)Connected As an Access Point (8)5. Customer Service (11)Be a Registered Owner (11)Firmware & Tools Updates (11)1. P a c k a g e C o n t e n tTake a look at the package content. If there is anything missed or damaged, please contact DrayTek or dealer immediately.VigorAP 1060C Main UnitQuick Start Guide15/16" and 9/16" Mount Base(for ceiling mounting)Fixings and Screws (for ceiling mounting)Mount Base (for wall mounting) Screw Set(for wall / ceiling mounting)Cable TieRJ-45 Cable (Ethernet)NotePower Input: 12V 2.5A PoE Input: 54V 0.6ATotal Rated Power Consumption: 21 Watts2.P a n e l E x p l a n a t i o nStatus ExplanationOn (Blue)The system is in boot-loader mode.OffThe system is not ready or fails.1Blinking(Blue)The system is in TFTP mode.Off The system is not ready or fails.2Blinking(Blue) The system is ready and can work normally.ExplanationEthernet Port Connects to LAN or router.Supports PoE power & Gigabit (2.5Gbps).Power Jack(12V 2.5A)Connecter for a power adapter.ExplanationFactory Reset Restores the unit back to factory default settings.To use, insert a small item such as an unbentpaperclip into the hole. You will feel the buttoninside depress gently. Hold it for 5 seconds.The VigorAP will restart with the factory defaultconfiguration and the LED will blink blue.Security Hole A security hole for installing the anti-theft lock.Note For the sake of security, make the accessory kit away fromchildren.FactoryResetPower Jack LEDSecurityHole3.I n s t a l l a t i o nVigorAP can be installed under certain locations: wooden ceiling, plasterboard ceilings, light-weighted steel frame and wall.3.1C e i l i n g-m o u n t I n s t a l l a t i o n(W o o d e n C e i l i n g)Determine where the Access Point to be placed and mark location on the surface for the two mounting holes. Use the appropriate drill bit to drill two holes in the markings and hammer the bolts into the openings.1.Place the mount base under the wooden ceiling and fasten it on the ceilingwith two screws firmly.2.When the mount base is in place, slide the AP into the slot of the mountbase.3.2C e i l i n g-m o u n t I n s t a l l a t i o n(P l a s t e r b o a r d C e i l i n g)1.Place the Mount Base under the plasterboard ceiling and fasten twoturnbuckles firmly.2.Make the screws pass through the Mount Base and insert into the turnbuckles.Fasten them to offer more powerful supporting force.3.When the Mount Base is in place, slide the mount base into the slot of theAP.3.3 S u s p e n d e d C e i l i n g (L i g h t w e i g h t S t e e l F r a m e ) I n s t a l l a t i o nYou cannot screw into ceiling tiles as they are weak and not suitable for bearing loads. Your VigorAP is supplied with mounts (Mount Base) which will be used to attach directly to the ceiling frame of your suspended ceiling.1. Slide the mount base into the slot of the AP.2. Hold the Access Point with one hand to reach the other hand over the T-Railsides of the bracket.3. Rotate and hook the stationary end of the ceiling mount base onto the T-Railceilingframe.Note Warning: The screw set shown below is for wall mounting only.Do not use such set for ceiling mounting due to the danger offalling.3.4W a l l-M o u n t e d I n s t a l l a t i o nFor wall-mounting, the VigorAP has keyhole type mounting slots on the underside.e the appropriate drill bit to drill two 8.1mm diagram and 26mm depthholes in the markings and hammer the bolts into the openings.2.Screw the anchors unto the holes until they are flush with the wall; screwthe included screws into the anchors.3.Place the Access Point against wall with the mounting screw heads.4.C o n n e c t i o n a n d C o n f i g u r a t i o n4.1C o n n e c t t o a V i g o r R o u t e r u s i n g A P M a n a g e m e n tYour VigorAP can be used with Vigor routers which support AP management (such as the Vigor2865 or Vigor2927 series). AP Management enables you to monitor and manage multiple DrayTek APs from a single interface.1.Connect VigorAP to PoE switch (via LAN port) with Ethernet cable. VigorAPwill get the power from the switch directly. Then, connect the VigorSwitchto a Vigor router.2.Access into the web user interface of Vigor router. Here we take Vigor2865as an example. Open Central Management>>AP>>Status.3.Locate VigorAP 1060C. Click the IP address assigned by Vigor router toaccess into web user interface of VigorAP 1060C.4.After entering the username and password (admin/admin), the main screenwill be displayed.4.2W e b C o n f i g u r a t i o n sThis section will guide you to install the AP and make configuration for VigorAP.C o n n e c t e d A s a M e s h N o d e(i n M e s h N e t w o r k)❶Install VigorAP on to the ceiling.❷As a mesh node, settings related to VigorAP 1060C must be configured by a remote Mesh Root (e.g., VigorAP 903) within the mesh network.The user must detect VigorAP 1060C via a Mesh Root to add it as amesh node.C o n n e c t e d A s a n A c c e s s P o i n tAs an access point, VigorAP 1060C must be connected to a router and configured in AP (Access Point) / Range Extender mode.❶Install VigorAP on to the ceiling.❷Use a twisted-pair cable with RJ-45 plugs at both ends, and plug into Ethernet device (e.g., Vigor router) and Ethernet port of VigorAP.❸ There are two methods to configure VigorAP.Method 1:(a) First, open a web browser on your PC and type https://192.168.1.2. Apop-up window will open to ask for username and password.Note You may either simply set up your computer to get IPdynamically from the router or set up the IP address of thecomputer to be in the same subnet as the IP address ofVigorAP 1060C.● If there is no DHCP server on the network, then VigorAP1060C will have an IP address of 192.168.1.2.● If there is DHCP available on the network, then VigorAP1060C will receive its IP address via the DHCP server.● If you connect to VigorAP by wireless LAN, you could tryto access the web user interface through .(b) After clicking Login, Quick Start Wizard for configuring wirelesssettings will appear as follows.(c)Follow the on-screen steps to finish the network connection. Method 2:(a)Use a mobile phone to scan the QR code named with DrayTek WirelessApp to download DrayTek Wireless APP.(b)After downloading, run the APP.(c)Click Quick Start Wizard. Next, scan the QR code named with ConnectSSID. Later, click Connect to access into the APP user interface ofVigorAP 1060C to set the device in AP or Range Extender mode.5.C u s t o m e r S e r v i c eIf the device cannot work correctly after trying many efforts, please contact your dealer/DrayTek for further help right away. For any questions, please feel freetosende-mailto“*******************”.B e a R e g i s t e r e d O w n e rWeb registration is preferred. You can register your Vigor router viahttps://.F i r m w a r e&T o o l s U p d a t e sDue to the continuous evolution of DrayTek technology, all routers will beregularly upgraded. Please consult the DrayTek web site for more information on newest firmware, tools and documents.https://GPL Notice This DrayTek product uses software partially or completely licensedunder the terms of the GNU GENERAL PUBLIC LICENSE. The author ofthe software does not provide any warranty. A Limited Warranty isoffered on DrayTek products. This Limited Warranty does not coverany software applications or programs.To download source codes please visit:GNU GENERAL PUBLIC LICENSE:https:///licenses/gpl-2.0Version 2, June 1991For any question, please feel free to contact DrayTek technical*************************************************.。
06-AP覆盖距离和信号衰耗指导书
室外测试案例
流量（Mbps）
下行性能
100 90 80 70 60 50 40 30 20 10
0 10 125 130 135 295 300 305 520 525 530
距离（m）
ANT2327D15T-120XP 增益 15dbi +-45
单体组合1垂直1水平 增益 14dbi
SL12839A 增益11dbi
下行性能 82Mbps 90Mbps
30m -47dbm 87Mbps
50m -53dbm 81Mbps
80m -58dbm 50Mbps
上行性能 82Mbps 86Mbps 82Mbps
77Mbps
40Mbps
测试环境
直线距离 信号强度
下行性能 上行性能
多径环境
穿墙型环境
-65dbm -70dbm -75dbm -80dbm -75dbm -80dbm
总吞吐量
8N (KB)
4580
16N (KB)
5009
24N (KB)
4534
32N (KB)
4515
16N+16G (KB)
2994
平均单STA 572.5 313
188
141 93.56
吞吐量
走廊部署AP的多用户性能
目前大部分的部署环境中，都会将AP放在走廊上，覆盖旁边的房间， 比如下图，走廊上的3个AP,覆盖7间教室(208-215)。
1 由于学校的网络比运营商便宜，学校网络开通后，运营商 的AP就只有beacon的干扰，并不严重，大概占用了每个信道10% 的带宽。
2 蓝牙设备功率小，而且数量少，影响不大。 3 将AP的功率调低，到10dbm，然后错开信道，隔楼层的 AP就不会互相干扰了。
G798_amend1_T13-SG15-140324-TD-PLEN-0191
Contact:Mark Loyd JonesXtera Communications, Inc. USATel: +1 214 436 3241Email: mark.jones@Contact:Jürgen RahnAlcatel Lucent Germany Germany Tel: +49 911 526 2776Email: juergen.rahn@Contact:Bert Klaps Altera NTCTel: +32 473 95 77 68 Email: bklaps@INTERNATIONAL TELECOMMUNICATION UNIONSTUDY GROUP 15TELECOMMUNICATIONSTANDARDIZATION SECTORSTUDY PERIOD 2013-2016TD 191 (PLEN/15)English only Original: EnglishQuestion(s): 11/1524 March - 4 April 2014TDSource: Rapporteur Q11/15, Editor G.798Title:Draft Amendment 1 to ITU-T Recommendation G.798 (2012) (for Consent, 4 April 2014)Abstract: This draft amendment is a combination of TD83/3 from the July 2013 SG15 meeting, a draft amendment prepared and posted to the IFA in June 2013 by the G.798 Editor (filename DRAFT_Am_G.798), and the additional changes listed below (based on contributions and discussion at the October 2013 Q11/15 interim meeting in Nuremberg, German):- corrections to the Payload Type for SBCON/ESCON clients and the frequency tolerance of ODUflex signals [1]- addition of CM-XGPON and the Payload Types for clients bit-synchronously mapped into ODUflex to the ODUkP to CBRx adaptation functions [2]- addition of ODU2eP to FC-1200 adaptation functions and extending of Annex A with Fibre Channel clients [3]- correction of FC-100 and FC-200 replacement signals (align with G.709)DRAFT Amendment 1 to ITU-T Recommendation G.798 (2012) Characteristics of optical transport network hierarchy equipment functionalblocks: Amendment 1SummaryThis amendment contains material to G.798 (02/2012) to complete the management interfaces of the optical modulation and wavelength multiplexing processes for support of WDM interfaces, to add a note to see the HAO capable ODUk to MPLS-TP adaptation function in G.8121, to add adaptation of multilane 40 Gigabit/s SDH signals with parallel interfaces (STL256.4) for mapping into LO OPU3, to add CM-XGPON and the Payload Types for clients bit-synchronously mapped into ODUflex to the ODUkP to CBRx adaptation functions, to add the ODU2eP to FC-1200 signal adaptation functions, to add Fibre Channel clients to Annex A, and to correct the Payload Type for SBCON/ESCON clients and the frequency tolerance of ODUflex signals.1ScopeThis amendment 1 contains modified text to be added to complete G.798, by adding missing MI with respect to OCH optical interface application code and frequency / Wavelength support of the wavelength assignment process for support of WDM interfaces and by completing content on ODUflex mapped signals, fibre channel client interfaces, and STM256 multilane interfaces.2 Updates8.11.1 Optical modulation and wavelength multiplexing processesUpdate clause 8.11.1 with the additional text:8.11.1 Optical modulation and wavelength multiplexing processesThe processes listed below are mandatory when they are listed in atomic functions. Specific parameters of these processes depend on the interface type. Refer to [ITU-T G.959.1], [G.694.2], [G.696.1], [G.695], [G.698.1], [G.698.2] and [ITU-T G.694.1] for the currently standardized OTN interfaces and central frequencies. The parameters are managed, if applicable, by theMI_nominalCentralFrequencyOrWavelength, MI_selectedApplicationIdentifier,MI_nominalCentralFrequencyOrWavelength and MI_supportableApplicationIdentifierList management interfaces.Optical carrier modulation (Mod):This process performs modulation of an optical carrier with the payload signal (PLD) by means of a defined modulation scheme. The modulation scheme and optical parameters (e.g., operating wavelength) depend on the specific interface type. This process is used for the generation of a non-coloured optical signal.Optical carrier modulation and wavelength assignment (Mod/WA):This process performs modulation of an optical carrier of a specific wavelength with the payload (PLD) signal by means of a defined modulation scheme. The modulation scheme and optical parameters for the individual channels (e.g., central frequency) depend on the specific interface type. This process is used for the generation of a coloured optical signal.Optical carrier demodulation (DMod): This process demodulates the payload signal (PLD) from the optical carrier. The modulation scheme depends on the specific interface type. This process is used for the termination of coloured and non-coloured optical signal.Optical multiplexing (OM): This process performs optical channel multiplexing to form an optical multiplex signal.Optical demultiplexing and wavelength selection (ODM/WS): This process performs the optical channel demultiplexing and provides access to the individual wavelength signals. The physical parameters (e.g., channel spacing) depend on the specific interface type.12.2.1 to 12.2.2.2 of the OCh and OChr trail termination functions Update the text in clauses 12.12.1 through 12.2.2.2 as follows: 12.2.1 OCh trail termination function (OCh_TT)The OCh_TT functions are responsible for the end-to-end supervision of the OCh trail. They provide full functionality based on the non-associated overhead information. Figure 12-7 shows thecombination of the unidirectional sink and source functions to form a bidirectional function.G.798(10)_F12-7Figure 12-7 – OCh_TT12.2.1.1 OCh trail termination source function (OCh _TT_So)The OCh_TT_So function conditions the data for transmission over the optical medium and presents it at the OCh_TCP. The information flow and processing of the OCh_TT_So function is defined with reference to Figures 12-8 and 12-9. SymbolFigure 12-8 – OCh_TT_So functionG.798(10)_F12-8InterfacesTable 12-2 – OCh_TT_So inputs and outputsProcessesThe processes associated with the OCh_TT_So function are as depicted in Figure 12-9.Payload generation: The function shall generate the OCh payload signal (baseband signal). The physical specifications of the signal are outside the scope of this Recommendation.Optical carrier modulation and wavelength assignment (Mod/WA): See clause 8.11.1. Optical signal pre-conditioning: Pre-conditioning of the single wavelength optical signal might be required. The specific conditioning processes depend on the OTM-n interface type and are outside the scope of this Recommendation. The processes OA, DAc, DAa and PMDC, as defined in clause 8.11.2, are possible.Figure 12-9 – OCh_TT_So processesDefects : None.Consequent actions : None. Defect correlations : None. Performance monitoring : None.12.2.1.2 OCh trail termination sink function (OCh_TT_Sk)The OCh_TT_Sk function recovers the OCh payload signal and reports the state of the OCh trail. It extracts the OCh overhead – including the FDI-P, FDI-O and OCI signals – from the OCh signal at its OCh_TCP, detects for LOS, OCI, FDI-P and FDI-O defects.AI_DOCh_AP OCh_TCPOCh_TT_So_MPSymbolG.798(10)_F12-10OCh_APOCh_TT_Sk_MPFigure 12-10 – OCh_TT_Sk functionInterfacesTable 12-3 – OCh_TT_Sk inputs and outputsProcessesThe processes associated with the OCh_TT_Sk function are as depicted in Figure 12-11. Optical carrier demodulation (DMod): See clause 8.11.1.Optical signal post-conditioning : Post-conditioning of the single wavelength signal might be required. The specific conditioning processes depend on the OTM-nr/OTM-0 interface type (see [ITU-T G.959.1]). and are outside the scope of this Recommendation. The processes OA, DAc, DAa and PMDC, as defined in clause 8.11.2, are possible.Payload recovery : This function shall recover the OCh payload signal. The physical specifications of the signal are outside the scope of this Recommendation.FDI-P : The FDI-P information (OCh-FDI-P) shall be extracted from the OCh overhead of the OOS. It shall be used for FDI-P defect detection. The specific implementation for extracting FDI-P from the OOS and detecting its value is outside the scope of this Recommendation.FDI-O : The FDI-O information (OCh-FDI-O) shall be extracted from the OCh overhead of the OOS. It shall be used for FDI-O defect detection. The specific implementation for extracting FDI-O from the OOS and detecting its value is outside the scope of this Recommendation.OCI : The OCI information (OCh-OCI) shall be extracted from the OCh overhead of the OOS. It shall be used for OCI defect detection. The specific implementation for extracting OCI from the OOS and detecting its value is outside the scope of this Recommendation.Figure 12-11 – OCh_TT_Sk processesC I _P L DC I _O HC I _S S F -OC I _S S F -PA I _T S F -P A I _T S F -O A I _DMI_cLOS-P MI_cSSF-P MI_cSSF-O MI_cOCIOCh_APOCh_TCPO C h _T T _S k _M PMI_cSSF MI_supportableApplicationIdentifierListDefectsThe function shall detect for dLOS-P, dFDI-P, dFDI-O and dOCI.NOTE – Detection of additional OOS-related defects might be required (see clause 6.2.8). This depends on the specific OOS format and is outside the scope of this Recommendation.dLOS-P: See clause 6.2.1.1.dFDI-P: See clause 6.2.6.1.1.dFDI-O: See clause 6.2.6.2.1.dOCI: See clause 6.2.6.8.1; dOCI shall be set to false during CI_SSF-O and dFDI-O. Consequent actionsThe function shall perform the following consequent actions:aTSF-P ←CI_SSF-P or dLOS-P or dOCI or dFDI-PaTSF-O ←CI_SSF-O or dFDI-ODefect correlationsThe function shall perform the following defect correlations to determine the most probable fault cause. This fault cause shall be reported to the EMF.cLOS-P ←dLOS-P and (not dOCI) and (not FDI-P) and (not CI_SSF-P)cOCI ←dOCI and (not CI_SSF-P) and (not CI_SSF-O) and (not FDI-O) and (not FDI-P) cSSF ←(CI_SSF-P or dFDI-P) and (CI_SSF-O or dFDI-O)cSSF-P ←(CI_SSF-P or dFDI-P) and (not cSSF)cSSF-O ←(CI_SSF-O or dFDI-O) and (not cSSF)Performance monitoringFor further study.12.2.2 OChr trail termination function (OChr_TT)The OChr_TT functions are responsible for the end-to-end supervision of the OChr trail. They provide only reduced functionality as no non-associated overhead information is available. Figure 12-12 shows the combination of the unidirectional sink and source functions to form a bidirectional function.G.798(10)_F12-12Figure 12-12 – OChr_TT12.2.2.1 OChr trail termination source function (OChr _TT_So)The OChr_TT_So function conditions the data for transmission over the optical medium and presents it at the OChr_TCP.The information flow and processing of the OChr_TT_So function is defined with reference to Figures 12-13 and 12-14.SymbolG.798(10)_F12-13Figure 12-13 – OChr_TT_So functionInterfacesTable 12-4 – OChr_TT_So inputs and outputsProcessesThe processes associated with the OChr_TT_So function are as depicted in Figure 12-14. Payload generation: The function shall generate the OChr payload signal (baseband signal). The physical specifications of the signal are defined in [ITU-T G.959.1].Optical carrier modulation (Mod): See clause 8.11.1. For the parameters, see [ITU-T G.959.1]. Optical signal pre-conditioning: Pre-conditioning of the single wavelength optical signal might be required. The specific conditioning processes depend on the OTM-0 interface type (see [ITU-T G.959.1]). The processes OA, DAc, DAa and PMDC, as defined in clause 8.11.2, are possible.Figure 12-14 – OChr_TT_So processesDefects : None.Consequent actions : None. Defect correlations : None. Performance monitoring : None.12.2.2.2 OChr trail termination sink function (OChr_TT_Sk)The OChr_TT_Sk function recovers the OCh payload signal and reports the state of the OChr trail. It detects for LOS of the payload signal.The information flow and processing of the OChr_TT_Sk function is defined with reference to Figures 12-15 and 12-16.OCh_AP CI_PLD OChr_TCPOChr_TT_So_MPSymbolOCh_APG.798(10)_F12-15Figure 12-15 – OChr_TT_Sk functionInterfacesTable 12-5 – OChr_TT_Sk inputs and outputsProcessesThe processes associated with the OChr_TT_Sk function are as depicted in Figure 12-16. Payload recovery: This function shall recover the OChr payload signal. The physical characteristics of the signal are defined in [ITU-T G.959.1].Optical signal post-conditioning:Post-conditioning of the single wavelength signal might be required. The specific conditioning processes depend on the OTM-0 interface type (see [ITU-T G.959.1]). The processes OA, DAc, DAa and PMDC, as defined in clause 8.11.2, are possible.Optical carrier demodulation (DMod): See clause 8.11.1. For the parameters, see [ITU-T G.959.1].Figure 12-16 – OChr_TT_Sk processesDefectsThe function shall detect for dLOS-P.dLOS-P: See clause 6.2.1.1.Consequent actionsThe function shall perform the following consequent actions:aTSF-P CI_SSF-P or dLOS-PDefect correlationsThe function shall perform the following defect correlations to determine the most probable fault cause:cLOS ←dLOS and (not CI_SSF-P)cSSF-P ←CI_SSF-PPerformance monitoringFor further study.14.1.1 ODUk connection function (ODU_C)Delete table 14-2 and replace references to Table 14-2 with references to Table 7-2 of [ITU-TG.709].Open connection indication (OCI): If an output of the connection function is not connected to an input, an ODU-OCI signal as defined in clause 16.5 of [ITU-T G.709] is generated for this output. The clock of the OCI signal has to be within the minimum and maximum clock frequencies specified for the ODU signals that are given in Table 7-2 of [ITU-T G.709]. The jitter and wander requirements as defined in Annex A of [ITU-T G.8251] (ODCa clock) apply. CI_SSF is false. CI_RP is is to be set to the default value “0” and CI_TSCC is to be set to the default value “0”for indicating no resize operation active.Alarm indication signal (AIS): If in a protection switch operation as defined in [ITU-T G.873.1] or [ITU-T G.873.1] Extra traffic is preemped and to be squelched or ODU Squeching to prevent misconnection is to be executed , an ODU-AIS signal as defined in clause 16.5 of [ITU-T G.709] is generated for this output. The clock of the AIS signal has to be within the minimum and maximum clock frequencies specified for the ODU signals that are given in Table 7-2 of [ITU-T G.709]. The jitter and wander requirements as defined in Annex A of [ITU-T G.8251] (ODCa clock) apply. CI_SSF is true. CI_RP is to be set to the default value “0” and CI_TSCC is to be set to the default value “0”for indicating no resize operation active.14.1.1.1 Subnetwork connection protection processReplace references to Table 14-2 with references to Table 7-2 of [ITU-T G.709].A permanent bridge, as defined in [ITU-T G.808.1], shall be used for the 1+1 protection. A broadcast bridge, as defined in [ITU-T G.808.1], shall be used for the 1:N protection. It permanently connects the normal traffic signal to the working transport entity. In case no normal or extra traffic signal is connected to the protection transport entity, an ODUk-OCI signal, as defined in clause 16.5 of [ITU-T G.709], is generated for the protection transport entity. The clock of the OCI signal has to be within the minimum and maximum frequencies of the specified ODU signal in Table 7-2 of [ITU-T G.709]. The jitter and wander requirements, as defined in Annex A of [ITU-T G.8251] (ODCa clock), apply. CI_SSF is false. In the case that the extra traffic signal of a 1:N protection configuration carried by the protection entity is pre-empted by a protection switch, an ODU-AIS signal is to be connected to the extra traffic ODU_CP output. The clock of the ODU-AIS signal has to be within the minimum and maximum frequencies of the specified ODU signal in Table 7-2 of [ITU-T G.709]. The jitter and wander requirements, as defined in Annex A of [ITU-T G.8251] (ODCa clock), apply.14.3.1 ODUkP to CBRx adaptation function using AMP and BMP (ODUkP/CBRx_A) Modify Table 14-5B as follows:Table 14-5B – Defined values for x for asynchronous mapping14.3.1.2 ODUkP to CBRx bit synchronous mapping adaptation source function(ODUkP/CBRx-b_A_So)Extend the inserted PT to include bit synchronous CBRx mapping into ODUflex as follows: •PT:The function shall insert the appropriate payload type code into the PT byte position of the PSI overhead as defined in clause 15.9.2.1 of [ITU-T G.709].14.3.1.3 ODUkP to CBRx adaptation sink function (ODUkP/CBRx_A_Sk)Extend the expected PT to include bit synchronous CBRx mapping into ODUflex as follows:DefectsThe function shall detect for dPLM and dCSF defects.dPLM: See clause 6.2.4.1. The expected payload type values are defined in clause 15.9.2.1 of [ITU-T G.709]; "0000 0010" is used for asynchronous CBRx mapping, other applicable values are used for bit synchronous CBRx mapping.–dCSF: See clause 6.2.10.14.3.4.1 ODUkP to NULL adaptation source function (ODUkP/NULL_A_So)Replace the reference to Table 14-2 with a reference to Table 7-2 of [ITU-T G.709].Clock and (multi)frame start signal generation: The function shall generate a local ODUk clock (ODUkP_AI_CK) with a clock frequency within the minimum to maximum values of the specified ODU signal as given in Table 7-2 of [ITU-T G.709] and provisioned by theMI_Nominal_Bitrate_and_Tolerance from a free-running oscillator. The jitter and wander requirements, as defined in Annex A of [ITU-T G.8251] (ODCa clock), apply.14.3.5.1 ODUkP to PRBS adaptation source function (ODUkP/PRBS_A_So)Replace the reference to Table 14-2 with a reference to Table 7-2 of [ITU-T G.709].Clock and (multi)frame start signal generation: The function shall generate a local ODUk clock with a clock frequency within the minimum to maximum values of the specified ODU signal as given in Table 7-2 of [ITU-T G.709] provisioned by the MI_Nominal_Bitrate_and_Tolerance from a free-running oscillator. The jitter and wander requirements, as defined in Annex A of [ITU-TG.8251] (ODCa clock), apply.14.3.7 ODU0P to cli ent adaptation function (ODU0P/CBRx_A) (0 ≤ x ≤ 1.25G)Correct the header for the Payload Type column and correct the Payload Type for SBCON/ESCON in Table 14-20.Table 14-20 – Defined values for x for ODU0 clients14.3.7.2 ODU0P to CBRx adaptation sink function (ODU0P/CBRx_A_Sk) (0 ≤ x ≤ 1.25G) Correct the header for the Payload Type column, the Payload Type for SBCON/ESCON and the FC-100 replacement signal in Table 14-22.Table 14-22 – Defined replacement signals and jitter specificationreferences for ODU0 clients14.3.8.1 ODUkP to CBRx adaptation source function using GMP (ODUkP/CBRx-g_A_So) Replace the reference to Table 14-2 with a reference to Table 7-2 of [ITU-T G.709].Clock and (multi)frame start signal generation: The function shall generate a local ODUk clock (ODUkP_AI_CK) as given in Table 7-2 of [ITU-T G.709] from a free-running oscillator. The clock parameters, including jitter and wander requirements, as defined in Annex A of [ITU-T G.8251] (ODCa clock), apply.14.3.8.2 ODUkP to CBRx adaptation sink function using GMP (ODUkP/CBRx-g_A_Sk) Correct the FC-200 replacement signal in Table 14-26.Table 14-26 – Defined replacement signals for ODUk clients14.3.10.1 ODUkP to ODUj payload type 21 adaptation source function(ODUkP/ODUj-21_A_So)Replace the reference to Table 14-2 with a reference to Table 7-2 of [ITU-T G.709].Buffer size: In the presence of jitter as specified by [ITU-T G.8251] and a frequency within the range specified in Table 7-2 of [ITU-T G.709], this mapping process shall not introduce any errors. The maximum buffer hysteresis, and therefore the maximum phase error introduced, shall be as listed in Table 14-35.14.3.10.2 ODUkP to ODUj payload type 21 adaptation sink function(ODUkP/ODUj-21_A_Sk)Replace the references to Table 14-2 with references to Table 7-2 of [ITU-T G.709].Buffer size: In the presence of jitter as specified by [ITU-T G.8251] and a frequency within the tolerance range specified for the ODUj signal in Table 7-2 of [ITU-T G.709], this justification process shall not introduce any errors.…ODUj-LCK, ODUj-AIS: The function shall generate the ODUj-LCK and ODUj-AIS signals as defined in [ITU-T G.709]. The clock, frame start and multiframes start shall be independent from the incoming clock. The clock has to be within the ODUj frequency tolerance range as specified in Table 7-2 of [ITU-T G.709] provisioned by the MI_Nominal_Bitrate_and_Tolerance from a free-running oscillator. Jitter and wander requirements, as defined in Annex A of [ITU-T G.8251] (ODCa clock), apply.…On declaration of aAIS, the function shall output an all-ONEs pattern/signal within 2 frames. On clearing of aAIS, the all-ONEs pattern/signal shall be removed within 2 frames, with normal data being output. The AIS clock, frame start and multiframe start shall be independent from the incoming clock, frame start and multiframe start. The clock has to be within the ODUj frequency tolerance range as specified in Table 7-2 of [ITU-T G.709] provisioned by the MI_Nominal_Bitrate_and_Tolerance from a free-running oscillator. Jitter and wander requirements, as defined in Annex A of [ITU-T G.8251] (ODCa clock), apply.14.3.12.1 HAO capable ODUk to ETH adaptation source function (ODUkP-h/ETH_A_So) Replace the reference to Table 14-2 with a reference to Table 7-2 of [ITU-T G.709].Adjustable Clock and (Multi)Frame Start signal generation:The function shall generate a local ODUk clock (ODUkP_AI_CK) with a clock rate within the minimum to maximum clock rate of the specified ODU ODUflex signal as given in Table 7-2 of [ITU-T G.709]. The jitter and wander requirements as defined in Annex A of [ITU-T G.8251] (ODCa clock) apply.14.3.13.1 HAO capable ODUkP to ODUj payload type 21 adaptation source function (ODUkP-h/ODUj_A_So)Replace the reference to Table 14-2 with a reference to Table 7-2 of [ITU-T G.709].Buffer size:In the presence of jitter as specified by [ITU-T G.8251] and a frequency within the range specified in Table 7-2 of [ITU-T G.709], this mapping process shall not introduce any errors. The maximum buffer hysteresis, and therefore the maximum phase error introduced, shall be as listed in Table 14-34hao.14.3.13.2 HAO capable ODUkP to ODUj payload type 21 adaptation sink function (HAO capable ODUkP-h/ODUj-21_A_Sk)Replace the references to Table 14-2 with references to Table 7-2 of [ITU-T G.709].Buffer size:In the presence of jitter as specified by [ITU-T G.8251] and a frequency within the tolerance range specified for the ODUj signal in Table 7-2 of [ITU-T G.709], this justification process shall not introduce any errors.…ODUj-LCK, ODUj-AIS: The function shall generate the ODUj-LCK and ODUj-AIS signals as defined in [ITU-T G.709]. The clock, frame start and multiframes start shall be independent from the incoming clock. The clock has to be within the ODUj frequency tolerance range as specified in Table 7-2 of [ITU-T G.709] provisioned by the MI_Nominal_Bitrate_and_Tolerance from a free-running oscillator. Jitter and wander requirements, as defined in Annex A of [ITU-T G.8251] (ODCa clock), apply.…On declaration of aAIS the function shall output an all-ONEs pattern/signal within 2 frames. On clearing of aAIS the all-ONEs pattern/signal shall be removed within 2 frames, with normal data being output. The AIS clock, frame start and multiframe start shall be independent from the incoming clock, frame start and multiframe start. The clock has to be within the ODUj frequency tolerance range as specified in Table 7-2 of [ITU-T G.709] provisioned by the MI_Nominal_Bitrate_and_Tolerance from a free-running oscillator. Jitter and wander requirements, as defined in Annex A of [ITU-T G.8251] (ODCa clock), apply.Annex A, Table A.1Update Table A.1 to include multilane 40 Gigabit/s SDH signals and add Tables for Fibre Channel signals:The parameter x defines the supported bit rate or bit-rate range. The values x = 2G5, 10G and 40G are defined for client signals that comply to the SDH bit rates as defined in Table A.1. The values x = FC-100, FC-200, FC-400, FC-800, FC-1200 and FC-1600 are defined for client signals that comply to the Fibre Channel bit rates as defined in Table A.1A. Support for other bit rates and bit-rate ranges is for further study.Table A.1 – Defined values for x (SDH)Table A.1A – Defined values for x (Fibre Channel)Table A.1B – Jitter standard and replacement signals (Fibre Channel)Note: FC-y is used throughout this clause as shorthand for the defined values for x for Fibre Channel type interfaces.A.2.1 OSx trail termination function (OSx_TT) (x = 2G5, 10G, 40G)Update text as follows:A.2.1 OSx trail termination function (OSx_TT) (x = 2G5, 10G, 40G, FC-y)The OSx_TT functions are responsible for the end-to-end supervision of the OSx trail. Figure A.2 shows the combination of the unidirectional sink and source functions to form a bidirectional function.NOTE – For the case where an STM-N signal is to be transported as a CBR signal, the OSx_TT functions are equivalent to the OSn_TT or OSMn.m_TT functions specified in [ITU-T G.783].A.2.1.1 OS trail termination source function (OSx_TT_So) (x = 2G5, 10G, 40G)Update text as follows:A.2.1.1 OS trail termination source function (OSx_TT_So) (x = 2G5, 10G, 40G, FC-y)The information flow and processing of the OSx_TT_So function is defined with reference to Figures A.3 and A.4. The OSx_TT_So generates an optical signal. The physical parameters of the signal depend on the application. For SDH OSn type interfaces, the specifications in [ITU-T G.957] or [ITU-T G.691] apply. For SDH OSM256.4 type interfaces, Recommendation G.783 clause 9.2.3 and the specifications in [ITU-T G.695] apply.A.2.1.2 OSx trail termination sink function (OSx_TT_Sk) (x = 2G5, 10G, 40G)Update text as follows:A.2.1.2 OSx trail termination sink function (OSx_TT_Sk) (x = 2G5, 10G, 40G, FC-y)The information flow and processing of the OSx_TT_Sk function is defined with reference to Figures A.5 and A.6. The OSx_TT_Sk reports the state of the OSx trail. The OSx_TT_Sk accepts an optical signal. The physical parameters of the signal depend on the application. For SDH OSn type interfaces, the specifications in [ITU-T G.957] or [ITU-T G.691] apply. For SDH OSM256.4 type interfaces, Recommendation G.783 clause 9.2.3 and the specifications in [ITU-T G.695] apply.A.3.1 OSx to CBRx adaptation (OSx/CBRx_A) (x = 2G5, 10G, 40G)Update header as follows:A.3.1 OSx to CBRx adaptation (OSx/CBRx_A) (x = 2G5, 10G, 40G, FC-y)A.3.1.1 OSx to CBRx adaptation source function (OSx/CBRx_A_So) (x = 2G5, 10G, 40G) Update text as follows:A.3.1.1 OSx to CBRx adaptation source function (OSx/CBRx_A_So) (x = 2G5, 10G, 40G,FC-y)For SDH OSn type interfaces and Fibre Channel type interfaces,the information flow and processing of the OSx/CBRx_A_So function is defined with reference to Figures A.7 and A.8. NOTE: For SDH OSM256.4 type interfaces, please see A.3.1.1.3…For SDH type interfaces, the jitter and wander requirements, as defined in clause 9.3.1.1 of [ITU-T G.783], apply. For Fibre Channel type interfaces, the input clock ranges are defined in Table A.1A and the jitter and wander requirements, as defined in the specifications referenced in Table A.1B, apply.A.3.1.2 OSx to CBRx adaptation sink function (OSx/CBRx_A_Sk) (x = 2G5, 10G, 40G) Update text as follows:A.3.1.2OSx to CBRx adaptation sink function (OSx/CBRx_A_Sk) (x = 2G5, 10G, 40G, FC-y)For SDH OSn type interfaces and Fibre Channel type interfaces , the information flow and processing of the OSx/CBRx_A_Sk function is defined with reference to Figures A.9 and A.10. NOTE: For SDH OSM256.4 type interfaces, please see A.3.1.1.4 …Clock recovery : The function shall recover the clock signal from the incoming data. For SDH type interfaces, the input clock ranges are defined in Table A.1 and the jitter and wander requirements, as defined in clause 9.3.1.2 of [ITU-T G.783], apply. For Fibre Channel type interfaces, the input clock ranges are defined in Table A.1A and the jitter and wander requirements, as defined in the specifications referenced in Table A.1B, apply.To ensure adequate immunity against the presence of consecutive identical digits (CID) in the signal, the function shall comply with the specification in clause 15.1.4 of [ITU-T G.783] for SDH type interfaces.Figure A.10 – OSx/CBRx_A_Sk processesDefects : None. Consequent actionsThe OSx/CBRx_A_Sk function performs the following consequent actions. aSSF ← AI_TSF aAIS←AI_TSFreplacement signal as defined in clause 16.6 of [ITU-T G.709] for SDH type interfaces and in Table A.1B for Fibre Channel type interfaces within X ms. On clearing of aAIS, the replacement signal shall be removed within Y ms, with normal data being output. The values for X and Y are for further study.CBRx_CPCI_D CI_CKCI_SSFOSx_AP。
ap物理考试圆周运动公式
ap物理考试圆周运动公式
圆周运动的公式主要包括：
1. 线速度v=ωr，其中ω是角速度，r是半径。
这个公式用于求线速度，除了可以用ωr，也可推导出v=2πr/T（T为周期）。
2. 角速度ω=θ/t=2π/T=2πn（θ表示角度或者弧度，T为周期，n为转速，其中n与T可以互相转换，公式为T=1/n）。
3. 周期T=2πr/v=2π/ω。
4. 频率f=1/T。
5. 向心力Fn=mrω²=mv²/r=mr4π²/T²=mr4π²f²。
6. 向心加速度an=rω²=v²/r=r4π²/T²=r4π²n²。
7. 在最高点时的最小速度vmax=√gr（无杆支撑）。
此外，还有周期、转速、向心力、向心加速度等相关的公式。
这些公式可以用于描述圆周运动的基本性质和运动规律。
以上信息仅供参考，如有需要，建议查阅物理书籍或咨询专业人士。
Futaba T7PX T7XC 无线遥控器软件更新指南说明书
1M23Z05402T7PX/T7XC Software Update MethodWhenever improvements and new functions are available, the software of your T7PX/T7XC radio transmitter can be updated easily online free of charge. The updated software file will be shown on our website. Y ou can download it and make a copy on your microSD card. Below is the procedure for the software update.Procedure for the software updateCaution: Before you update the software, the battery that is connected to the T7PX/T7XC should be fully charged.Note: During the software update, the model data that is stored in the T7PX/T7XC should be kept without any change. (NOT erased and NOT changed.) However, for your safety, making a backup of your model data before the software update is highly recommended.1. Download the zip file of the update data from our website.2. Extract the zip file on your computer.3. The "FUTABA" folde r will be cre ate d on your computer.4. Copy the "FUT ABA" folder onto your microSD card.7. W h e n t h e s o f t wa r e u p d a t e i s c o m p l e t e d , "Completed" message is shown on the LCD display of your T7PX/T7XC. (See attached picture.)Tap the [Reset] button for "min./max." to re se t the maximumvalue indicate d by the whitepointe r on the me te r on thehome scre e n. At the same time,the "Min" and "Max." displays one ach te le me try se tting screare reset.A menu for home screen setting has been added. The display method of the meter displayed on the home screen and the display content have been changed. The steering and throttle operation can also be dis-played on the meter.n display toSelect [Instrument panel] in the home screen display settings. T ap the meter to be set on the home screen to select it. Use the following procedure to select the data to be displayed.Other-Added support to change SR mode of HPS-CT700.The condition function has been enhanced.*Up to 4 conditions can be used.*It is possible to name the condition.*Switching or condition can be switched by switch or trim / dial.3 T ap the [Condition] button to change the number of available conditions.A list of condition numbers is displayed in the "Condition name " group box. Up to 4 conditions can be used.This function allows you to assign a fifte e n characte r name to econdition.1 From the "Condition Name " list, tap the condition button whose nameyou want to change.2 Since the condition name setting screen is displayed, edit the name.3 T ap the title button [Condition name] to return to the condition screen.Condition nameThis function copies condition data to other conditions.1 T ap the [copy condition] button. The condition copy screen will be displayed.2 T ap the “Copy from” [Condition name], select the sondition list so it will tap. The source condition is selected and the list isclosed. In the same way, use the "Copy to" condition button to select the copy destination condition.Condition copy3 T ap the [Copy], The confirmation message “Are you sure” appears. T o execute copy, tap [Y es] and to cancel copy, select [No].When the copy destination condition name becomes the same name as the copy source, copying is complete.This function sets the switch to change the condition. There are two kinds of change methods as follows.- With one switch, change the Condition 1 and Condition 2.- Assign a condition to each switch, and operate the switch to change the condition.1 T ap the [Switch select] button to display a "Switch select " screen. (The "Switch select " screen can also be displayed fromthe "Linkage menu " or the "User menu ".)2 T ap the switch you want to use to display the function selection screen. By selecting [Condition 12] from the function list,you can change Condition 1 and Condition 2 by operating the switch. If you select [Condition 1] to [Condition 4] for each switch, you can change to the condition assigned by each switch operation.This function can change the condition by trim or dial. By operating T rim or Dial, you can change the condition as Conditionplayed from the "Linkage menu " or the "User menu ".)2 T ap the trim or dial you want to use to display the function selection screen. Since the function selection screen is dis-played, select [Condition] from the function list.Condition change switch settingCondition change trim / dial settingIt corresponds to the Kyosho Mini-Z EVO dedicated receiver RA-42. For futher instruction, Please also read the instruc-2 T ouch [Link] on the transmitter T7PX / T7XC screen, you will hear a chime sound and T7PX / T7XC will enter the link modefor 20 seconds.The following servos support SR mode setting.S3470SV / S9370SV / S9470SV / S9570SV / S9571SV / S9670SV * Only "SR type 1" can be selected for SR type.Additional function / MC (ESC) Link (MC970CR)When the trim or the dial is operated, the value of the function is displayed for a few seconds at the top of the screen.The MC970CR has been added to the "MC (ESC) link " function of Futaba ESC parameter change. *MC970CR is available only in the Japanese market. (As of Sep 2018)Example:The trim/dial is assigned to the gyro mixing function.For ESC in the past, ple asechoose Other.*Improvement in SR mode setting*Even if a servo that is not compatible with SR mode is connected to a T7PX/T7XC with softwareV2.0 to V2.2, the transmitter can switch the servo to SR mode, but the incompatible servo will not work and the servo program is damaged when you forcibly switch the servo to SR mode. Thus, the servo does not work. So, please never switch when you connect an incompatible servo to SR mode.The software has been improved so that a transmitter prohibits you from switching an incompatible servo to SRmode.Added support to change SR mode of HPS-CB700.When connecting a servo that is not com-patible with SR mode, a message "Unsup-ported" is displayed on the screen, but you can operate the SR mode select button.Please never select the SR mode setting when you see "Unsupported " on the display.When connecting a servo that is not com-patible with SR mode, you cannot operate the SR mode switching button.Futaba S.BUS / S.BUS 2 The "S. BUS servo " function (Instruction manual page 135) that allows you to change the servo parameters can now be set up wirelessly by connecting to the receiver.* A receiver compatible with the wireless setting function is required. (As of April 2018, R334SBS / R334SBS-E is compatible with wireless setting. Please update the previous receiver to version 2.0 or later.)When the link is completed, power cycle the receiver.ou can check the software version on the receiver screen.configure the syste Please update the receiver to below version 2.0.Home button· Set for T -FHSS system· Link with link buttonReceiver software versionConnect the S. BUS / S. BUS 2 servo as shown in the figure and the receiver battery to the channel of the receiver.- ReferenceWhe ste e and 2nd channeOther changes and additions- Operation change in the "Acceleration " range (instruction manual page 60) within EPA setting range.- Added poll number setting and gear ratio setting on Telemetry Link setting screen of non-Futaba sensor (Castle TL 0).- Added support to change SR mode of BLS373SV.the DISP side. T urn on the battery switch of the receiver and confirm that the servos can operate.The S.BUS servo screen is displayed in the following way.Menu screenS.Bus servo1 Tap the Read] button. The notes on wireless setting are displayed. T ap the[Close] button.Once this screen is displayed, it will not be displayed again until you turn the power back on.2 T setting data from the servo.- Communication port :T7PX communication port (conventional wired setting). - Wireless 1 (Rx Ch1) :Receiver channel 1- Wireless 2 (Rx Ch2):Receiver channel 2-"Reading succeeded" is displayed on the screen and the servo’s ID cord and currently set con-tents are read.normally.Che ck the T7PX and se rvo conne ction to se rvo and re pe at [Read]. (Che ck re ce ive r powe supply etc.)Futaba has added a function to program your Futaba R334SBS / R334SBS-E receiver from the T7PX.To update the receiver, you need a PC that can be connected to the Internet, a mini driver (to push the switch of the receiver), a micro SD card (commercial product), and a cord for CGY750 / GY701 / GY520 (optional) or DSC cord (optional).Preparing for update- Download the zip file of the update data from our website or your local distributor’s website.- Extract the zip file on your computer. A folder named "FUT ABA" is created.- Insert the micro SD card that contains the "FUT ABA" folder into the T7PX (see page 31 of the manual).Connection between T7PX and receiverIt conne cts to CH1 of there ce ive r and the communi-cation port of the transmitter.Hold down the Link switch first, and turn ON the receiver.After the LED flashes red once, release the Link switch and then press it again.2T ap the "Update" button on the screen. The update will start. A progress barwill be displayed indicating the progress. The LED of the receiver turns green,and it blinks green for a moment every time it accepts data from the T7PX.- Do not turn off the power of T7PX while updating.3Whe n the update is comple te d, a me ssage is displaye d on the scre e n, andthe LED of the receiver stays flashing green. Please turn off the power of thereceiver.Please check the operation before running (cruising).In the unlikely event that the model data is damaged and the T7PX stops working properly, it is possible to initial-ize the current model data in the following way.Note:This operation completely initializes the model data. Please do not use it except when data is broken.will be initialized, please re-set the data and check the operation carefully before use. T ocancel the operation, touch [No]. The power is turned off without initializing the data.- After initialization, the current model data will be initialized, so please set the data again before using and con-firm the operation.4When finished, return to the System menu screen by pressing the HOME button.ErrorIf an error display appeared, reinstall the update from the beginning.- The receiver is not in the update wait state- The cable is disconnected.- The power has been turned off- The micro SD card is not inserted in the T7PX.- There is no data on micro SD card.。
APtools 6.8.8 用户手册说明书
Package‘APtools’October12,2022Type PackageTitle Average Positive Predictive Values(AP)for Binary Outcomes andCensored Event TimesVersion6.8.8Depends graphics,stats,utils,survival,cmprskAuthor Hengrui Cai<********************>,Yan Yuan<*****************>,Qian Michelle Zhou<****************>,Bingying Li<*********************>Maintainer Hengrui Cai<********************>Description We provide tools to estimate two prediction accuracy metrics,the average positive predictive values(AP)as well as the well-known AUC(the area under the receiver operator characteristic curve)for risk scores.The outcome of interest is either binary or censored event time.Note that for censored event time,our functions'estimates,the AP and theAUC,are time-dependent for pre-specified time interval(s).A function thatcompares the APs of two risk scores/markers is also included.Optionaloutputs include positive predictive values and true positive fractions atthe specified marker cut-off values,and a plot of the time-dependent APversus time(available for event time data).License LGPL-3Encoding UTF-8LazyData trueNeedsCompilation noRepository CRANDate/Publication2018-09-2104:40:09UTCR topics documented:APBinary (2)APSurv (3)CompareAP (5)mayo (6)Index812APBinary APBinary Estimating the AP and the AUC for Binary Outcome Data.DescriptionThis function calculates the estimates of the AP and AUC for binary outcomes as well as their confidence intervals using the perturbation or the nonparametric bootstrap resampling method. UsageAPBinary(status,marker,cut.values=NULL,method="none",alpha=0.95,B=1000,weight=NULL)Argumentsstatus Binary indicator,1indicates case/the class of prediction interest and0other-wise.marker Numeric risk score.Data can be continuous or ordinal.cut.values risk score values to use as a cut-off for calculation of positive predictive values (PPV)and true positive fractions(TPF).The default value is NULL.method Method to obtain confidence intervals.The default is method="none",in which case only point estimates will be given without confidence intervals.If method="perturbation",then perturbation based CI will be calculated.If method="boot-strap",then nonparametric bootstrap based CI will be calculated.alpha Confidence level.The default level is0.95.B Number of resampling to obtain confidence interval.The default value is1000.weight Optional.The default weight is1,same object length as the"status"and"marker"ers can use their own weights,and the length of weight is required tobe the same as the length of status.Valuean object of class"APBinary"which is a list with components:ap_summary Summary of the AP,including the proportion of cases,a point estimate of AP, and their corresponding confidence intervals.auc_summary Summary of the AUC,including a point estimate of AUC with a confidence interval.PPV Available object,positive predictive values at the unique risk score in the data.TPF Available object,true positive fractions at the unique risk score in the data. ReferencesYuan,Y.,Su,W.,and Zhu,M.(2015).Threshold-free measures for assessing the performance of medical screening tests.Frontiers in Public Health,3.57.Bingying Li(2015)Threshold-free Measure for Assessing the Performance of Risk Prediction with Censored Data,MSc.thesis,Simon Fraser University,CanadaExamplesstatus=c(rep(1,10),rep(0,1),rep(1,18),rep(0,11),rep(1,25),rep(0,44),rep(1,85),rep(0,176))marker=c(rep(7,11),rep(6,29),rep(5,69),rep(4,261))cut.values=sort(unique(marker)[-1])out1<-APBinary(status,marker,cut.values)out1out2<-APBinary(status,marker,method="perturbation",alpha=0.90,B=1500)out2APSurv Estimating the Time-dependent AP and AUC for Censored Time toEvent Outcome Data.DescriptionThis function calculates the estimates of the AP and AUC for censored time to event data as well as their confidence intervals using the perturbation or the nonparametric bootstrap resampling method.The estimation method is based on Yuan,Y.,Zhou,Q.M.,Li,B.,Cai,H.,Chow,E.J.,Armstrong,G.T.(2018).A threshold-free summary index of prediction accuracy for censored time to eventdata.Statistics in medicine,37(10),1671-1681.UsageAPSurv(stime,status,marker,t0.list,cut.values=NULL,method="none",alpha=0.95,B=1000,weight=NULL,Plot=TRUE)Argumentsstime Censored event time.status Binary indicator of censoring.1indicates observing event of interest,0other-wise.Other values will be treated as competing risk event.marker Numeric risk score.Data can be continuous or ordinal.t0.list Prediction time intervals of interest.It could be one numerical value or a vector of numerical values,which must be in the range of stime.cut.values Risk score values to use as a cut-off for calculation of time-dependent positive predictive values(PPV)and true positive fractions(TPF).The default value isNULL.method Method to obtain confidence intervals.The default is method="none",in which case only point estimates will be given without confidence intervals.If method="perturbation",then perturbation based CI will be calculated.If method="boot-strap",then nonparametric bootstrap based CI will be calculated.alpha Confidence level.The default level is0.95.B Number of resampling to obtain a confidence interval.The default value is1000.weight Optional.The default value is NULL,in which case the observations are weighted by the inverse of the probability that their respective time-dependent event status(whether the event occurs within a specified time period)is observed.In esti-mating the probability,the survival function of the censoring time is estimatedby a Kaplan-Meier estimator under the assumption that the censoring time isindependent of both the event time and risks ers can use their ownweights,in which case the t0.list should be a scalar and the length of weight isrequired to be the same as the length of status.Plot Whether to plot the time-dependent AP versus the prediction time intervals.The default value is TRUE,in which case the AP is evaluated at the time points whichpartition the range of the event times of the data into100intervals.ValueAn object of class"APsurv"which is a list with components:ap_summary Summary of estimated AP(s)at the specified prediction time intervals of interest.For each prediction time interval,the output includes the estimated event rate,apoint estimate of the AP,the estimated scaled AP(ratio of the AP versus eventrate),and their corresponding confidence intervals.auc_summary Summary of AUC at the specified prediction time intervals of interest.For each prediction time intervals,the output includes the estimated event rate and a pointestimate of AUC with a confidence interval.PPV Available object,time-dependent positive predictive values at the unique risk score in the data.TPF Available object,time-dependent true positive fractions at the unique risk score in the data.ReferencesYuan,Y.,Zhou,Q.M.,Li,B.,Cai,H.,Chow,E.J.,Armstrong,G.T.(2018).A threshold-free summary index of prediction accuracy for censored time to event data.Statistics in medicine, 37(10),1671-1681.Bingying Li(2015)Threshold-free Measure for Assessing the Performance of Risk Prediction with Censored Data,MSc.thesis,Simon Fraser University,CanadaExampleslibrary(APtools)data(mayo)t0.list=seq(from=min(mayo[,1]),to=max(mayo[,1]),length.out=5)[-c(1,5)]cut.values=seq(min(mayo[,3]),max(mayo[,3]),length.out=10)[-10]out<-APSurv(stime=mayo[,1],status=mayo[,2],marker=mayo[,3],t0.list=t0.list,cut.values=cut.values,method= bootstrap ,alpha=0.90,B=500,weight=rep(1,nrow(mayo)),Plot=FALSE)outCompareAP5CompareAP Comparison of two risk scores based on the differences and ratio oftheir APs.DescriptionThis function estimates the difference between and the ratio of two APs in order to compare two markers for censored time to event data or binary data.The corresponding confidence intervals are provided.UsageCompareAP(status,marker1,marker2,stime=NULL,t0.list=NULL,method="none",alpha=0.95,B=1000,weight=NULL,Plot=TRUE)Argumentsstatus Binary indicator.For binary data,1indicates case and0otherwise.For survival data,1indicates event and0otherwise.marker1Risk score1(to be compared to risk score2).Its length is required to be the same as the length of status.marker2Risk score2(to be compared to risk score1).Its length is required to be the same as the length of status.stime Censored event time.If dealing with binary outcome,skip this argument which is set to be NULL.t0.list Prediction time intervals of interest for event time outcome.It could be one numerical value or a vector of numerical values,which must be in the range ofstime.It is set to be NULL if stime is NULL.method Method to obtain confidence intervals.The default is method="none",in which case only point estimates will be given without confidence intervals.If method="perturbation",then perturbation based CI will be calculated.If method="boot-strap",then nonparametric bootstrap based CI will be calculated.alpha Confidence level.The default level is0.95.B Number of resampling for obtaining a confidence interval.The default value is1000.weight Optional argument for event time data,i.e.stime is not NULL.Its default value is NULL,in which the observations are weighted by the inverse of the probabil-ity that their respective time-dependent event status(whether the event occurswithin a specified time period)is observed.In estimating the probability,thesurvival function of the censoring time is estimated by a Kaplan-Meier estima-tor under the assumption that the censoring time is independent of both the eventtime and risks ers can use their own weights,in which case the t0.listshould be a scalar and the length of weight is required to be the same as thelength of status.6mayo Plot Optional argument for event time data,i.e.stime is not NULL.For binary data, it is set to FALSE.For event time data,its default value is TRUE and threeplots are generated:1)the time-dependent AUC of two markers;2)the time-dependent AP of two markers;and3)the time-dependent ratio of APs,all versusthe prediction time intervals.The quantities in1)-3)are evaluated at the timepoints which partition the range of the event times of the data to100intervals.Valuedap_summary Summary of the APs of two markers and the differences(AP1-AP2)and their ratio(AP1/AP2).For event time data,these quantities are estimated at thespecified prediction time intervals.The output includes the estimated eventrate/proportion of cases,point estimates of the APs of the two markers,pointestimates of the difference between and ratio of the two APs as well as theirrespective confidence intervals.ReferencesYuan,Y.,Zhou,Q.M.,Li,B.,Cai,H.,Chow,E.J.,Armstrong,G.T.(2018).A threshold-free summary index of prediction accuracy for censored time to event data.Statistics in medicine, 37(10),1671-1681.Yuan,Y.,Su,W.,and Zhu,M.(2015).Threshold-free measures for assessing the performance of medical screening tests.Frontiers in Public Health,3.57.Bingying Li(2015)Threshold-free Measure for Assessing the Performance of Risk Prediction with Censored Data,MSc.thesis,Simon Fraser University,CanadaExampleslibrary(APtools)status=c(rep(1,10),rep(0,1),rep(1,18),rep(0,11),rep(1,25),rep(0,44),rep(1,85),rep(0,176))marker1=c(rep(7,11),rep(6,29),rep(5,69),rep(4,261))marker2=c(rep(7,17),rep(6,29),rep(5,70),rep(4,254))out_binary<-CompareAP(status,marker1,marker2)out_binarydata(mayo)t0.list=seq(from=min(mayo[,1]),to=max(mayo[,1]),length.out=5)[-c(1,5)]out_survival<-CompareAP(status=mayo[,2],marker1=mayo[,3],marker2=mayo[,4],stime=mayo[,1],t0.list=t0.list,method= bootstrap ,alpha=0.90,B=500,weight=rep(1,nrow(mayo)),Plot=FALSE)out_survivalmayo Mayo Marker dataDescriptionTwo marker values with event time and censoring status for the subjects in Mayo PBC datamayo7FormatA data frame with312observations and4variables:time(event time/censoring time),censor(cen-soring indicator),mayoscore4,mayoscore5.The two scores are derived from4and5covariates respectively.SourceT Therneau,P Grambsch(2000)Modeling Survival Data:Extending the Cox Model Springer-Verlag,New York,ISBN:0-387-98784-3.ReferencesFleming T,Harrington D.(1991)Counting Processes and Survival Analysis Wiley,New York.Heagerty,P.J.,Zheng,Y.(2005)Survival Model Predictive Accuracy and ROC Curves Biometrics, 61,92–105Index∗survivalmayo,6APBinary,2APSurv,3CompareAP,5mayo,68。
难点探究专题：全等三角形中的动点问题(3类热点题型讲练)(解析版)--初中数学北师大版7年级下册
第07讲难点探究专题：全等三角形中的动点问题(3类热点题型讲练)目录【题型一利用分类讨论思想求解动点中三角形全等问题】..................................................................................1【题型二利用三角形全等求证线段之间的关系问题】........................................................................................11【题型三利用三角形全等求证角之间的关系问题】.. (21)【题型一利用分类讨论思想求解动点中三角形全等问题】例题：（23-24八年级上·重庆·阶段练习）如图，在长方形ABCD 中，4,6AB AD ==，延长BC 到点E ，使2CE =，连接DE ，动点P 从点B 出发，以每秒2个单位的速度沿BC CD DA →→向终点A 运动，设点P 的运动时间为t 秒，当t 的值为秒时，ABP 与DCE △全等．【答案】1或7【分析】本题考查了全等三角形的判定，判定方法有：ASA,SAS,AAS,SSS,HL ．根据题意，分两种情况进行讨论，根据题意得出22BP t ==和1622AP t =-=即可求得．【详解】解：由题意得：AB CD =，若90,2ABP DCE BP CE ∠=∠=︒==，根据SAS 证得ABP DCE ≌△△，∴22BP t ==，即1t =，若90,2BAP DCE AP CE ∠=∠=︒==，根据SAS 证得BAP DCE ≌ ，∴1622AP t =-=，即7t =．∴当t 的值为1或7秒时．ABP 与DCE △全等．故答案为：1或7．【变式训练】1．（23-24八年级上·山东日照·阶段练习）如图，CA AB ⊥，垂足为点A ，12AB =米，6AC =米，射线BM AB ⊥，垂足为点B ，动点E 从A 点出发以2米/秒沿射线AN 运动，点D 为射线BM 上一动点，随着E 点运动而运动，且始终保持ED CB =，当点E 经过秒时（不包括0秒），由点D E B 、、组成的三角形与BCA V 全等．【答案】3秒或9秒或12【分析】本题考查了三角形全等的判定与性质，分四种情况：当点E 在线段AB 上，AC BE =时，ACB BED ≌；当E 在BN 上，AC BE =时，ACB BED ≌；当E 在线段AB 上，AB EB =时；当E 在BN上，AB EB =时，ACB BDE ≌；分别利用三角形全等的性质进行求解即可，熟练掌握三角形全等的判定与性质是解此题的关键．【详解】解：当点E 在线段AB 上，AC BE =时，ACB BED ≌，6AC = ，6BE ∴=，1266AE AB BE ∴=-=-=，∴点E 的运动时间为623÷=（秒）；当E 在BN 上，AC BE =时，ACB BED ≌，6AC = ，6BE ∴=，12618AE AB BE ∴=+=+=，∴点E 的运动时间为1829÷=（秒）；当E 在线段AB 上，AB EB =时，此时E 在A 点未动，时间为0秒，不符合题意；当E 在BN 上，AB EB =时，ACB BDE ≌，12AB = ，12BE ∴=，121224AE AB BE ∴=+=+=，∴点E 的运动时间为24212÷=（秒）；综上所述，当点E 经过3秒或9秒或12秒时（不包括0秒），由点D E B 、、组成的三角形与BCA V 全等，故答案为：3秒或9秒或12．2．（23-24八年级上·北京西城·期中）如图，在平面直角坐标系xOy 中，()5,0A ，()0,7B ，动点P ，Q 分别按照A O B --和B O A --的路线同时开始运动，到各自的终点时停止．直线l 经过原点O ，且l AB ∥，过P ，Q 分别作l 的垂线段，垂足分别为F ，E ．若点P 的速度为每秒2个单位长度，点Q 的速度为每秒4个单位长度，运动时间为t 秒，当OPE 与OQF △全等时，t 的值为．【答案】1或2或5【分析】本题主要考查了全等三角形的性质和一元一次方程的应用，解题的关键是恰当分类并利用全等三角形的性质建立方程．判断出OP OQ =再分三种情况讨论，表示出OP ，OQ 建立一元一次方程求解即可．【详解】解：∵()5,0A ，()0,7B ，∴5OA =，7OB =，由题意，OP 和OQ 是两直角三角形的斜边，当OPE 与OQF △全等时，OP OQ =，①当点P 在OA 上，点Q 在OB 上时，根据题意可得∶s t 时，2AP t =，4BQ t =，∴52OP OA AP t =-=-，74OQ OB BQ t =-=-，∴5274t t -=-，解得∶1t =；②当点P ，Q 都在OA 上时，点P ，Q 重合时，两三角形重合时，P 点行程为2t ，Q 点行程为4t ，∴2457t t +=+，解得2t =；③当点P 在OB 上，点Q 在OA 上且点Q 与点A 重合时，25OP t =-，5OQ =∴255t -=．解得：5t =当OPE 与OQF △全等时，满足题意的t 的值为1或2或5．故答案为：1或2或5．3．（23-24八年级下·江苏泰州·阶段练习）如图，在长方形ABCD 中，3cm AB DC ==，2cm BC AD ==，现有一动点P 从点A 出发，以1cm /s 的速度沿长方形的边A B C D A →→→→运动，到达点A 时停止；点Q在边DC 上，DQ BC =，连接AQ ．设点P 的运动时间为s t ，则当t =s 时，以长方形的两个顶点及点P 为顶点的三角形与ADQ △全等．（不考虑两个三角形重合的情况）【答案】1或2或7【分析】本题考查了全等三角形的判定和长方形的性质，掌握全等三角形的判定和恰当分类是解题的关键．先确定ADQ △是等腰直角三角形，再分三种情况：点P 在AB 边上，BP BC =或AP AD =，点P 在CD 边上，CP BC =，利用动点运动的路径求解即可．【详解】解：在长方形ABCD 中，90DAB B C D ∠=∠=∠=∠=︒，∵DQ BC =，∴DQ AD =，∴ADQ △是等腰直角三角形，分三种情况：当点P 在AB 边上，BP BC =时，BPC ADQ ≌，则1cm AP AB PB =-=，∴1s t =；当点P 在AB 边上，AP AD =时，DAP ADQ ≌，则2s=t 点P 在CD 边上，CP BC =时，BCP ADQ ≌，则(322)s =7s t =++，综上，当1s t =或2s 或7s 时，以长方形的两个顶点及点P 为顶点的三角形与ADQ △全等．故答案为：1或2或7．4．（23-24八年级上·福建泉州·阶段练习）如图，CA AB ⊥，垂足为点A ，射线BM AB ⊥，垂足为点B ，16cm AB =，8cm AC =．动点E 从A 点出发以4cm/s 的速度沿射线AN 运动，动点D 在射线BM 上，随着E 点运动而运动，始终保持ED CB =．若点E 的运动时间为()0t t >，则当t =秒时，DEB 与BCA V 全等．12cm BC =，现有一动点P 从点A 出发，沿着三角形的边AC CB BA →→运动，回到点A 停止，速度为2cm/s ，设运动时间为s t ．(1)如图1，当t =s 时，12BPC ABC S S =；(2)如图2，在DEF 中，90E ∠=︒，8cm DE =，10cm DF =，D A ∠=∠．在ABC 的边上，若另外有一个动点Q ，与点P 同时从点A 出发，沿着边AB BC CA →→运动，回到点A 停止．在两点运动过程中的某一时刻，恰好APQ △与DEF 全等，求点Q 的运动速度．②点P 在AB 上时，过点∴点P 的运动路程为（2）∵在DEF∴①当点P在AC∴点Q的速度为：②当点P在AB上，点∴点Q的速度为：③当点P在AB上，④当点P 在AC 上，点∴点Q 的速度为：综上所述，两点运动过程中的某一时刻，19cm /s 10cm /s 或8cm 56．（2023·广西南宁·二模）如图，在ABC 中，AD 为高，18AC =．点E 为AC 上的一点，2CE AE =，连接BE ，交AD 于O ，若BDO ADC △≌△．(1)猜想线段BO 与AC 的位置关系，并证明；(2)有一动点Q 从点A 出发沿射线AC 以每秒6个单位长度的速度运动，设点Q 的运动时间为t 秒，是否存在t 的值，使得BOQ △的面积为27？若存在，请求出t 的值；若不存在，请说明理由；(3)在（2）条件下，动点P 从点O 出发沿线段OB 以每秒2个单位长度的速度向终点B 运动，P 、Q 两点同时出发，当点P 到达点B 时，P 、Q 两点同时停止运动，设运动时间为t 秒，点F 是直线BC 上一点，且CF AO =，当AOP 与FCQ 全等时，求t 的值．1118(1222BOQ S BO QE ∆=⨯=⨯⨯-解得：32t =（舍去）；当2t >时，Q 在射线EC 上，如图1118(612)22BOQ S BO QE t ∆=⨯=⨯⨯-=解得：52t =，此时Q 与C 重合；综上所述，存在t 的值，使得BOQ △（3）由（1）可知，BDO ADC △≌△BOD ACD \Ð=Ð，当点F 在线段BC 延长线上时，如图BOD ACD Ð=ÐQ ，BOD ACD Ð=ÐQ ，AOP FCQ \Ð=Ð，AO CF =Q ，∴当OP CQ =时，AOP FCQ ≌此时，2618t t =-，解得：92t =；综上所述，当AOP 与FCQ 全等时，【点睛】本题是三角形综合题目，考查了全等三角形的判定与性质、三角形面积、三角形面积和定理、对顶角相等以及分类讨论等知识，本题综合性强，熟练掌握全等三角形的判定与性质，进行分类讨论是解题的关键．【题型二利用三角形全等求证线段之间的关系问题】例题：（23-24八年级上·北京海淀·阶段练习）在ABC 中，AC BC =，90ACB ∠=︒，点D 在BC 的延长线上，M 是BD 的中点，E 是射线CA 上一动点，且CE CD =，连接AD ，作DF AD ⊥，DF 交EM 延长线于点F ．(1)如图1，当点E 在CA 上时，填空：AD ________DF （填“=”、“<”或“>”）．(2)如图2，当点E 在CA 的延长线上时，请根据题意将图形补全，判断AD 与DF 的数量关系，并证明你的结论．【答案】(1)=，详见解析；(2)AD DF =，详见解析．【分析】本题考查了全等三角形的判定与性质的综合应用等知识；（1）连接BE ，先证SAS ACD BCE ≌（），得AD BE EBM DAC =∠=∠，，再证ASA EBM FDM ≌（），得BE DF =，即可得出结论；（2）连接BE ，先证SAS ACD BCE ≌（），得AD BE ADC BEC =∠=∠，，再证ASA BME DMF ≌（），得BE DF =，即可得出结论．证明三角形全等是解题的关键．【详解】（1）AD DF =，理由如下：连接BE ，如图1所示：∵90ACB ∠=︒，∴90DCA ∠=︒，在ACD 和BCE 中，CD CE DCA ECB AC BC =⎧⎪∠=∠⎨⎪=⎩，∴SAS ACD BCE ≌（），∴AD BE EBM DAC =∠=∠，，∵9090DAC ADC FDM ADC ∠+∠=︒∠+∠=︒，，∴DAC FDM ∠=∠，∴EBM FDM ∠=∠，∵M 是BD 的中点，∴BM DM =，在EBM △和FDM 中，EBM FDM BM DM EMB FMD ∠=∠⎧⎪=⎨⎪∠=∠⎩，∴ASA EBM FDM ≌（），∴BE DF =，∴AD DF =，故答案为：=；（2）根据题意将图形补全，如图2所示：AD 与DF 的数量关系：AD DF =，证明如下：连接BE ，∵90ACB ∠=︒，点D 在BC 的延长线上，∴90ACD BCE ∠=∠=︒，在ACD 和BCE 中，CD CE DCA ECB AC BC =⎧⎪∠=∠⎨⎪=⎩，∴SAS ACD BCE ≌（），∴AD BE ADC BEC =∠=∠，，∵90ACB DF AD ∠=︒⊥，，∴90BEC MBE ADC MDF ∠+∠=∠+∠=︒，∴MBE MDF ∠=∠，∵M 是BD 的中点，∴MB MD =，在BME 和 DMF 中，MBEMDF MB MD EMB FMD ∠=∠⎧⎪=⎨⎪∠=∠⎩，∴ASA BME DMF ≌（），∴BE DF =，∴AD DF =．【变式训练】1．（22-23八年级上·山西大同·阶段练习）如图1，在等腰直角三角形ABC 中，90AB AC BAC =∠=︒，，点P 为BC 边上的一个动点，连接AP ，以AP 为直角边，A 为直角顶点，在AP 右侧作等腰直角三角形PAD ，连接CD ．(1)当点P 在线段BC 上时(不与点B 重合)，求证：BAP CAD ≌V V ．(2)当点P 在线段BC 的延长线上时(如图2)，试猜想线段BP 和CD 的数量关系与位置关系分别是什么？请给予证明．【答案】(1)见解析(2)猜想：BP CD BP CD =⊥，，证明见解析【分析】（1）先证明BAP CAD ∠=∠，再根据三角形全等的判定定理证明BAP CAD ≌V V ，即可；（2）先证明BAP CAD ∠=∠，再根据三角形全等的判定定理证明BAP CAD ≌V V ，由全等三角形的性质，即可得证．【详解】（1）90BAC PAD ∠=∠=︒BAC PAC PAD PAC ∴∠-∠=∠-∠即∶BAP CAD∠=∠在BAP △和CAD 中AB AC BAP CAD PA DA =⎧⎪∠=∠⎨⎪=⎩()BAP CAD SAS ∴ ≌（2）猜想∶,BP CD BP CD=⊥90BAC PAD ∠=∠=︒Q BAC PAC PAD PAC∴∠+∠=∠+∠即∶BAP CAD∠=∠在BAP △和CAD 中ABAC BAP CAD PA DA =⎧⎪∠=∠⎨⎪=⎩()BAP CAD SAS ∴ ≌BP CD ∴=(全等三角形的对应边相等)B ACD ∠=∠(全等三角形的对应角相等)90B ACB ∠+∠=︒90ACD ACB ∴∠+∠=︒即∶BP CD⊥综上所述，,BP CD BP CD =⊥．【点睛】本题主要考场三角形全等的判定定理和性质定理，熟练掌握全等三角形的判定定理和性质定理，是解题的关键．2．（23-24八年级上·河北沧州·期末）问题情境：如图，等腰Rt ABC △，D 是斜边BC 上一点，连接AD ，在AD 右侧作AF AD ⊥，且AF AD =，AE 平分DAF ∠交边BC 于点E ，连接EF 和CF ，请直接写出线段BE CF EF 、、的关系：；猜想验证：若D 是斜边BC 上一动点，且AE 平分DAF ∠交边BC 于点E ，其他条件不变，此时上面的结论是否还成立，请说明理由．拓展延伸：若点D 运动到斜边CB 的延长线上，AE 平分DAF ∠交边BC 于点E ，其他条件不变，请直接写出线段BE CF EF 、、的关系：．【答案】问题情景：BE CF EF =+；猜想验证：成立，见解析；拓展延伸：BE EF CF=-【分析】本题主要考查了等腰三角形的性质、全等三角形的判定与性质等知识点，灵活运用全等三角形的判定与性质是解题的关键．问题情景：根据作图过程可解决问题情境；猜想验证：根据等腰直角三角形和已知条件可证明()SAS CAF BAD ≌可得=CF BD ，进而证明()SAS EAF EAD ≌可得EF ED =，然后根据BE BD ED =+即可证明结论；拓展延伸：先根据题意画出图形，然后参照猜想验证进行解答即可．【详解】解：问题情境：BE CF EF =+．猜想验证：BE CF EF =+，理由如下：∵ABC 是等腰直角三角形∴,90=∠=︒AC AB BAC ∵AF AD⊥∴90DAF =︒∴DAF CAD BAC CAD ∠-∠=∠-∠，即：CAF BAD∠=∠在CAF V 和BAD 中，AC AB CAF BAD AF AD=∠=∠=，，∴()SAS CAF BAD ≌∴=CF BD ，∵AE 平分DAF ∠，∴EAF EAD∠=∠在EAF △和EAD 中，AF AD EAF EAD AE AE =∠=∠=，，，∴()SAS EAF EAD ≌，∴EF ED =，∴BE BD ED CF EF =+=+，∴BE CF EF =+．拓展延伸：BE EF CF =-，理由如下：∵ABC 是等腰直角三角形∴,90=∠=︒AC AB BAC ∵AF AD⊥∴90DAF =︒∴DAF CAD BAC CAD ∠-∠=∠-∠，即：CAF BAD∠=∠在CAF V 和BAD 中，AC AB CAF BAD AF AD=∠=∠=，，∴()SAS CAF BAD ≌∴=CF BD ，∵AE 平分DAF ∠，∴EAF EAD∠=∠在EAF △和EAD 中，AF AD EAF EAD AE AE =∠=∠=，，，∴()SAS EAF EAD ≌，∴EF ED =，∴BE ED BD EF CF =-=-，∴BE EF CF =-．3．（23-24八年级上·湖北武汉·期末）如图，在等腰Rt ABC △中，90A ∠=︒，AB AC =，点E 为线段AB 上一动点（不与点B 重合），CE CF ⊥且CE CF =．(1)连接BF 交AC 于点M ，设BE m AB =．①当1m =时，如图1，则BM MF =______．②当49m =时，如图2，若18AB =，求MC 的长．(2)如图3，作FP CF ⊥交CA 的延长线于点P ，EQ EC ⊥交BC 于点Q ，连接PQ ，求证：PQ PF EQ =-．∵49BE AB =，AB =∴8,BE AE AB ==∵FCN ACE ∠+∠∴FCN CEA∠=∠∵FNC CAE ∠=∠∵CE CF =，FG EQ =，90CFG CEQ ∠=∠=︒，∴CFG CEQ△≌△∴CG CQ =，FCG ECQ∠=∠∵90ECF FCG ECG ∠=∠+∠=︒，∴90ECQ ECG QCG ∠+∠=∠=︒∵,AB AC AB AC=⊥∴45PCQ PCG∠=︒=∠∵PC PC=∴PCG PCQ△≌△∴PQ PG=∵PG PF FG PF EQ=-=-PQ PF QE∴=-4．（23-24八年级上·广东阳江·期末）如图1，已知：90MCN ∠=︒，点A 、B 在MCN ∠的边CM CN 、上，AC BC =，点D 为直线CN 上一动点，连接AD ，过点A 作AE AD ⊥，且AE AD =，作EF CM ⊥，垂足为F ．(1)当点D 在线段BC 上时，证明：EF BC =；(2)如图2，当点D 在线段BC 延长线上时，（1）的结论是否仍然成立？若成立，请证明，若不成立，请说明理由；(3)如图3，在（2）的条件下，作点E 关于直线CM 的对称点E '，连接FE '、DE '，DE '与直线AB 交于点H ，求证：DH HE '=．【答案】(1)见解析(2)成立，见解析(3)见解析【分析】本题主要考查三角形全等的判定及性质，能熟练应用三角形全等证明线段相等是解题的关键．（1）根据“同角的余角相等”证明EAF ADC ∠=∠，再根据“AAS ”证明ACD EFA △≌△即可；（2）类比（1）的方法证明即可；（3）延长BA 交FE 的延长线于点G ，利用“ASA ”证明'BDH GE H △≌△即可得证．【详解】（1）证明： 90MCN ∠=︒，AE AD ⊥，∴90CAD EAF Ð+Ð=°，90CAD ADC ∠+∠=︒，∴EAF ADC ∠=∠，EF CM ⊥，∴90EFA ∠=︒，90EFA ACD ∴∠=∠=︒，在ACD 和EFA △中C EFA ADC EAF AD AE ∠=∠⎧⎪∠=∠⎨⎪=⎩∴ACD EFA△≌△∴EF AC =，AC BC =，∴EF BC =．（2）解：结论成立．90MCN ∠=︒，∴=90ACD ∠︒，AE AD ⊥，∴90CAD EAF Ð+Ð=°，90CAD ADC ∠+∠=︒，∴EAF ADC ∠=∠，EF CM ⊥，∴90EFA ∠=︒，90EFA ACD ∴∠=∠=︒在ACD 和EFA △中C EFA ADC EAF AD AE ∠=∠⎧⎪∠=∠⎨⎪=⎩∴ACD EFA △≌△，∴EF AC =，AC BC =，∴EF BC =．（3）证明：如图：如图，延长BA 交FE 的延长线于点G ，90MCN ∠=︒，AC BC =，∴45CAB ∠=︒，45FAG CAB Ð=Ð=°，EF CM ⊥，∴45FAG G Ð=Ð=°，∴FG FA =，又 E 、E '关于直线CM 对称，∴EF E F ='，EF CM ⊥，∴E 、F 、E '三点共线，由（2）可得，ACD EFA△≌△∴AF CD =，EF AC BC ==，∴GF E F CD BC +=+'，即GE BD '=，EF CM ⊥，90MCN ∠=︒，∴'GE BD ∥，∴HDB E ∠=∠'，HBD G Ð=Ð，在BDH △和GE H ' 中'HDB E GE BD HBD G ∠=∠⎧⎪=⎨⎪∠=∠⎩'∴BDH GE H' ≌∴DH HE ='．【题型三利用三角形全等求证角之间的关系问题】例题：（23-24八年级上·湖南永州·期中）在ABC 中，AB AC =，90BAC ∠=︒，点D 为AC 上一动点．(1)如图1，点E 、点F 均是射线BD 上的点并且满足AE AF =，90EAF ∠=︒．求证：ABE ACF ≌ ；(2)在（1）的条件下，求证：CF BD ⊥；(3)由（1）我们知道45AFB ∠=︒，如图2，当点D 的位置发生变化时，过点C 作CF BD ⊥于F ，连接AF ．那么AFB ∠的度数是否发生变化？请证明你的结论．【答案】(1)见解析(2)见解析(3)45AFB ∠=︒，不变化，理由见解析【分析】本题属于三角形综合题，主要考查了全等三角形的判定与性质，三角形内角和定理的综合应用，解决问题的关键是作辅助线构造全等三角形，根据全等三角形的性质进行推导．（1）根据90BAC BAE EAD ∠=∠+∠=︒，90EAF CAF EAD ∠=∠+∠=︒得出BAE CAF ∠=∠，即可根据SAS 证明ABE ACF ≌ ；（2）易得90ABE BDA ∠+∠=︒，根据ABE ACF ≌ ，得出ABE ACF ∠=∠，则90BDA ACF ∠+∠=︒，进而得出90CDF ACF ∠+∠=︒，则90BFC ∠=︒，即可求证CF BD ⊥；（3）过点A 作AF 的垂线交BM 于点E ，易得90ABD BDA ∠∠+=︒，90ACF CDF ∠∠+=︒，即可得出ABD ACF ∠∠=，通过求证()ASA ABE ACF ≌ 得出AE AF =，则AEF 是等腰直角三角形，即可求出45AFB ∠=︒．【详解】（1）解：∵90BAC BAE EAD ∠=∠+∠=︒，90EAF CAF EAD ∠=∠+∠=︒∴BAE CAF ∠=∠，在ABE 和ACF △中AB AC BAE CAF AE AF =⎧⎪∠=∠⎨⎪=⎩，∴()SAS ABE ACF ≌△△；（2）解：∵90BAC ∠=︒，∴90ABE BDA ∠+∠=︒，由（1）得ABE ACF ≌ ，∴ABE ACF ∠=∠，∴90BDA ACF ∠+∠=︒，又∵BDA CDF ∠=∠，∴90CDF ACF ∠+∠=︒，∴90BFC ∠=︒，∴CF BD ⊥；（3）解：45AFB ∠=︒，不变化，理由如下：过点A 作AF 的垂线交BM 于点E∵CF BD⊥∴90BAC ∠=︒∴90ABD BDA ∠∠+=︒同理90ACF CDF ∠∠+=︒∵CDF ADB∠∠=∴ABD ACF∠∠=同（1）理得BAE CAF∠∠=在ABE 和ACF 中BAE CAF AB AC ABD ACF ∠=∠⎧⎪=⎨⎪∠=∠⎩，∴()ASA ABE ACF ≌ ∴AE AF=∴AEF 是等腰直角三角形∴45AFB ∠=︒．【变式训练】1．（22-23八年级上·江苏徐州·阶段练习）点P 、Q 分别是边长为4cm 的等边ABC 的边AB 、BC 上的动点，点P 从顶点A ，点Q 从顶点B 同时出发，且它们的速度都是1cm /s ．(1)连接AQ 、CP 交于点M ，则在P 、Q 运动的过程中，CMQ ∠变化吗？若变化，则说明理由；若不变，则求出它的度数；(2)如图2，若点P 、Q 在运动到终点后继续在射线AB 、BC 上运动，直线AQ 、CP 交点为M ，则CMQ ∠变化吗？若变化，则说明理由；若不变，请求出它的度数．【答案】(1)不变，60CMQ ∠=︒(2)不变，120CMQ ∠=︒【分析】（1）因为点P 从顶点A 、点Q 从顶点B 同时出发，且它们的速度都为1cm /s ，所以AB CA =，BQ AP =，60B CAP ∠=∠=︒，因而运用边角边定理可知ABQ CAP ≌△△．再用全等三角形的性质定理及三角形的角间关系、三角形的外角定理，可求得CMQ ∠的度数．（2）首先利用边角边定理证得PBC QCA ≌△△，再利用全等三角形的性质定理得到BPC CQM ∠=∠，再运用三角形角间的关系求得CMQ ∠的度数．【详解】（1）解：60CMQ ∠=︒不变．等边三角形ABC 中，AB CA =，60B CAP ∠=∠=︒，又由条件得BQ AP =，∴()SAS ABQ CAP ≌△△，∴BAQ ACP ∠=∠，∴60CMQ ACP CAM BAQ CAM BAC ∠=∠+∠=∠+∠=∠=︒；（2）解：120CMQ ∠=︒不变．在等边三角形ABC 中，60ABC CAP ∠=∠=︒，∴120PBC QCA ∠=∠=︒，又由条件得BP CQ =，BC CA =，∴()SAS PBC QCA ≌△△，∴BPC CQM ∠=∠，又 PCB MCQ ∠=∠，∴120CMQ PBC ∠=∠=︒．【点睛】本题考查了等边三角形的性质、全等三角形的判定与性质，根据题意证明三角形全等是解题的关键．2．（23-24八年级上·贵州遵义·期末）在Rt ABC △中，90ACB AC BC ∠=︒=，，点E 为AC 上一动点，过点A 作AD BE ⊥于D ，连接CD ．(1)【观察发现】如图①，DAC ∠与DBC ∠的数量关系是；(2)【尝试探究】点E 在运动过程中，CDB ∠的大小是否改变，若改变，请说明理由，若不变，求CDB ∠的度数；(3)【深入思考】如图②，若E 为AC 中点，探索BE 与DE 的数量关系．【答案】(1)DAC DBC∠=∠(2)CDB ∠的大小不变，45CDB ∠=︒(3)5BE DE=【分析】此题考查等腰直角三角形的判定与性质、全等三角形的判定与性质等知识．（1）由90ACB ADB ∠=∠=︒，得9090DAC AED DBC BEC ∠+∠=︒∠+∠=︒，，而AED BEC ∠=∠，所以DAC DBC ∠=∠，于是得到问题的答案；（2）作CF CD ⊥交BD 于点F ，则90ACD BCF ACF ∠=∠=︒-∠，而DAC FBC AC BC ∠=∠=，，即可证明DAC FBC ≌ ，得CD CF =，则45CDB CFD ∠=∠=︒，所以CDB ∠的大小不改变，45CDB ∠=︒；（3）作CG CD ⊥交BD 于点G ，作CH BD ⊥于点H ，可证明CHE ADE ≌ ，得HE DE CH AD ==，，由DAC GBC ≌ ，得AD BG =，则CH BG =，由CG CD CH DG =⊥，，得DH GH =，则CH DH GH ==，所以2BG DH GH DE ===，即可推导出5BE DE =．【详解】（1）∵90ACB AD BE∠=︒⊥，∴90ACB ADB ∠=∠=︒，∴9090DAC AED DBC BEC ∠+∠=︒∠+∠=︒，，∵AED BEC ∠=∠，∴DAC DBC ∠=∠，故答案为：DAC DBC ∠=∠．（2）CDB ∠的大小不改变，如图①，作CF CD ⊥交BD 于点F ，则90DCF ∠=︒，∴90ACD BCF ACF ∠=∠=︒-∠，由（1）得DAC FBC ∠=∠，∵AC BC＝∴()ASA DAC FBC ≌，∴CHE ADE ∠=∠，∵E 为AC 中点，∴CE AE =，∵CEH AED ∠=∠，∴()AAS CHE ADE ≌，合)，以AD 为一边在AD 的右侧作ADE V ，使AD AE =，DAE BAC ∠=∠，连接CE ．(1)如图1，当点D 在线段CB 上时，BD 与CE 有何数量关系，请说明理由．(2)在（1）的条件下，当90BAC ∠=︒时，那么DCE ∠=________度．(3)设BAC DCE ∠α∠β==，．①如图2，当点D 在线段CB 上，90BAC ∠≠︒时，请探究α与β之间的数量关系．并证明你的结论；②如图3，当点D 在线段CB 的延长线上，90BAC ∠≠︒时，请将图3补充完整并直接写出此时α与β之间的数量关系．【答案】(1)BD CE =，理由见解析；(2)90；(3)①180αβ+=︒，证明见解析；②图见解析，αβ=．【分析】本题考查了全等三角形的判定，考查了全等三角形对应边相等的性质（1）由题意可得BAD CAE ∠=∠，即可证明BAD CAE ≌，可得BD CE =，ACE B ∠=∠，即可解题；（2）由题意可得BAD CAE ∠=∠，即可证明BAD CAE ≌，可得BD CE =，ACE B ∠=∠，即可解题；（3）①由题意可得BAD CAE ∠=∠，即可证明BAD CAE ≌，可得ACE B ∠=∠，根据180B ACB α∠+∠=︒-即可解题；②由题意可得BAD CAE ∠=∠，即可证明BAD CAE ≌，可得ACE B ∠=∠，根据180ADE AED α∠+∠+=︒，180CDE CED β∠+∠+=︒即可解题；【详解】（1）解：BD CE =，理由：90BAD DAC ∠+∠=︒ ，90DAC CAE ∠+∠=︒，BAD CAE ∴∠=∠，在BAD 和CAE V 中，AB AC BAD CAE AD AE =⎧⎪∠=∠⎨⎪=⎩，()BAD CAE SAS ∴ ≌，BD CE ∴=；（2）解：BAD CAE △≌△，ACE B ∴∠=∠，90B ACB ∠+∠=︒ ，90DCE ACE ACB ∴∠=∠+∠=︒；故答案为：90；（3）解：①BAD DAC α∠+∠= ，DAC CAE α∠+∠=，BAD CAE ∴∠=∠，在BAD 和CAE V 中，AB AC BAD CAE AD AE =⎧⎪∠=∠⎨⎪=⎩，()BAD CAE SAS ∴ ≌，ACE B ∴∠=∠，180B ACB α∠+∠=︒- ，180DCE ACE ACB αβ∴∠=∠+∠=︒-=，180αβ∴+=︒；②作出图形，BAD BAE α∠+∠= ，BAE CAE α∠+∠=，BAD CAE ∴∠=∠，在BAD 和CAE V 中，AB AC BAD CAE AD AE =⎧⎪∠=∠⎨⎪=⎩，()BAD CAE SAS ∴ ≌，AEC ADB ∴∠=∠，180ADE AED α∠+∠+=︒ ，180CDE CED β∠+∠+=︒，CED AEC AED ∠=∠+∠，αβ∴=．。