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Delta 水龙头产品说明书
2 5/16"58mm12"305mm9 3/8"238mm7 7/16"188mmFor 1/2" NPSM Male Thread)Compression FittingsFor Clarity 3/8" NPT x 32" RiserFinger HookItems Not Shown For 5/8" O.D. Copper Tubing BushingLock Nut &Mounting SurfaceSteel Supply Hoses18" Flexible Stainless EasyInstall (Remove Compression Nut Quarter-TurnEterna Cartridges w/Spring Checks &Lever Handles w/ Color Coded Indexes __________________________Date_________Product Specifications:Model No.Item No.T&S BRASS AND BRONZE WORKS, INC.B-0111-CModel Specified_____________________ Quantity______ Customer/Wholesaler______________________________ Contractor_______________________________________Flexible Hose & 0.65 GPM Low Flow Spray Valve12" L-Tube, Flexible Stainless Steel Supply Hoses, 32" Riser, 20" Travelers Rest, SC 296902 Saddleback Cove / P.O. Box 1088Quarter-Turn Eterna Cartridges w/ Spring Checks, Lever Handles, Pre-Rinse Unit: EasyInstall Single Hole Deck Mount Mixing Faucet, Architect/Engineer_________________________________Travelers Rest, SC: 800-476-4103 • Simi Valley, CA: 800-423-0150 • Fax: 864-834-3518 • This Space for Architect/Engineer ApprovalJob Name Product Compliance:ASME A112.18.1 / CSA B125.1NSF 61 - Section 9NSF 372 (Low Lead Content)2019 DOE PRSV - Class IRough-In Requirement:Ø 1 1/2" [38mm] Mounting HoleLow Flow 0.65 GPM Deck FlangeØ 2 1/4" [57mm]Spray Valve B-0107-C B-0020-HFlexible Stainless Steel Hose38 9/16"980mm1 7/8"48mm Maximum ThicknessITEM NO.SALES NO.DESCRIPTION1B-0107-C 0.65 GPM Low Flow Spray Valve 2010476-45#27 Washer3000907-45Spray Valve Hold Down Ring 4002987-40Grip Handle5001014-45Washer, B-0100 Hose Barrel6B-0020-H2A 20" Flexible Stainless Steel Hose, Less Handle7B-0020-H 20" Flexible Stainless Steel Hose 8002882-4012" L-Tube 9004R Finger Hook10000376-403/8" NPT x 32" Riser11EZ-K EasyInstall Kit: Nut, Bushing, O-Ring & Lock Washer 12001065-45O-Ring13014200-45Star Washer, Anti-Rotation14012442-40NS Quarter-Turn Eterna Cartridge w/ Spring Check, LTC15002711-40NS Quarter-Turn Eterna Cartridge w/ Spring Check, Handle, Blue Index & Screw, LTC16018506-19NS Blue Button Index, Press-in 17002290-45Lock Washer 18000965-45Lock Nut19012534-4518" Flexible Supply Hose (2)20012443-40NS Quarter-Turn Eterna Cartridge w/ Spring Check, RTC21001638-45NS Lever Handle (New Style)22002712-40NS Quarter-Turn Eterna Cartridge w/ Spring Check, Handle, Red Index & Screw, RTC 23000925-45Lab Handle Screw24001193-19NSRed Button Index, Press-in1234567282423222120171819910131211141516Model No.Item No.T&S BRASS AND BRONZE WORKS, INC.Travelers Rest, SC: 800-476-4103 • Simi Valley, CA: 800-423-0150 • Fax: 864-834-3518 • B-0111-C2 Saddleback Cove / P.O. Box 1088Travelers Rest, SC 29690Product Compliance:ASME A112.18.1 / CSA B125.1NSF 61 - Section 9NSF 372 (Low Lead Content)2019 DOE PRSV - Class IPre-Rinse Unit: EasyInstall Single Hole Deck Mount Mixing Faucet, Quarter-Turn Eterna Cartridges w/ Spring Checks, Lever Handles, 12" L-Tube, Flexible Stainless Steel Supply Hoses, 32" Riser, 20" Flexible Hose & 0.65 GPM Low Flow Spray ValveProduct Specifications:。
重力传感器产品说明书
HEAVY-DUTY INDUSTRIAL SWITCHESSINgLE oR DUAL SETPoINT,PSW-700 SeriesDual external setpoint calibrationadjustment PSW-700 Series pressure switches are built for the rugged industrial setting. The internal setpoints allow adjustments while keeping the electrical component isolated from the environment. Both the internal and external setpoints have a range scale, allowing fast, easy setup.PSW-722, ±10 inH 2O range, shown much smaller than actual size.U Division 1 RatingU Single or Dual Setpoints, Tamper ResistantU Heavy-Duty Enclosure U Rated NEMA 4X, 7, 9 (IP66)U Terminal Block Wiring U High-TemperatureOperation to 200°C (392°F) Process Temperature (Stainless Steel Model Only)PSW-710, 715-7171/4 NPT1/4 NPT (F)PSW-731-7351/2 NPTPSW-702-704, 708, 709SPECIFICATIONSApprovals: UL listed; Class I, Division 1 and 2, Groups B, C and D; Class II, Groups E, F and G; Class III Repeatability: ±1% range Process Temperature:Stainless Steel: -57 to 204°C (-70 to 400°F)Brass: -40 to 149°C (-40 to 300°F) Buna-N: -23 to 93°C (-10 to 200°F)Ambient Temperature:-50 to 71°C (-58 to 160°F), except for models 703 to 705, which are -18 to 71°C (0 to 160°F). Setpoint typically shifts less than 1% of range for a 28°C (50°F) ambient temperature change.Shock: Setpoint repeats after 15 g, 10 ms durationVibration: Setpoint repeats after 2.5 g at 5 to 500 HzOutput: 1 SPDT or 2 SPDT 15 A 125/250/480 VacEnclosure: Low copper-cast epoxy-coated aluminumElectrical Connection: 3⁄4 NPT conduit; internal screw terminals Dimensions:psi Ranges:230 (max) H x 125 W x 108 mm D (9 x 4.9 x 4.3") H 2O Ranges:W and D = 153 mm (6") Weight: Approx. 1.7 kg (4 lb)PSW-721-72INDUSTRIAL SWITCHES PSW-707, 0 to 500 psirange, shown smallerthan actual size。
冀教版六年级英语上册期中测试题及答案
满分:100分时间:60分钟得分:听力部分一、听录音,选出你所听到的单词。
(10分)( )1.A. Mr. B. Ms. C. Mrs.( )2.A. clock B. card C. class( )3.A. time B. table C. them( )4.A. home B. house C. him( )5.A. dirty B. driver C. do二、听录音,写单词,补全句子。
(10分)1. We have nine today.2. I have a small .3. My bedroom is on the second .4. It s past ten now.5. I go to school on foot.三、听录音,判断下列句子与所听内容是(T)否(F)相符。
(10分)( )1. Here s the kitchen.( )2. What would you like for breakfast?( )3. The tomatoes are in the fridge.( )4. I live too far from my school.( )5. I often help my mother on Sunday.四、听录音,选择与所听内容相符的图片。
(10分)( )1. A. B.( )2. A. B.( )3. A. B.( )4. A. B.( )5. A. B.笔试部分五、给单词选择正确的汉语意思。
(5分)( )1.Mr. A. 先生 B. 太太 C. 女士( )2.put A. 穿 B. 有 C. 放;安置( )3.always A . 总是;永远 B. 有时 C. 从不( )4.him A. 他们 B. 他 C. 她( )5.breakfast A. 早餐 B. 午餐 C. 晚餐六、看图片,写单词,补全句子。
(5分)1. She is so .2. We have anew .3. We have a big .4. Look atthe .5. This is an English .七、按要求写单词。
重庆市巴蜀中学2020届高三高考适应性月考卷(十)文科数学
巴蜀中学2020届高考适应性月考卷（十）文科数学注意事项：1．答题前，考生务必用黑色碳素笔将自己的姓名准考证号、考场号、座位号在答题卡上填写清楚． 2．每小题选出答案后，用2B 铅笔把答题卡上对应题目的答案标号涂黑，如需改动，用橡皮擦干净后，再选涂其他答案标号．在试题卷上作答无效．3．考试结束后，请将本试卷和答题卡一并交回．满分150分，考试用时120分钟．一、选择题（本大题共12小题，每小题5分，共60分．在每小题给出的四个选项中，只有一项是符合题目要求的）．1．已知全集U R =，集合{}2430A x x x =-+，{1,0,1,2,3}B =-，则A B =（ ）A ．{}1,0-B ．{}1,2C ．{}0,1,2D ．{}1,2,3 2．已知等差数列{}n a 的前n 项和为n S ，55a =，则9S =（ ） A ．25 B ．45 C ．60 D ．903．已知双曲线222:1y C x b-=的一条渐近线是y =，则双曲线C 的离心率是（ ）A ．2BC ．3D ．44．渝康码是腾讯和支付宝与重庆市政府合作推出的重庆电子健康码，用户申请使用渝康码，凭此码出入小区，学校，医院，商业，公共交通，办公楼宇，交通卡口等．如图，健康人员的渝康码是黑白相间的．已知某个重庆市民的渝康码是边长为15cm 的正方形，利用随机模拟的方法向该渝康码内投入900个点，其中落入黑色部分的点的个数为480个，则该渝康码的黑色部分的面积约为（ ）2cm ．A ．105B ．115C ．120D ．1355．已知1ln 3a =，lg3b =，122c =，则a ，b ，c 的大小关系为（ ）A ．a b c <<B ．a c b <<C ．b c a <<D ．b a c <<6．抛物线2:2(0)C y px p =>的焦点为F ，抛物线上一点(2,)(0)M b b >到焦点的距离为3，则b 的值为（ ）A B ．2 C ． D ．4 7．已知平面αβ⊥，l αβ=，m α⊂，n β⊂，则m n ⊥是m l ⊥的（ ）A ．充分不必要条件B ．必要不充分条件C ．充要条件D ．既不充分也不必要条件 8．一个算法的程序框图如图所示，则该程序输出的结果是（ ）A ．5B ．1C ．15 D ．179．已知在矩形ABCD 中，24AB BC ==，E 为AB 的中点，沿着DE 将ADE △翻折到PDE △，使平面PDE ⊥平面EBCD ，则PC 的长为（ ）A ．B ．C ．4D ．610．如图，重庆欢乐谷的摩天轮被称为“重庆之眼”，其旋转半径为50米，最高点距离地面120米，开启后按逆时针方向旋转，旋转一周大约18分钟．将摩天轮看成圆面，在该平面内，以过摩天轮的圆心且垂直于地平面的直线为y 轴，该直线与地平面的交点为坐标原点建立平面直角坐标系，某人在最低点的位置坐上摩天轮的座舱，摩天轮开始启动，并记该时刻为0t =，则此人距离地面的高度()f t 与摩天轮运行时间t （单位：分钟）的函数关系式为（ ）A ．()50sin20(0)9f t t t π=+ B ．()50sin 70(0)92f t t t ππ⎛⎫=-+ ⎪⎝⎭C ．()50sin 20(0)92f t t t ππ⎛⎫=-+⎪⎝⎭ D ．()50sin 70(0)9f t t t ππ⎛⎫=-+ ⎪⎝⎭11．以罗尔中值定理、拉格朗日中值定理、柯西中值定理为主体的“中值定理”反映了函数与导数之间的重要联系，是微积分学重要的理论基础，其中拉格朗日中值定理是“中值定理”的核心内容．其定理陈述如下：如果函数()y f x =在闭区间[,]a b 上连续，在开区间(,)a b 内可导，则在区间(,)a b 内至少存在一个点0(,)x a b ∈，使得()0()()()f b f a f x b a '-=-，0x x =称为函数()y f x =在闭区间[,]a b 上的中值点，则函数()sin f x x x =在区间[0,]π上的“中值点”的个数为（ ）1.41≈ 1.73≈， 3.14π≈．A ．1B ．2C ．3D ．412．已知平面向量OA ，OB ，OP ，OQ ，满足：||2OA =，||1OB =，且()0OB OB OA ⋅-=，若OP tOA =，(1)OQ t OB =-，其中01t ，则||PQ 的最小值为（ ）A ．27 B ．37C ．7D ．7二、填空题（本大题共4小题，每小题5分，共20分）． 13．已知复数22z i=-，其中i 为虚数单位，则z 的共轭复数z =________． 14．已知甲、乙两个盒子，其中甲盒中有大小完全相同的红、黄、白三个球，乙盒中有大小完全相同的红、黄两个球，现从两个盒子中各取一个球，则两个小球颜色不同的概率为________．15．已知函数32()(1)3f x x a x ax =+--为一个奇函数，则()f x 在[2,3]-上的最大值为________．16．已知数列{}n a 中11a =-，当2n 时，1123,,n n n a a a n n --⎧=⎨+⎩为奇数为偶数，记26n n b a =+，则1n nbb +=________；数列{}n b 前n 项和n S =________．（第一空2分，第二空3分） 三、解答题（共70分．解答应写出文字说明，证明过程或演算步骤）． 17．（本小题满分12分）ABC △的内角A ，B ，C 的对边分别为a ，b ，c ，A 是锐角，且sin 2cos b A a B c +=．（1）求角A ；（2）若D 为AC 边上一点，2BC BD =， 5AB =，且ABD △的面积为2，求sin C ． 18．（本小题满分12分）如图，在四棱锥P ABCD -中，BP ⊥平面PDC ，四边形ABCD 是一个直角梯形，AD BC ∥，90ABC ∠=︒，12AD AB BC ==．（1）求证：CD ⊥平面PBD ；（2）若AB BP PA ==，且P ABCD V -=P ABD -的侧面积． 19．（本小题满分12分）新型冠状病毒肺炎是一种传染性极强的肺炎临床上，核酸检测是新冠肺炎患者确诊的重要依据、是最关键的一环．为什么要做核酸检测呢？简单来说，核酸类似病毒的“指纹”、身份证，找到核酸，就等于确定了病毒的身份与性质．核酸是生物的最基本组成物质和生物学研究的基础物质．病毒是一种个体微小，结构简单的非细胞生物，病毒中也有核酸，且只含一种核酸（DNA 或RNA ），所以，检测到核酸，也就等于揪住了病毒的尾巴．新型冠状病毒感染者，经过治疗，如果核酸检测第一种为阴性，就说明病毒已经消失或者已不再具备造成感染的能级、数量．某生物制药公司生产了两种不同规格型号的新冠病毒核酸检测试剂盒．检测单个样本得知核酸检测结果所需的时间记为X （单位：分钟）．现两种试剂盒检测的样本各有20个，统计检测所需时间，得到如图的茎叶图．（1）试通过平均数比较两种试剂盒哪一种检测更快捷；（2）在改变了试剂盒的生产工艺后，组织了2000名志愿者参加了核酸检测，记录检测时间，得到如下统计数据：800 1200判断是否有99.5%的把握认为核酸检测时间与试剂盒生产工艺有关？附：22()()()()()n ad bc K a b c d a c b d -=++++，其中n a b c d =+++．20．（本小题满分12分）已知函数()()a xf x x e a R =∈，()()ln ()g x f x f x =-． （1）当0a =时，求曲线()y g x =在点(1,(1))g 处的切线方程； （2）当1a =时，若()01g x =，求证：01325x <<． 21．（本小题满分12分）已知椭圆2222:1(0)x y C a b a b+=>>的焦距为4，短轴长为4．（1）求该椭圆的标准方程；（2）已知点P ，过点P 作相互垂直的两条直线分别交椭圆于另一点A ，B ，求点P 到AB 距离的最大值．请考生在第22、23两题中任选一题作答，并用2B 铅笔在答题卡上把所选题目的题号涂黑．注意所做题目的题号必须与所涂题目的题号一致，在答题卡选答区域指定位置答题．如果多做，则按所做的第一题计分． 22．（本小题满分10分）【选修4-4：坐标系与参数方程】在直角坐标系中，以原点为极点，x 轴的正半轴为极轴建立极坐标系，已知曲线:4cos C ρθ=，直线l 的参数方程为321x t y t =+⎧⎨=-+⎩（t 为参数），直线l 与曲线C 分别交于M ，N 两点．（1）写出曲线C 和直线l 的普通方程； （2）若点(3,1)P -，求||||PM PN ⋅的值． 23．（本小题满分10分）【选修4-5：不等式选讲】 已知函数()|21||21|f x x x =+--．（1）若不等式()|4|f x ax +的解集包含[1,2]，求a 的取值范围； （2）若()f x 的值域为A ，且,a b A ∈，证明：|4||22|ab a b ++．巴蜀中学2020届高考适应性月考卷（十）文科数学参考答案一、选择题（本大题共12小题，每小题5分，共60分）．【解析】 1．[1,3]A =，{1,2,3}AB =，故选D ．2．()199599452a a S a +===，故选B ．3．依题意b =A ．4．设该渝康码的黑色部分的面积为x ，则480120225900x x =⇒=，故选C ． 5．1ln ln 303=-<，0lg31<<，1221>，所以a b c <<，故选A ．6．由焦半径公式232pMF =+=，2p =，24y x =，∴28b =，b =，故选C ． 7．m n ⊥不能推出m l ⊥，由面面垂直的性质定理可知m l m n ⊥⇒⊥，故选B ．8．第一次进入循环体：1i =，是，2i =，1T =，1553P ==；第二次进入循环体：2i =，是，3i =，2T =，515P ==；第三次进入循环体：3i =，是，4i =，3T =，17P =；第四次7进入循环体：4i =，否，输出17P =，故选D ．9．当平面PDE ⊥平面EBCD 时，∵CE DE ⊥，平面PDE平面EBCD DE =，∴CE ⊥平面PDE ，CE DP ⊥，∵DP PE ⊥，PE EC E =，∴DP ⊥平面PEC ，DP PC ⊥，所以PC =A ．10．由已知()sin()(0,0)f t A t B A ωϕω=++>>，205012070A B A A B B ⎧-+==⎧⇒⎨⎨+==⎩⎩，18T =，2189ππω==，当0t =时，sin 1ϕ=-，2πϕ=-，()50sin 70(0)92f t t t ππ⎛⎫=-+⎪⎝⎭，故选B ．11．由()sin 2sin 3f x x x x π⎛⎫==+⎪⎝⎭，知()2cos 3f x x π⎛⎫'=+⎪⎝⎭．由拉格朗日中值定理：令()0()()f b f a f x b a -'=-，即00()(0)2cos cos 303f f x x ππππ-⎛⎫⎛⎫+==⇒+= ⎪ ⎪-⎝⎭⎝⎭，0(0,)x π∈，由11,2π⎛⎫--- ⎪⎝⎭，结合余弦函数图象易知方程在区间(0,)π内有2解，故在2区间[0,]π上的“中值点”有2个，故选B ．12．由()0OB OB OA ⋅-=，得到OA 与OB 的夹角60θ=︒，进而||2OP t =，|1OQ t =-∣，且OP 与OQ的夹角60θ=︒，||4PQ t ==．当27t =时，min ||7m OP OQ =-=，故选D ．二、填空题（本大题共4小题，每小题5分，共20分）．【解析】 13．242255z i i ==+-，4255z i =-． 14．甲盒中的三个球记为R ，Y ，W ，乙盒中的两个球记为r ，y ，则共有(,)R r ，(,)R y ，(,)Y r ，(,)Y y ，(,)W r ，(,)W y ，6种情况，则42()63P A ==． 15．10a -=，3()3f x x x =-，2()333(1)(1)f x x x x '=-=+-，(1)2f -=，(3)18f =，∴max ()18f x =． 16．()2122212222366262666n n n n n n n n a b a a b a a a +++⋅+++⋅+====+++，则1264b a =+=，则数列{}n b 是首项为14b =，公比2q =的等比数列，()24122412n n n S +-==--．三、解答题（共70分．解答应写出文字说明，证明过程或演算步骤）． 17．（本小题满分12分）解：（1）由正弦定理：sin sin 2sin cos sin sin()B A A B C A B +==+， （1分） 所以sin sin 2sin cos sin cos cos sin B A A B A B A B +=+，因为sin 0B >，即有sin 2cos A A =， （3分）2sin cos cos A A A ⇒=，因为A 是锐角，cos 0A >，所以12sin 1sin 2A A =⇒=，所以6A π=． （6分） （2）如图，因为5AB =，6A π=，所以1sin 22ABD S AB AD A =⋅⋅⋅=△，解得AD = （8分）在ABD △中，由余弦定理2cos 6π=，解得BD =BC = （10分）在ABC △中，由正弦定理15sin sin sin 28AB BC C C A ⨯=⇒==． （12分）18．（本小题满分12分）（1）证明：如图，设E 是BC 的中点，连接DE ，设12AD AB BC a ===，则BE EC a ==，因为AD BC ∥，90ABC ∠=︒，易得DE a =，且DE BC ⊥，所以BD DC ==．又2BC a =，由勾股定理得CD BD ⊥， （3分） 因为BP ⊥平面PDC ，CD ⊂平面PDC ，所以BP CD ⊥． （5分） 又因为BD ，BP 相交，所以CD ⊥平面PB D ． （6分）（2）解：设AB BP a ==，由（1）可得BD =，因为BP ⊥平面PDC ，所以BP PD ⊥．∵BP a =，∴PD a ==，在等腰三角形PBD 中，设O 是BD 的中点，∴PO BD ⊥，由（1）知：CD ⊥平面PBD ，所以CD PO ⊥．从而PO ⊥平面ABCD ，且122PO BD a ==， （8分） 由（1）中数据得2(2)322ABCDa a a a S +⋅==梯形， （9分）所以21134332P ABCDABCD a V S PO a -==⨯=⋅=梯形． （10分） 因为PAB △和PAD △为边长为4的等边三角形，PBD △是一个等腰直角三角形，所以88PAB PAD PBD S S S S =++==侧△△△． （12分）19．（本小题满分12分）解：（1）第一种更快， （1分） 第一种的平均时间为11531819212232324230231333543464826.820X ⨯++++⨯++⨯+⨯++++++==， （3分）第二种的平均时间为21821932324252262734352363840414923020X ⨯+⨯+++⨯++++⨯+++++⨯==， （5分）因为12X X <，所以第一种试剂盒检测更快捷． （6分） （2）由题可知400a =，600b =，800c =，200d =，1000a b +=，1200a c +=，1000c d +=，800b d +=，2000n a b c d =+++=，（8分） 所以2K 检验的估计值为222000(400200600800)333.333100010001200800K ⨯⨯-⨯=≈⨯⨯⨯， （10分）由于333.3337.879>， （11分） 所以有99．5%的把握认为核酸检测时间与试剂盒生产工艺有关． （12分）20．（本小题满分12分）（1）解：当0a =时，()xg x e x =-，()1xg x e '=-， ∴(1)1g e '=-，又(1)1g e =-，∴曲线()y g x =在点(1,(1))g 处的切线方程为(1)y e x =-． （4分）（2）证明：当1a =时，令()xt f x xe ==，则()ln g x t t =-， 由0t >，则0x >．令()ln h t t t =-，则11()1t h t t t-'=-=． 当(0,1)t ∈时，()0h t '<，()h t 单调递减； 当(1,)t ∈+∞时，()0h t '>，()h t 单调递增，∴min min ()()(1)1g x h t h ===，当且仅当1t =时取等号， （8分） 所以()01g x =．当且仅当()0001x t f x x e ===时，∵()(1)0(0)xf x x e x '=+>>，∴()f x 在(0,)+∞上递增．又1211122f e ⎛⎫== ⎪⎝⎭，3533155f e ⎛⎫==≈> ⎪⎝⎭， ∴()01325f f x f ⎛⎫⎛⎫<< ⎪ ⎪⎝⎭⎝⎭，又()f x 在(0,)+∞上递增， ∴01325x <<．（12分） 21．（本小题满分12分）解：（1）由题意得，2c =，2b =，所以方程为22184x y +=． （4分） （2）设()11,A x y ，()22,B x y ，若直线AB 的斜率不存在，则设直线:AB x t =，()()(221212122(2)20PA PB x x y yt y ⋅=--+=-+-=又∵22128t y +=，∴2t =或23t =，∴2t =时舍去，此时距离为43． （5分） 若直线AB 的斜率存在，设该直线为y kx m =+，代入椭圆方程得()222214280k x kmx m +++-=，122421kmx x k -+=+，21222821m x x k -=+． （6分）()()(121222PA PB x x kx m kx m ⋅=--+++ ()()2212121((2)4(k x x k m x x m =++-+++()()22222128((2)44(2121k m k m km m k k +--=-++++0==，∴(230k m k m +++=， （9分）∴2m k =-此时AB 过点P ）或者m =， （10分） ∴AB过定点2,33Q ⎛⎫-⎪ ⎪⎝⎭，距离d的最大值为||PQ = （12分） 22．（本小题满分10分）【选修4-4坐标系与参数方程】 解：（1）∵4cos ρθ=，∴24cos ρρθ=，∴224x y x +=，∴22(2)4x y -+=．∵321x ty t =+⎧⎨=-+⎩，∴250x y --=． （5分）（2）∵321x t y t =+⎧⎨=-+⎩，∴31x y ⎧=⎪⎪⎨⎪=-+⎪⎩，代入224x y x +=，得220t +-=，∴12t t +=，122t t =-，故12||||2PM PN t t ⋅==． （10分） 23．（本小题满分10分）【选修4-5：不等式选讲】（1）解：依题意得，当[1,2]x ∈时，不等式|21||21||4|x x ax +--+恒成立，即(21)(21)|4|x x ax +--+，即|4|2ax +恒成立， （3分） 展开得242ax -+，即62ax x--恒成立， ∵[1,2]x ∈，∴max 63x -⎡⎤=-⎢⎥⎣⎦，min22x -⎡⎤=-⎢⎥⎣⎦，∴32a --． （5分）（2）证明：∵()212121(21)2f x x x x x =+--+--=，所以()f x 的值域[2,2]A =-． （7分）又∵()()222222|4||22|81642ab a b a b ab a ab b +-+=++-++()()222222441644a b a b a b =--+=--，∵,[2,2]a b ∈-，∴24a ，24b ，∴()()22440a b --，所以22|4||22|ab a b ++，所以|4||22|ab a b ++． （10分）。
2020年普通高等学校招生全国统一考试理科数学全国3卷
1.【ID:4002701】已知集合，，则中元素的个数为()A.B.C.D.【答案】C【解析】解：集合，，．中元素的个数为．故选：C．2.【ID:4002702】复数的虚部是()A.B.C.D.【答案】D【解析】解：，复数的虚部是．故选：D．3.【ID:4002703】在一组样本数据中，，，，出现的频率分别为，，，，且，则下面四种情形中，对应样本的标准差最大的一组是()A. ，B. ，C. ，D. ，【答案】B【解析】解：选项A：，所以；同理选项B：，；选项C：，；选项D：，；故选：B．4.【ID:4002704】模型是常用数学模型之一，可应用于流行病学领域．有学者根据公布数据建立了某地区新冠肺炎累计确诊病例数(的单位：天)的模型：，其中为最大确诊病例数．当时，标志着已初步遏制疫情，则约为()A.B.C.D.【答案】C【解析】解：由已知可得，解得，两边取对数有，解得，故选：C．5.【ID:4002705】设为坐标原点，直线与抛物线：交于，两点，若，则的焦点坐标为()A.B.C.D.【答案】B【解析】解：将代入抛物线，可得，，可得，即，解得，所以抛物线方程为：，它的焦点坐标．故选：B．6.【ID:4002706】已知向量，满足，，，则()A.B.C.D.【答案】D【解析】解：向量，满足，，，可得，．故选：D．7.【ID:4002707】在中，，，，则()A.B.C.D.【答案】A【解析】解：在中，，，，由余弦定理可得；故；，故选：A．8.【ID:4002708】右图为某几何体的三视图，则该几何体的表面积是()A.B.C.D.【答案】C【解析】解：由三视图可知几何体的直观图如图：几何体是正方体的一个角，，、、两两垂直，故，几何体的表面积为：，故选：C．9.【ID:4002709】已知，则()A.B.C.D.【答案】D【解析】解：由，得，即，得，即，即，则，故选：D．10.【ID:4002710】若直线与曲线和圆都相切，则的方程为()A.B.C.D.【答案】D【解析】解：直线与圆相切，那么直线到圆心的距离等于半径，四个选项中，只有A，D满足题意；对于A选项：与联立可得：，此时：无解；对于D选项：与联立可得：，此时解得；直线与曲线和圆都相切，方程为，故选：D．11.【ID:4002711】设双曲线：的左、右焦点分别为，，离心率为，是上一点，且，若的面积为，则()A.B.C.D.【答案】A【解析】解：由题意，设，，可得，，，，可得，可得，解得．故选：A．12.【ID:4002712】已知，．设，，，则()A.B.C.D.【答案】A【解析】解：，；，，，；，，，，综上，．故选：A．13.【ID:4002713】若，满足约束条件，则的最大值为________．【答案】7【解析】解：先根据约束条件画出可行域，由解得，如图，当直线过点时，目标函数在轴上的截距取得最大值时，此时取得最大值，即当，时，．故答案为：．14.【ID:4002714】的展开式中常数项是________（用数字作答）．【答案】24015.【ID:4002715】已知圆锥的底面半径为，母线长为，则该圆锥内半径最大的球的体积为________．【答案】【解析】解：因为圆锥内半径最大的球应该为该圆锥的内切球，如图，圆锥母线，底面半径，则其高，不妨设该内切球与母线切于点，令，由，则，即，解得，，故答案为：．16.【ID:4002716】关于函数有如下四个命题：①的图象关于轴对称．②的图象关于原点对称．③的图象关于直线对称．④的最小值为．其中所有真命题的序号是________．【答案】②③【解析】解：对于①，由可得函数的定义域为，故定义域关于原点对称，由；所以该函数为奇函数，关于原点对称，所以①错②对；对于③，由，所以该函数关于对称，③对；对于④，令，则，由双勾函数的性质，可知，，所以无最小值，④错；故答案为：②③．17. 设数列满足，．（1）【ID:4002717】计算，，猜想的通项公式并加以证明．【答案】见解析【解析】解：，，，，由此可猜测的通项公式为．证明：当时，左边，右边，等式成立．假设当时等式成立，即，则当时，，等式成立．综上所述，对都成立．（2）【ID:4002718】求数列的前项和．【答案】，【解析】解：由得，，，①，②，得：，综上，数列的前项和，．18. 某学生兴趣小组随机调查了某市天中每天的空气质量等级和当天到某公园锻炼的人次，整理数据得到下表(单位：天)：（1）【ID:4002719】分别估计该市一天的空气质量等级为，，，的概率．【答案】见解析【解析】解：设表示事件“该市一天的空气质量等级”．由表格数据得：；；；．（2）【ID:4002720】求一天中到该公园锻炼的平均人次的估计值(同一组中的数据用该组区间的中点值为代表)．【答案】【解析】由题意得：一天中到该公园锻炼的平均人次的估值一天中到该公园锻炼的平均人次的估值为．（3）【ID:4002721】若某天的空气质量等级为或，则称这天“空气质量好”；若某天的空气质量等级为或．则称这天“空气质量不好”，根据所给数据，完成下面的列联表．并根据列联表，判断是否有的把握认为一天中到该公园锻炼的人次与该市当天的空气质量有关？附：，【答案】见解析【解析】由题意得：(空气质量好，人数)；(空气质量好，人数)；(空气质量不好，人数)；(空气质量不好，人数)；，可以有的把握认为一天中到该公园锻炼的人次与该市当天的空气质量有关．19. 如图，在长方体中，点，分别在棱，上，且，．（1）【ID:4002722】证明：点在平面内．【答案】见解析【解析】解：连接，；取的三等分点，，且，四边形为平行四边形，，又长方体性质易得：，，，，，在同一平面内，在平面内．（2）【ID:4002723】若，，，求二面角的正弦值．【答案】【解析】解：以为坐标原点，方向为轴，方向为轴，方向为轴，在长方体内建立空间直角坐标系，易得：，，，，，，，，设平面的法向量，则，，令，则可以为，设平面的法向量，，，令，则可以为，，二面角的正弦值为．20. 已知椭圆：的离心率为，，分别为的左、右顶点．（1）【ID:4002724】求的方程．【答案】【解析】，，，，即，的方程为．（2）【ID:4002725】若点在上，点在直线上，且，，求的面积．【答案】【解析】设，，，则，，①，又，②，由①，，代入②式：，，，不妨设，代入①：，时，；时，；，或，，①，，，：，即，且，，．②，，，：，即，且，，，综上所述，．方法：由，设，点，根据对称性，只需考虑的情况，此时，，，有①，又，②，又③，联立①②③得或，当时，，，，同理可得当时，，综上，的面积是．21. 设函数，曲线在点处的切线与轴垂直．（1）【ID:4002726】求．【答案】【解析】解：，，．（2）【ID:4002727】若有一个绝对值不大于的零点，证明：所有零点的绝对值都不大于．【答案】见解析【解析】，，令，，，，，，，时，，，，，，，若，，则，则，，，，所有零点都在上．解法：设为的一个零点，根据题意，，且，则，由，令，，当时，，当时，可知在，上单调递减，在上单调递增．又，，，，．设为的零点，则必有，即，，得，即．所有零点的绝对值都不大于．22. 在直角坐标系中，曲线的参数方程为(为参数且)，与坐标轴交于，两点．（1）【ID:4002728】求．【答案】【解析】解：与坐标轴交于，，则令或，即或，则或(舍)或或(舍)，，，，，，，则，坐标为，，．（2）【ID:4002729】以坐标原点为极点，轴正半轴为极轴建立极坐标系，求直线的极坐标方程．【答案】【解析】：，即，由，，则直线极坐标方程为：．23. 设，，，，．（1）【ID:4002730】证明：．【答案】见解析【解析】解：，且，，．（2）【ID:4002731】用表示，，的最大值，证明：．【答案】见解析【解析】不妨设为最大值，，则由，，，，，即．。
Frymaster 电子炸锅使用说明书
Frymaster L.L.C., PO Box 51000, Shreveport, Louisiana 71135-1000 Shipping Address: 8700 Line Avenue, Shreveport, Louisiana 71106FRYMASTER ELECTRIC FRYERS ARE MANUFACTURED FOR USE WITH THE TYPE VOLTAGE SPECIFIED ON THE FRYER RATING PLATE LOCATED ON THE FRYER DOOR. FOR PROPER INSTALLATION PROCEDURES IN THE UNITED STATES, REFER TO THE LATEST EDITION OF THE NATIONAL ELECTRIC CODE ANSI/N.F.P.A. NO. 70; IN CANADA, CANADIAN ELECTRICAL CODE PART 1, CSA-22.1. INFORMATION ON THE CONSTRUCTION AND INSTALLATION OF VENTILATING HOODS MAY BE OBTAINED FROM THE LATEST EDITION OF THE "STANDARD FOR THE INSTALLATION OF EQUIPMENT FOR THE REMOVAL OF SMOKE AND GREASE LADEN VAPORS FROM COMMERCIAL COOKING EQUIPMENT", N.F.P.A. NO. 96. COPIES OF THESE ELECTRICAL STANDARDS ARE AVAILABLE FROM THE NATIONAL FIRE PROTECTION ASSOCIATION, BATTERY MARCH PARK, QUINCY, MASS. 02269THE FRYER(S) MUST BE INSTALLED WITH A 15 CM (six inch) CLEARANCE AT BOTH SIDES AND ADJACENT TO COMBUSTIBLE CONSTRUCTION. A MINIMUM OF 60 CM (24-inches) SHOULD BE PROVIDED AT THE FRONT OF THE FRYER(S)DOOR.THIS MANUAL SHOULD BE KEPT IN A CONVENIENT LOCATION AND REFERRED TO WHEN ANY PROBLEM OCCURS AND FOR FUTURE REFERENCE.FOR YOUR SAFETY, DO NOT STORE OR USE GASOLINE OR OTHER FLAMMABLE VAPORS AND LIQUIDS IN THE VICINITY OF THIS OR ANY OTHER APPLIANCE.TABLE OF CONTENTSPAGE ORDERING/SERVICEINFORMATION (2)1. PARTSINFORMATION (2)2. IMPORTANTINSTRUCTIONS (4)3. INSTALLATION4. INITIAL STARTUP INSTRUCTIONS (5)5. DAILYOPERATIONS (7)6. CLEANING AND MAINTENANCE (9)PROCEDURES (10)7. SERVICEDIAGRAMS (11)8. WIRINGLIST (12)9. PARTS1. PARTS ORDERING/SERVICE INFORMATIONParts orders must be placed directly with your local Frymaster Parts Distributor. A list of International Factory Authorized Service Centers was included with the fryers when shipped from the factory. If you do not have access to this list, please contact the Frymaster Technical Services Department at 1-800-551-8633 or 1-318-865-1711.To help speed your order, the following information is required:Model Number:Serial Number:Type of Gas or Voltage:Part Number:Service information may be obtained by calling your local Factory Authorized Service Center. A list of these agencies was packed with your fryer.Service information may also be obtained by calling the Frymaster Technical Services Department. When calling, please have the following information available:Model Number:Serial Number:Type of Gas or Voltage:Nature of Service Problem:Please have ready any other information that you think may be helpful in solving your service problem.PARTS ORDERING/SERVICE INFORMATION CANADA -- Garland Commercial Ranges, Ltd., 1177 Kamato Road, Mississauga, Ontario L4W1X4.Note: Retain and store this manual in a safe place for future use. Additional copies may be obtained from your authorized service center.2. IMPORTANT INFORMATION2.1. IntroductionThe V-14 and V-17 Series are deep-well, open-pot fryers designed for cooking a variety of fried products. Read the instructions in this manual thoroughly before attempting to install, operate or service this equipment.2.2. Operating, Installation, and Service PersonnelOperating information for FRYMASTER equipment has been prepared for use by qualifiedand/or authorized operating personnel only.All installation and service on FRYMASTER equipment must be performed by qualified,certified, licensed, and/or authorized installation or service personnel.Service may be obtained by contacting your local Factory Authorized Service Center.2.3. DefinitionsQualified and/or Authorized Operating PersonnelQualified or authorized operating personnel are those who have carefully read the information in this manual and have familiarized themselves with the equipment functions or have hadprevious experience with the operation of equipment covered in this manual.Qualified Installation PersonnelQualified installation personnel are: individuals, a firm, corporation, or a company whicheither in person or through a representative are engaged in, and are responsible for theinstallation of electrical wiring from the building electric meter, main control box, or service outlet to the electrical appliance. Qualified installation personnel must be experienced in such work, be familiar with all electrical precautions required, and have complied with allrequirements of applicable national, European Community and local codes.Qualified Service PersonnelQualified service personnel are those familiar with FRYMASTER equipment and have been authorized by THE FRYMASTER CORPORATION. All authorized service personnel are required to be equipped with a complete set of service parts manuals and stock a minimum amount of parts for FRYMASTER equipment.A list of Frymaster Factory Authorized Service Centers was included with the fryer whenshipped from the factory. If you do not have access to this list, please contact the FrymasterCustomer Service Department, using the number listed on the front of this manual. Failure to use qualified service personnel will void the Frymaster warranty.2.4. Shipping Damage Claim ProcedurePlease note that the FRYMASTER equipment was carefully inspected and packed by skilled personnel before leaving the factory. The transportation company assumes full responsibility for safe delivery upon acceptance of the equipment.What to do if equipment arrives damaged:A. File Claim for Damages Immediately--Regardless of extent of damage.B. Visible Loss or Damage--Be sure this is noted on the freight bill or express receipt and issigned by the person making the delivery.C. Concealed Loss or Damage--If damage is unnoticed until equipment is unpacked, notifyfreight company or carrier immediately and file a concealed damage claim. This should bedone within 15 days of date of delivery. Be sure to retain container for inspection.FRYMASTER DOES NOT ASSUME RESPONSIBILITYFOR DAMAGE OR LOSS INCURRED IN TRANSIT3. INSTALLATION INSTRUCTIONSPROPER INSTALLATION IS ESSENTIAL TO EFFICIENT AND TROUBLE-FREE OPERATION. ANY ALTERATION OF THE EQUIPMENT VOIDS THE FRYMASTERWARRANTY.Note: Before installing the newly-arrived equipment, inspect it carefully for visible and concealed damage. See Section 2.4.3.1. Caster/Leg InformationIf it is necessary to install legs or casters, follow the instructions provided in the accessories package shipped with the fryer.3.2. LevelingPlace a carpenter’s spirit level across the top of the fryer and level the unit both front-to-back and side-to-side. If it is not level, the unit may not function efficiently, the oil may not drain properly for filtering and in a line-up it may not match adjacent units.If the floor is uneven or has a decided slope, a smooth platform is recommended for placingthe unit on and not relying on leg/caster thread adjustment.3.3. Electrical ConnectionsPOWER REQUIREMENTSThe electrical power supply for the fryers MUST be the same as indicated on the rating and serial number plate located on the fryer door.MODEL VOLTAGE PHASE WIRESERVICE MIN.SIZEAWG(mm2)AMPS PER LEGL1 L2 L3V14 230/380 3 4 6 (16) 21 21 21 V14 240/415 3 4 6 (16) 20 20 20 V17 230/380 3 4 6 (16) 26 26 26 V17 240/415 3 4 6 (16) 24 24 24Plan and carry out installation in accordance with local codes.Connections: Connections to the terminal block and grounding lug should be made through the hole provided for this purpose in the junction box.Wiring Diagram: It is attached to the inside of the fryer door. Amperage for each unit depends on the type of installation and accessories supplied with the unit.4. INITIAL STARTUP INSTRUCTIONS4.1. CleaningNew units are wiped clean with solvents at the factory to remove any visible signs of dirt, oil, grease, etc. remaining from the manufacturing process, then coated lightly with oil. Wash thoroughly with hot, soapy water to remove any film residue and dust or debris before food preparation, then rinse out and wipe dry. Wash any accessories shipped with the unit as well.Close the drain valve completely and remove the crumb screen. Make sure the screws holding the thermostat and high-limit control sensing bulbs into the vessel are tight.4.2. Heating The VesselThis step checks heater element operation, initial thermostat calibration, and cleans the vessel for initial food production.A. Fill the fryer vessel with hot or cold water to the oil level line scribed in the back of thetank.B. Set the thermostat/temperature controller dial to approximately 105ºC (220ºF), just abovethe boiling point of water.C. Turn the power switch to ON. The heater elements will begin heating.D. When the water starts to boil, turn the dial to below 100ºC (210ºF). The elements willturn off and the water will stop boiling.E. When satisfied that the elements and thermostats operate properly, drain the vessel anddry thoroughly. Refill fry vessel with shortening as directed in Section 4.3.4.3. Fill With Cooking Oil/ShorteningNote: Cooking oil/shortening capacity of Value-H14 and Value-H17 Series fryers is 25 liters. (50 lbs.) at 21ºC (70ºF).A. Close the frypot drain valve.B. Place the power switch to the OFF position.C. Remove the baskets and basket support rack.D. When using liquid shortening, fill the empty frypot to the bottom oil-level line.E. When using solid shortening, either melt it first, or cut into small pieces and pack intocool zone (bottom) of the frying vessel. Be careful to not leave any air spaces or disturbthe thermostat and high limit bulbs. Continue to tightly pack the shortening, then lowerthe elements. Pack additional shortening in between and on top of the elements until levelwith the bottom oil level line.F. Replace the basket support rack on top of the heating element.G. Place the ON/OFF switch in the ON position. Melt shortening by turning the heaters“ON” for about five or ten seconds, “OFF” for a minute, repeating cycle until shorteningis melted. If oil starts to smoke while melting this way, shorten the “ON” cycle andlengthen the “OFF” cycle. Smoke shows that you are scorching the shortening and cuttingits useful life.H. Once the shortening is melted, set the thermostat for normal cooking temperature.4.4. Before Relocating Fryermoving. If a leg becomes damaged during movement, contact your service agent forimmediate repair/replacement.A. Turn fryer ON/OFF switch to OFF. Unplug the power cord from the source.B. Relocate the fryer for service accessibility.C. After servicing is complete, return the fryer to the operating position. Plug all powercords into source. Attach the restraining devices.5. DAILY OPERATION5.1. General UseA. For consistent quality product, convenience and long-term savings, use a high-qualityliquid frying oil.B. Although a temperature of 177ºC (350ºF) is recommended for most cooking operations,set the fryer at the lowest possible temperature which produces a high quality end productwhile ensuring maximum life of frying oil/shortening.C. When the fryer is not in use, the thermostat should be set lower than that used duringcooking.5.2. Turn On ProceduresA. Always be sure vessel is full before turning fryer on. Follow instructions in Section 4.3.B. Turn fryer on, and set thermostat to the desired cooking temperature.5.3. FilteringAlways consult the filter manufacturer's operation instructions for the recommended filtering procedure.The following procedure is recommended to drain and filter your cooking oil/shortening whena filter machine is not available:A. Turn the fryer ON/OFF switch to the OFF position. Screw the drain pipe (provided withfryer) into the drain valve. Make sure the drain extension is firmly screwed into the drain valve and that the curved end is pointing down.B. Position a metal container with sealable cover under the drain extension. The metal containerand cover must be able to withstand the hot cooking oil/shortening and hold hot liquids.Frymaster recommends that a Frymaster filter cone holder and filter cone be used when a filter machine is not available. If you are using the Frymaster filter cone holder and cone, be sure that the cone holder rests securely on the metal container.C. Open the drain valve slowly to avoid splattering. If splattering occurs, exercise extremecaution.D. If the drain valve becomes clogged with food particles, use the Fryer's Friend (poker-liketool). Use this tool from the inside of the frypot ONLY. Grip the tool on the handle as far as possible away from the cooking oil/shortening in the frypot. DO NOT hammer on the drain valve. This damages the drain valve ball.Note: For safe, convenient draining and disposing of used oil/shortening, Frymaster recommends the use of the Frymaster shortening disposal unit (SDU). The SDU is available through your local distributo r.E. After draining the oil/shortening, clean all food particles and residual oil/shortening fromthe frypot before refilling.F. Close the drain valve and refill the frypot with clean, filtered oil/shortening.5.4. ClosingA. When closing for the night, turn the fryer ON/OFF switch to OFF position.B. Filter oil in fryers.C. Put frypot cover in place over frypot.5.5. ShutdownWhen shutting down for periods longer than overnight, drain the frying oil/shortening andclean the vessel thoroughly. Either discard the frying oil/shortening or filter it and return it to the vessel and cover the vessel. Turn the power switch and the thermostat to OFF.If the vessel is not stainless steel, and it is to be left empty, apply a light coat of shortening to the entire interior of the vessel to prevent corrosion and possible rust.6. CLEANING AND MAINTENANCE6.1. General:Any piece of equipment works better and lasts longer when maintained properly and keptclean. Cooking equipment is no exception. The fryer should be kept clean during theworking day and thoroughly cleaned at the end of each day.6.2. Daily:Wash all removable parts. Be sure to dry all parts thoroughly. Clean all exterior surfaces of the fryer. Do not use cleansers, steel wool, or any other abrasive material on the stainlesssteel or enamel surfaces.Filter the cooking oil and replace if necessary. Under heavy use conditions, the oil should be filtered more often than once a day.6.3. WeeklyA. Completely drain the oil from the fryer into either the filter or a steel container. Do notuse a glass or plastic container.B. Clean the vessel in the following manner:1. Close the drain valve and refill with either a good commercial cleaning solution andwater, or water and strong detergent.2. Set the operating thermostat to 104ºC (220ºF). Bring to a rolling boil, then turn theheat down to a simmer and let the mixture stand until the deposits and/or carbon spots canbe readily removed with scrub pad or scrub brush.3. Scrub the vessel walls, bottom and heating elements.4. Drain vessel and rinse with clean water.5. Refill with water, set operating thermostat to above 100ºC (212ºF), and boil again.Once boiling is completed, turn operating thermostat off, drain, rinse, and dry thevessel and elements thoroughly.C. Immediately refill with cooking oil or frying compound as directed in Section 4.3.6.4. PeriodicThe fryer should be checked and adjusted periodically by qualified service personnel as partof a regular kitchen maintenance program.6.5. Stainless Steel CareAll stainless steel fryer cabinet parts should be wiped regularly with hot soapy water duringthe day, and with a liquid cleanser designed for stainless steel at the end of each day.A. Do not use steel wool or abrasive cloths, cleansers or powders.B. Do not use a metal knife, spatula or any other metal tool to scrape stainless steel!Scratches are almost impossible to remove.C. If it is necessary to scrape the stainless steel to remove any encrusted materials, soak thearea first to soften the deposit, then use a wood or nylon scraper only.7. SERVICE PROCEDURES7.1. Thermostat CalibrationA. Insert a good grade thermometer or pyrometer probe approximately 8-10cm (3-4 inches)into the cooking oil/shortening near the fryer temperature sensing probe.B. Turn thermostat knob to the desired frying temperature.C. Turn the fryer ON/OFF switch to the ON position and heat the shortening to thethermostat temperature setting. Stir if necessary to get all cooking oil/shortening in bottomof frypot melted.D. Allow the heating elements to cycle ON and OFF three times after reaching the thermostattemperature setting. When the elements come on the fourth time, the thermometer readingshould be within 2ºC (5ºF) of the thermostat knob setting. If it is not, calibrate as follows:1. Remove the thermostat knob by pulling straight out on the knob with a firm steadypull.2. Insert a small flat blade screwdriver into the center of the thermostat shaft and turn theadjusting screw clockwise to decrease and counter-clockwise to increase. DO NOTallow the thermostat shaft to turn while turning the adjusting screw. Turn the screw in¼ turn increments, checking calibration after each adjustment.3. After each adjustment, reinstall the thermostat knob, and allow the shortening to cooluntil the heating element comes on.4. Compare the thermometer or pyrometer reading and the thermostat knob setting whenthe elements come on.5. Repeat Steps 5.a. through 5.d. until thermometer or pyrometer reading and knobsetting agree within 2ºC (5ºF).6. If calibration cannot be obtained for any reason, call a Factory Authorized ServiceCenter.7. Remove thermometer or pyrometer probeNote: The heating element must cycle ON at the calibration point.8. WIRING DIAGRAM9. PARTS LISTS9.1. Control/Component BoxItem No. Part Number Description1 807-1692 Thermostat, SunneThermostat816-0139 Knob,2 807-0044 Switch, Red On/Off3 810-1202 Contactor, 40 Amp, 3 Pole4 807-1169 Transformer,208-220-240 / 24 volt5 807-1174 Fuse, 250V, 3 Amp, Slow Blow6 807-1268 Terminal Block, Single Pole (Neutral)7 807-0065 Terminal Block, Field Wiring8 807-0070 Terminal Lug, Ground9.2. Miscellaneous PartsItem No. Part Number Description1 810-0356 Caster, 5” without Brake2 806-5043 Leg* 806-3811 Legs (Package of 4)3 810-0357 Caster, 5”, With BrakeAssembly4 806-4926 DoorHanger5 803-0028 BasketCap6 910-4408 Topthermostat* 807-0063 Hi-Limit* 910-1614 Guard, Operating Thermostat* 806-6993 Drain Valve, 1-1/4”* 810-0820 Handle, Drain ValveExtension* 812-1226SP DrainV14/17* 823-1775SP Frypot,* 807-2645 Heating Element, V14 / 220V* 807-2641 Heating Element, V17 / 220V* 807-2644 Heating Element, V14 / 240/415V* 807-2645 Heating Element, V17 / 240/415V* 807-2647 Heating Element, V14 / 380V* 807-2648 Heating Element, V17 / 380VFrymaster, L.L.C., 8700 Line Avenue, PO Box 51000, Shreveport, Louisiana 71135-1000Shipping Address: 8700 Line Avenue, Shreveport, Louisiana 71106 TEL 1-318-865-1711FAX (Parts) 1-318-219-7140(Tech Support) 1-318-219-7135Price: $6.00 PRINTED IN THE UNITED STATESSERVICE HOTLINE 1-800-551-8633819-5250。
高考数学一轮复习第六章数列课时规范练30等比数列
课时规范练30等比数列基础巩固组1.(2020河南开封定位考试)等比数列{a n}的前n项和为S n,若a3+4S2=0,则公比q=()A.-1B.1C.-2D.22.(2020东北师大附中、重庆一中、吉大附中、长春十一中等高三联合考试)等比数列{a n}各项均为正数,若a1=1,a n+2+2a n+1=8a n,则{a n}的前6项和为()A.1365B.63C.6332D.136510243.(多选)设等比数列{a n}的前n项和为S n,且满足a6=8a3,则()A.数列{a n}的公比为2B.数列{a n}的公比为8C.63=8D.63=94.(2020全国2,理6)数列{a n}中,a1=2,a m+n=a m a n.若a k+1+a k+2+…+a k+10=215-25,则k=()A.2B.3C.4D.55.(2020福建龙岩高三教学质量检查)由实数构成的等比数列{a n}的前n项和为S n,a1=2,且a2-4,a3,a4成等差数列,则S6=()A.62B.124C.126D.1546.(多选)设等比数列{a n}的公比为q,则下列结论正确的是()A.数列{a n a n+1}是公比为q2的等比数列B.数列{a n+a n+1}是公比为q的等比数列C.数列{a n-a n+1}是公比为q的等比数列D.数列1是公比为1的等比数列7.(2020浙大附中模拟)已知数列{a n}的前n项和为S n,且+1=pS n+q(n∈N*,p≠-1),则“a1=q”是“{a n}为等比数列”的()A.充分不必要条件B.必要不充分条件C.充要条件D.既不充分也不必要条件8.设等比数列{a n}的前n项和为S n,若63=3,则96=.9.已知{a n}是递减的等比数列,且a2=2,a1+a3=5,则{a n}的通项公式为;a1a2+a2a3+…+a n+1(n∈N*)=.10.(2018全国3,理17)等比数列{a n}中,a1=1,a5=4a3.(1)求{a n}的通项公式;(2)记S n为{a n}的前n项和,若S m=63,求m.公众号：一枚试卷君11.在①数列{a n}的前n项和S n=12n2+52n;②函数f(x)=sinπx-23cos2π2x+3的正零点从小到大构成数列{x n},a n=x n+83;③2-a n--12−-1=0(n≥2,n∈N*),a n>0,且a1=b2这三个条件中任选一个,补充在下面的问题中,若问题中的M存在,求出M的最小值;若M不存在,说明理由.问题:数列{b n}是首项为1的等比数列,b n>0,b2+b3=12,且,设数列1log3r1的前n项和为T n,是否存在M∈N*,使得对任意的n∈N*,T n<M?综合提升组12.(多选)(2020山东威海模考)设等比数列{a n}的公比为q,其前n项和为S n.前n项积为T n,并且满足条件a1>1,a7·a8>1,7-18-1<0.则下列结论正确的是()A.0<q<1B.a7·a9>1C.S n的最大值为S9D.T n的最大值为T713.(2020辽宁大连第二十四中学模拟)《九章算术》中的“两鼠穿墙题”是我国数学的古典名题:“今有垣厚若干尺,两鼠对穿,大鼠日一尺,小鼠也日一尺,大鼠日自倍,小鼠日自半,问何日相逢,各穿几何?”题意是:“有两只老鼠从墙的两边打洞穿墙,大老鼠第一天进一尺,以后每天加倍;小老鼠第一天也进一尺,以后每天减半.”如果墙足够厚,S n为前n天两只老鼠打洞长度之和,则S n=尺.14.设数列{a n}的前n项和为S n,已知a1=1,a2=2,且a n+2=2S n-S n+1+3,记b n=log2a2n-1+log2a2n,则b n=.创新应用组15.(多选)(2020山东青岛高三模拟)在悠久灿烂的中国古代文化中,数学文化是其中的一朵绚丽的奇葩.《张丘建算经》是我国古代有标志性的内容丰富的众多数学名著之一,大约创作于公元五世纪.书中有如下问题:“今有女善织,日益功疾,初日织五尺,今一月织九匹三丈,问日益几何?”.其大意为:“有一女子擅长织布,织布的速度一天比一天快,从第二天起,每天比前一天多织相同数量的布,第一天织5尺,一个月共织了九匹三丈,问从第二天起,每天比前一天多织多少尺布?”.已知1匹=4丈,1丈=10尺,若这一个月有30天,记该女子这一个月中的第n天所织布的尺数为a n,b n=2,对于数列{a n},{b n},下列选项中正确的为()A.b10=8b5B.{b n}是等比数列C.a1b30=105D.3+5+72+4+6=20919316.(2020浙江十校联考)已知数列{a n}满足a1=35,a n+1=32+1,n∈N*.(1)求证:数列1-1为等比数列.(2)是否存在互不相等的正整数m,s,t,使m,s,t成等差数列,且a m-1,a s-1,a t-1成等比数列?如果存在,求出所有符合条件的m,s,t;如果不存在,请说明理由.参考答案课时规范练30等比数列1.C因为a3+4S2=0,所以a1q2+4a1+4a1q=0.因为a1≠0,所以q2+4q+4=0,所以q=-2.故选C.2.B∵等比数列{a n}各项均为正数,且a n+2+2a n+1=8a n,∴a n q2+2a n q=8a n,即q2+2q=8,可得q=2或q=-4(舍去),∴S6=1(1-6)1-=63.故选B.3.AD因为等比数列{a n}的前n项和为S n,且满足a6=8a3,所以63=q3=8,解得q=2,所以63=1-61-3=1+q3=9.故选AD.4.B设该女子第一天织布x尺,则(1-25)1-2=5,得x=531,所以前n天所织布的总尺数为531(2n-1).由531(2n-1)≥30,得2n≥187,则n的最小值为8.故选B.5.C由题意知2a3=a2-4+a4,设{a n}的公比为q,则212=1-4+13,1=2,解得q=2,则S6=2(1-26)1-2=126.故选C.6.AD对于A,由r1-1=q2(n≥2)知,数列{a n a n+1}是公比为q2的等比数列,故A正确;对于B,当q=-1时,数列{a n+a n+1}的项中有0,不是等比数列,故B错误;对于C,当q=1时,数列{a n-a n+1}的项中有0,不是等比数列,故C错误;对于D,1r11=r1=1,所以数列1是公比为1的等比数列,故D正确.故选AD.7.C因为a n+1=pS n +q ,所以当n ≥2时,a n =pS n-1+q ,两式相减得a n+1-a n =pa n ,即当n ≥2时,r1=1+p.当n=1时,a 2=pa 1+q.所以当a 1=q 时,21=1+p ,满足上式,故数列{a n }为等比数列,所以满足充分性;当{a n }为等比数列时,有a 2=pa 1+q=(1+p )a 1,解得a 1=q ,所以满足必要性.故选C .8.73(方法1)由等比数列的性质可知S 3,S 6-S 3,S 9-S 6仍成等比数列,由已知得S 6=3S 3,∴6-33=9-66-3,即S 9-S 6=4S 3,S 9=7S 3,∴96=73.(方法2)因为{a n }为等比数列,由63=3,设S 6=3k ,S 3=k (k ≠0),所以S 3,S 6-S 3,S 9-S 6为等比数列,即k ,2k ,S 9-S 6成等比数列,所以S 9-S 6=4k ,解得S 9=7k ,所以96=73=73.9.a n =4×12n-1323×1-14n由a 2=2,a 1+a 3=5,{a n }是递减的等比数列,得a 1=4,a 3=1,所以q=12,a n =4×12n-1,则a 1a 2+a 2a 3+…+a n +1是首项为8,公比为14的等比数列的前n 项和.故a 1a 2+a 2a 3+…+a n +1=8+2+12+…+8×14n-1=8×[1-(14)]1-14=323×1-14n .10.解(1)设{a n }的公比为q ,由题设得a n =q n-1.由已知得q 4=4q 2,解得q=0(舍去),q=-2或q=2.故a n =(-2)n-1或a n =2n-1.(2)若a n =(-2)n-1,则S n =1-(-2)3.由S m =63得(-2)m =-188,此方程没有正整数解.若a n =2n-1,则S n =2n -1.由S m =63得2m =64,解得m=6.综上,m=6.11.解设数列{b n }的公比为q (q>0),因为数列{b n }是首项为1的等比数列,且b n >0,b 2+b 3=12,所以q 2+q-12=0,解得q=3(q=-4不合题意,舍去),所以b n =3-1.若选①,由S n =12n 2+52n ,可得-1=12(n-1)2+52(n-1)(n ≥2),两式相减可得a n =n+2(n ≥2),又因为a 1=S 1=3也符合上式,所以a n =n+2,所以1log 3r1=1(r2)=121−1r2,则T n =121-13+12−14+13−15+…+1−1r2=34−121r1+1r2.因为1r1+1r2>0,所以T n <34,由题意可得M≥34,又因为M∈N*,所以存在M满足题意,并且M的最小值为1.若选②,f(x)=sinπx-23cos2π2x+3=sinπx-3cosπx=2sinπx-π3,令f(x)=0,可得πx-π3=kπ,k∈Z,解得x=k+13,k∈Z,即x n=n-1+13=n-23,故a n=x n+83=n+2,同上①,则存在M满足题意,并且M的最小值为1.若选③,则由2-a n--12−-1=0,得(a n--1-1)(a n+-1)=0.又因为a n>0,所以a n--1-1=0,即a n-=1,所以数列{a n}是公差为1的等差数列.又因为a1=b2,则a1=3,所以a n=n+2.-1同上①,则存在M满足题意,并且M的最小值为1.12.AD∵a1>1,a7·a8>1,可知q>0,又7-18-1<0,∴a7>1,a8<1,∴0<q<1,故A正确;a7a9=82<1,故B错误;∵a1>1,0<q<1,∴数列{a n}为各项均为正数的递减数列,∴S n无最大值,故C错误;又a7>1,a8<1,∴T7是数列{T n}中的最大项,故D正确.故选AD.13.2n-12-1+1由题意可知,大老鼠每天打洞的距离是以1为首项,2为公比的等比数列,前n天打洞的距离之和为1-21-2=2n-1.小老鼠每天打洞的距离是以1为首项,12为公比的等比数列,前n天打洞的距离之和为1-(12)1-12=2-12-1.所以S n=2n-1+2-12-1=2n-12-1+1.14.2n-1∵a1=1,a2=2,且a n+2=2S n-S n+1+3,∴当n=1时,a3=2-3+3=2.∵a n+2=2S n-S n+1+3,∴当n≥2时,a n+1=2S n-1-S n+3.两式相减可得,a n+2-a n+1=2(S n-S n-1)-(S n+1-S n)(n≥2),即当n≥2时,a n+2-a n+1=2a n-a n+1,即a n+2=2a n.∵a3=2a1,∴数列{a n}的奇数项和偶数项分别成等比数列,公比均为2,∴a2n=2×2n-1=2n,a2n-1=1×2n-1=2n-1,∴b n=log2a2n-1+log2a2n=n-1+n=2n-1.15.BD由题意可知,数列{a n}为等差数列,设数列{a n}的公差为d,a1=5,由题意可得30a1+30×292=390,解得d=1629,∴a n=a1+(n-1)d=16r12929.∵b n=2,∴r1=2r12=2r1-=2d(非零常数),则数列{b n}是等比数列,故B正确;∵5d=5×1629=8029≠3,∴105=(2)5=25d≠23,∴b10≠8b5,故A错误;a30=a1+29d=5+16=21,∴a1b30=5×221>105,故C错误;∵a4=a1+3d=5+3×1629=19329,a5=a1+4d=5+4×1629=20929,∴3+5+72+4+6=3534=54=209193,故D正确.故选BD.16.(1)证明因为a n+1=32+1,所以1r1=13+23,所以1r1-1=131-1.因为a1=35,则11-1=23.所以数列1-1是首项为23,公比为13的等比数列.(2)解不存在.理由如下,由(1)知,1-1=23×13n-1=23,所以a n=33+2.假设存在互不相等的正整数m,s,t满足条件,则有+=2,(-1)2=(-1)(-1).由a n=33+2与(a s-1)2=(a m-1)(a t-1),得33+2-12=33+2-133+2-1.即3m+t+2×3m+2×3t=32s+4×3s.因为m+t=2s,所以3m+3t=2×3s.因为3m+3t≥23r=2×3s,当且仅当m=t时等号成立,这与m,s,t互不相等矛盾.所以不存在互不相等的正整数m,s,t满足条件.。
【高三英语】Z20名校联盟2023-2024学年高三上学期第一次联考英语试题(解析版)
Z20名校联盟（浙江省名校新高考研究联盟）2023-2024学年高三上学期第一次联考英语试题学校:___________姓名：___________班级：___________考号：___________二、阅读理解The ebike has become an essential item, and even the King has been spotted riding one. According to the market research company Mintel, sales have almost tripled over the past five years. While ebikes have become increasingly commonplace, they are still undeniably expensive. You can pick up a perfectly adequate push bike for £300, but most ebikes cost nearly £2,000. Now, Cycling Electric, designed to help consumers choose an ebike, offers the following recommendations.Best folding bikeCarbo Model XPrice: £2, 799 | Weight: 13.3kgRange: up to 34 milesThis is one of the most convenient bikes, from a little-known label. The lightweight Carbo X is the perfect example of convenience thanks to its carbon frame and belt drive, instead of a metal bike chain. This makes it lighter and less likely to get messy than an electric Brompton, with its more traditional, oily chain.Most stylishTemple Cycles ClassicPrice: from £2, 995 | Weight: 19kgRange: up to 74 milesThis Bristol-based brand is known for its elegant pushbikes, which are hand-built in the city.This is its electric version. It’s a very sleek and functional commuter option and not too heavy. Temples have fewer proprietary (品牌专卖的) parts and so are serviceable in any bike shop. Stylish as they may be, the VanMoofs and the Cowboys can be a bit more complex to get back-up and service.The money-no-object optionRiese & Müller Nevo4 GT Vario GXPrice: £5, 380 | Weight: 28.4kgRange: up to 93 milesThis is a prime example of the attention to detail delivering a high-quality experience in functionality, comfort and practicality — if you can afford it. It has the capacity to handle 25kg of luggage in a pannier, powerful road lights and a beautifully smooth motor.21．What is the advantage of the Temples over other stylish ebike brands?A．They are more lightweight. B．They have more functions.C．They have easier access to service. D．They are more comfortable.22．Which ebike will a consumer probably choose, who cares most about an excellent experience?A．Carbo Model X. B．The VanMoofs and the Cowboys.C．Temple Cycles Classic. D．Riese & Müller Nevo4 GT Vario GX. 23．Where is the text probably taken from?A．An online post. B．A magazine column.C．A market research report. D．An official document.【答案】21．C 22．D 23．B【导语】本文是一篇应用文，主要介绍的是Cycling Electric推荐的三款电动自行车。
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2020年我国高端装备制造业增速将超30%
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随着我国制造2025战略的提出，我国装备制造特别是高端装备制造业迎来了发展的春天。
信息技术与先进制造技术高速发展，我国智能制造装备的发展深度和广度日益提升，以新型传感器、智能控制系统、工业机器人、自动化成套生产线为代表的智能制造装备产业体系初步形成，一批具有知识产权的重大智能制造装备实现突破，2010年工业自动化控制系统和仪器仪表、数控机床、工业机器人及其系统等部分智能制造装备产业领域销售收入超过3000亿元。
高端装备制造业增速将超30%
我国高端装备制造业2012年的销售收入约为2.58万亿元。
按照《高端装备制造产业十二五规划》，到2015年，我国高端装备制造业销售收入超过6万亿元，在装备制造业中的占比提高到15%；根据前瞻产业研究院发布的《2014-2020年高端装备制造产业发展前瞻与投资战略规划分析报告》，2011-2015年我国高端装备制造产业的销售收入复合增长率达到32.3%。
到2020年，高端装备制造产业销售收入在装备制造业中的占比提高到25%，工业增加值率较十二五末提高2个百分点，将高端装备制造业培育成。