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Circular Math Review

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1) A particularly scary roller coaster contains a loop-the-loop in which the car and rider are completely upside down. If the radius of the loop is with what minimum speed must the car traverse the loop so that the rider does not fall out while upside down at the top? Assume the rider is not strapped to the car. A) 11.4 m/s B) 12.5 m/s C) 10.1 m/s D) 14.9 m/s

2) A 1000-kg car is moving at 30 m/s around a horizontal unbanked curve whose diameter is 0.20 km. What is the magnitude of the friction force required to keep the car from sliding? A) 9000 N B) 9800 N C) 300 N D) 900 N E) 3000 N

3) The curved section of a horizontal highway is a circular unbanked arc of radius 740 m. If the coefficient of static friction between this roadway and typical tires is 0.40, what would be the maximum safe driving speed for this horizontal curved section of highway? A) 54 m/s B) 52 m/s C) 50 m/s D) 48 m/s E) 46 m/s

6) A jet plane flying 600 m/s experiences an acceleration of 4.0 g when pulling out of a circular dive. What is the radius of curvature of the circular part of the path in which the plane is flying? A) 640 m B) 1200 m C) 7100 m D) 9200 m

8) A Ferris wheel has radius 5.0 m and makes one revolution every 8.0 s with uniform rotation. A person who normally weighs 670 N is sitting on one of the benches attached at the rim of the wheel. What is the apparent weight (the normal force exerted on her by the bench) of the person as she passes through the highest point of her motion?

17) A 20-g bead is attached to a light 120-cm-long string as shown in the figure. This bead moves in a horizontal circle with a constant speed of 1.5 m/s. What is the tension in the string if the angle α is measured to be 25°?

A) 0.089 N B) 0.041 N C) 0.20 N D) 0.22 N E) 0.46 N 18) A 20-g bead is attached to a light 120 cm-long string as shown in the figure. If the angle α is measured to be 18°, what is the speed of the mass?

A) 0.55 m/s B) 2.0 m/s C) 3.8 m/s D) 1.3 m/s E) 1.1 m/s 32) As a 70-kg person stands at the seashore gazing at the tides (which are caused by the Moon), how large is the gravitational force on that person due to the Moon? The mass of the Moon is 7.35 × 1022 kg, the distance to the Moon is 3.82 × 108 m, and G = 6.67 × 10-11 N ∙ m2/kg2. A) 0.24 N B) 0.024 N C) 0.0024 N D) 0.00024 N 1) Answer: A 2) Answer: A 3) Answer: A 6) Answer: D 8) Answer: 460 N 17) Answer: D 18) Answer: E 32) Answer: C 33) A very dense 1500-kg point mass (A) and a dense 1200-kg point mass (B) are held in place 1.00 m apart on a frictionless table. A third point mass is placed between the other two at a point that is 20.0 cm from B along the line connecting A and B. When the third mass is suddenly released, find the magnitude and direction (toward A or toward B) of its initial acceleration. (G = 6.67 × 10-11 N ∙ m2/kg2)

44) Planet Z-34 has a mass equal to one-third that of Earth and a radius equal to one-third that of Earth. With g representing, as usual, the acceleration due to gravity at the surface of Earth, the acceleration due to gravity at the surface of Z-34 is A) g/3. B) 3g. C) 6g. D) g/9. E) 9g.

53) An object weighs 432 N on the surface of the earth. The earth has radius R. If the object is raised to a height of 3R above the earth's surface, what is its weight? A) 108 N B) 48.0 N C) 27.0 N D) 305 N E) 144 N

69) A satellite having orbital speed V orbits a planet of mass M. If the planet had half as much mass, the orbital speed of the satellite at the same distance from the center would be A) V. B) 2V. C) V. D) V/. E) V/2.

4) A satellite is in orbit around a planet. The orbital radius is 34.0 km and the gravitational acceleration at that height is 2.3 m/s2. What is the satellite's orbital speed? A) 280 m/s B) 8.8 m/s C) 28 m/s D) 88 m/s

5) A 23 kg mass is connected to a nail on a frictionless table by a (massless) string of length 1.3 m. If the tension in the string is 51 N while the mass moves in a uniform circle on the table, how long does it take for the mass to make one complete revolution? A) 4.8 s B) 3.8 s C) 4.5 s D) 5.2 s

6) A new roller coaster contains a loop-the-loop in which the car and rider are completely upside down. If the radius of the loop is 13.2 m, with what minimum speed must the car traverse the loop so that the rider does not fall out while upside down at the top? Assume the rider is not strapped to the car. A) 11.4 m/s B) 12.5 m/s C) 10.1 m/s D) 14.9 m/s

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2. Letter writing (1)

2. Letter writing (1)

Quiz1. chose the right words for the blanks.1.Traditional values of older generationsinclude hard work, _____, _____, _____ and so on. (diligent/ diligence, brave/ bravery,honest/ honesty)2. A larger _____ (amount / number) of cementwas used for this building.3.I _____ (doubt/ suspect) whether this willwork.4.This _____ (practice/ principle) increases theincome of colleges, so…Quiz2. correct the following sentences.5.Modern people try to success in everything.6.Traffic accidents arise the number of trafficjams.7.If more people accept higher education, oursociety will be much better.8.If they don’t want to be absorbed by the society,they must work harder than before.9.The biggest benefiter is the government.10.It is due to the more competitive of our societies.Letter Writing: Reading and Thoughtfully CorrespondingLetter Writing Etiquette Etiquette is good manners or appropriate or accepted social practices that reflect and promote civility.When should you write a letter?To thank someone who has been gracious, kind or helpful to you.When you need assistance or answers to help you make intelligent decisions.To respond to a letter or letter request that you have recently received. (do not wait too long)To create legal documents that record information and support claims.Types of letters you may be askedto writeApology Complaint Enquiry Recommendation RequestThank you letterAt least100 words;20 minutesLetter Mechanics –Active VS. Passive VoiceExamplesPASSIVE Sentence : It was discovered that thesalary totals were incorrect.Who discovered “it” [the problem]? The underpaidemployee, The payroll specialist, The AccountingDepartment, An Intern, The IRS? (Be specific.)Revised ACTIVE sentence: The AccountingDepartment discovered that the salary totals wereincorrect.Letter Mechanics –Clear Date10/1/93 ?To Americans:Oct.1, 1993To British and most Europeans:Jan.10,1993October 1, 1993 = 1(st) October(,) 1993= 1 Oct. ’93Abbreviation:Jan. Feb. Mar. Apr. Aug. Sept. Oct. Nov. Dec. May June July (No abbr.)Two categories of lettersBusiness Letters (format writing; more formal writing that may share elements of essay writing)Personal Letters (often informal; may be addressed to a friend or familiar acquaintance about a personal subject; may regard a personal problem or issue)Types of Personal LettersApologiesAppreciation and Thank You:For favors, kindness orgenerosityCongratulationsPersonal ComplaintsInvitationsOffering Condolences(sympathy or get well)Source:Personal Letters . . .whether typed or handwritten, may include personal touchesthat reflect your style or personality.December 4, 2007 Dear Maxwell,I just wanted to take a moment to write to you to express my thanksfor the extra tutoring help you gave me this fall as I struggled in my Math 1112 course. People like you make our world a better placesimply because you take the extra time to help others overcomefears and learn important skills. I think I can safely say, you aregoing to make a great math teacher one day!You stand head and shoulders above others in the field of math andI so appreciate the information, time and patience you provided tome. So, once again, thank you so much for everything, andespecially for encouraging me!Best wishes,Rita PersonSalutation(Greeting)DateComplimentaryClosingSignatureBusiness letter Writing •Acceptance Letter (yes/ legal)•Acknowledgement Letter (Receipt)•Application Letter (request jobconsideration/ interview)•Complaint Letter (a legal document)•Cover Letter (accompanies resumeor order)•Inquiry Letter (posing a question)•Order Letter (request letter)Common Types of Business Letters•Identify your reader•Establish your objective•Determine your scope (howmuch researched info’ to include )•Organize your letter•Draft your letter•Close (End) Your Letter•Review and Revise Your Letter(proof for physical problems andedit for logic issues)To write any type ofbusiness letter, followthese basic steps:General Parts of every Business Letter1.Heading 信头 (sender’s return address & date)2.Inside Address 信内地址 (recipient’s address)3.Salutation 称呼(greeting)4.Body 正文(paragraphs)plimentary Close 结尾客套语6.Signature 签名 (with or without title)7.Enclosure 附件 (optional)Heading:Read and find out the difference:Ms. Jennifer Stone, Ms. Jennifer Stone 20 Fairview Drive, 20 Fairview DriveEastbourne, BN18 2BU, Eastbourne, BN18 2BU England. EnglandMay 27, 2007 May 27, 2007British AmericanExample ：求职信（Applications for Job ）1）Layout ：a.写给某个单位的个人Mr. Allen SmithYun Qing Oil Company 207 Huai Hai Road Shanghai 200000b.写给某单位不知名的负责人： The ManagerUni’Tech Electronics Corporation 216 Dahua RoadJinjiang, Guangdong 519032C.写给某个单位的人事部门：Personnel Department Shumei Textiles Industries 6 Nanchang Street Wuxi, Jiangsu 2140011. Block Style (Simplified) LetterFormat SAMPLESignature Block:Align this with the Complimentary Close. Leave four blank lines to sign your name. Don’t forget to s ign your name exactly as you typed it.Y our title is optional and depends on the relevancy and degree of formality you need or want to establish.Letter headEverything flush to left margin withno indents.Company Logo or LetterheadMarch 15, 2007Mr. John Smith, Director of Operations SomeGroup Group 100 SomeStreet DriveSometown, Alabama 34567Dear Mr. Smith:Thank you for your inquiry about Semi-Block format for letters. What follows is a quick summary of the format and the conventions it uses.Semi-block format or style is frequently called modified semi-blockbecause it is a slightly less formal modification of full block format. This letter style places the date line in alignment with, or slightly to the right of dead center. Another option for placing the date line in semi-block is flush right. Similar to full block, semi-block places the inside address, salutation and any end notations flush with the left margin. However, unlike full block, each body paragraph of semi-block is indented five spaces. The complimentary close and signature block are aligned under the date.This page illustrates the spacing and layout of semi-block format. Both full block and semi-block formats generally contain all of the necessary parts of a letter.Sincerely yours ,Dr. Sheila Carter-T odd2. Semi-block Style Letter Format SAMPLEIndent paragraphs 5 spaces. Everything else is flush at the left margin.1. Salutation / GreetingA Business letter’s text starts with a simple and professional greeting such as,Dear, Mr./Ms./Title, & Last name of Person:ExamplesDear Dr. Smithsonian: Dear Ms. Cleopatra:The difference between personal and business letter greetings is that a colon (:) follows the greeting of a business letter and a comma (,) follows the greeting of a personal letterIn letters to organizations , or to persons whose names you do not know , the following greetings are used: Dear Sir:(or Dear Madam: or Dear Sir or Madam) To whom it may concern:(only for testimonials （证明书/介绍信/推荐信）and things of that kind)Dear colleague:(to a person who is of the same professionas the writer, and usually used when you are sending a circular （通知/广告） to many people)2. BodyA generally acceptable format for the body of most business letters is block style, with no indentions or centering of any parts .Paragraphs should be single spaced within the paragraph,and double spaced between different paragraphs.Business Letter ContentEach paragraph in the business letter should contain different topics .The first paragraph should grab attention and state the reason for the letter.The middle paragraphs , as in most letters,should support your reason and go into details.In the final paragraph, it professional etiquette for the writer to thank the reader for taking his or her time to read the letter.3. ClosingIt marks the biggest difference between business and personal letters.The ending of a business letter usually states ‘Sincerely’, followed by three blank lines for the writer’s signature and then the writer’s typed name .Complimentary closeThe closing of a business letter consists of three parts:Complimentary close Signature Typed nameeg:"Yours truly," "Yours Sincerely," "Sincerely yours,” "Sincerely,""Cordially yours" "Yours Cordially." only the first word is capitalized . The close is followed by a comma The close of a personal letter is of a more free choice. "Affectionately ," "Fondly ," "Yourswith love ," "With best wishes ,” “Love , ” “Yours ,” “As ever ,” etc., can be used apart from "Yours sincerely," "Yours truly," etc.; which one of these you use depends on your exact relationship with the addressee.The closing can be put either on the right-hand side or left-hand side of the page. Some writers even prefer to have it in the middle one or two spaces below the last line of the letter.Complimentary closeSignature 亲笔签名In a business letter the handwritten signature is placed between the complimentary close and the typed name of the writer, and the writer‘s official capacity （官职） is indicated after the typed name. If you send along with your letter such things as a resume, a check, a receipt, etc., write Enclosure (s) or Enc. to remind the addressee that besides the letter, there is another material in the envelope.没有亲笔签名的文件、单据、信函场被认为不是写信人本意的表现，如果求职信是打印的话，务必要在结束语和打印好的姓名之间所空的二、三行处，亲笔署名。

《圆的复习课》教学反思

《圆的复习课》教学反思

《圆的复习课》教学反思数学的复习课一贯难于把控, 枯燥, 很难调动课堂的气氛。

那是因为复习课除了知识点多, 想面面俱到, 深层挖掘, 特别的困难之外, 学生对已经学习的知识, 再次重新, 没有了新鲜感, 很难提起学习的兴趣。

这次的研修活动, 有幸地听了潮安区实验学校黄奕敏老师的《“圆”的复习》一课。

这节课, 黄老师以自然的课堂对话引入课题——“圆”的复习。

在复习反馈的这一环节中, 首先以复习卡和课件同步依次重现圆的主要内容：圆的特征、圆的周长、圆的面积。

再每一部分展开提问, 总体以教师提问——学生用复习卡汇报作答——课件显示的方式开展课堂。

提问的问题有：问题1: 什么是圆？圆的有什么特征？如何画圆？问题2: 什么叫做圆的周长？圆的周长计算公式是什么？如何推导的？根据圆的周长计算公式我们还推导了那些计算公式？计算周长用什么单位？常见的长度单位有哪三个？问题3: 什么叫做圆的面积？圆的面积计算公式是什么？如何推导的？根据圆的面积计算公式我们还推导了那些面积公式？计算面积用什么单位？常见的面积单位有哪三个？问题4: 什么叫做弧？什么叫扇形？什么叫做圆心角？什么叫做环形？从提问中, 可看出圆的知识点多, 涉及面广, 知识点之间的联系密切。

其中, 特别圆的周长和面积公式的推导和圆的知识的延伸——扇形、环形, 这两方面是学习的重中之中, 难中之难。

而通过黄老师精心的备课, 总结出的这些问题非常全面。

并且有顺序地展现, 在依次提问中, 帮学生理清了复习圆的知识的思路, 从而在学生的大脑中形成了一条圆的完整知识链。

在练习这一环节中, 黄老师设置了形式多样、有层次性的练习。

从基础知识的填表到填写最简整数比, 再到联系生活的解决问题, 最后是拓展练习, 以此提高学生的空间思维能力。

这些练习环环相扣, 层层深入, 实现了本节课的教学目标。

综观这节课, 黄老师比较凸显的特色有: 第一, 思路清晰, 复习全面。

第二, 能结合多年的工作经验, 总结出更适合学生的计算方式。

新课标人教版小学数学英语词汇(c 字表)

新课标人教版小学数学英语词汇(c 字表)

新课标人教版小学数学英语词汇（c 字表）怎样掌握好数学公式这个问题被很多学生问起，其实学好数学并不难，只要掌握一定的学习方法，就能提高学习能力，小编特地为大家整理了新课标人教版小学数学英语词汇(c 字表),希望对大家有所帮助。

calculation 计算calculator 计算器;计算器calculus (1) 微积分学; (2) 演算cancel 消法;相消canellation law 消去律canonical 典型; 标准capacity 容量cardioid 心脏?Cartesian coordinates 笛卡儿坐标Cartesian equation 笛卡儿方程Cartesian plane 笛卡儿平面Cartesian product 笛卡儿积category 类型;范畴catenary 悬链?Cauchy sequence 柯西序列Cauchys principal value 柯西主值Cauchy-Schwarz inequality 柯西 - 许瓦尔兹不等式central limit theorem 中心极限定理central line 中线?central tendency 集中趋centre 中心;心centre of a circle 圆心centre of gravity 重心centre of mass 质量中心centrifugal force 离心力centripedal acceleration 向心加速度centripedal force force 向心力centroid 形心;距心certain event 必然事件chain rule 链式法则chance 机会change of axes 坐标轴的变换change of base 基的变换change of coordinates 坐标轴的变换change of subject 主项变换change of variable 换元;变量的换characteristic equation 特征(征)方程characteristic function 特征(征)函数characteristic of logarithm 对数的首数; 对数的定位部characteristic root 特征(征)根chart 图;图表check digit 检验数位checking 验算chord 弦chord of contact 切点弦circle 圆circular 圆形;圆的circular function 圆函数;三角函数circular measure 弧度法circular motion 圆周运动circular permutation 环形排列; 圆形排列; 循环排列circumcentre 外心;外接圆心circumcircle 外接圆circumference 圆周circumradius 外接圆半径circumscribed circle 外接圆cissoid 蔓叶?class 区;组;类class boundary 组界class interval 组区间;组距class limit 组限;区限class mark 组中点;区中点classical theory of probability 古典概率论classification 分类clnometer 测斜仪clockwise direction 顺时针方向clockwise moment 顺时针力矩closed convex region 闭凸区域closed interval 闭区间coaxial 共轴coaxial circles 共轴圆coaxial system 共轴系coded data 编码数据coding method 编码法co-domain 上域coefficient 系数coefficient of friction 摩擦系数coefficient of restitution 碰撞系数; 恢复系数coefficient of variation 变差系数cofactor 余因子; 余因式cofactor matrix 列矩阵coincide 迭合;重合collection of terms 并项collinear 共线?collinear planes 共线面collision 碰撞column (1)列;纵行;(2) 柱column matrix 列矩阵column vector 列向量combination 组合common chord 公弦common denominator 同分母;公分母common difference 公差common divisor 公约数;公约common factor 公因子;公因子common logarithm 常用对数common multiple 公位数;公倍common ratio 公比common tangent 公切? commutative law 交换律comparable 可比较的compass 罗盘compass bearing 罗盘方位角compasses 圆规compasses construction 圆规作图compatible 可相容的complement 余;补余complement law 补余律complementary angle 余角complementary equation 补充方程complementary event 互补事件complementary function 余函数complementary probability 互补概率complete oscillation 全振动completing the square 配方complex conjugate 复共轭complex number 复数complex unmber plane 复数平面complex root 复数根component 分量component of force 分力composite function 复合函数; 合成函数composite number 复合数;合成数composition of mappings 映射构合composition of relations 复合关系compound angle 复角compound angle formula 复角公式compound bar chart 综合棒形图compound discount 复折扣compound interest 复利;复利息compound probability 合成概率compound statement 复合命题; 复合叙述computation 计算computer 计算机;电子计算器concave 凹concave downward 凹向下的concave polygon 凹多边形concave upward 凹向上的concentric circles 同心圆concept 概念conclusion 结论concurrent 共点concyclic 共圆concyclic points 共圆点condition 条件conditional 条件句;条件式conditional identity 条件恒等式conditional inequality 条件不等式conditional probability 条件概率cone 锥;圆锥(体)confidence coefficient 置信系数confidence interval 置信区间confidence level 置信水平confidence limit 置信极限confocal section 共焦圆锥曲?congruence (1)全等;(2)同余congruence class 同余类congruent 全等congruent figures 全等图形congruent triangles 全等三角形conic 二次曲?; 圆锥曲?conic section 二次曲?; 圆锥曲?conical pendulum 圆锥摆conjecture 猜想conjugate 共轭conjugate axis 共轭conjugate diameters 共轭轴conjugate hyperbola 共轭(直)径conjugate imaginary / complex number 共轭双曲? conjugate radical 共轭虚/复数conjugate surd 共轭根式; 共轭不尽根connective 连词connector box 捙接框consecutive integers 连续整数consecutive numbers 连续数;相邻数consequence 结论;推论consequent 条件;后项conservation of energy 能量守恒conservation of momentum 动量守恒conserved 守恒consistency condition 相容条件consistent 一贯的;相容的consistent estimator 相容估计量constant 常数constant acceleration 恒加速度constant force 恒力constant of integration 积分常数constant speed 恒速率constant term 常项constant velocity 怛速度constraint 约束;约束条件construct 作construction of equation 方程的设立continued proportion 连比例continued ratio 连比continuity 连续性continuity correction 连续校正continuous 连续的continuous data 连续数据continuous function 连续函数continuous proportion 连续比例continuous random variable 连续随机变量contradiction 矛盾converge 收敛convergence 收敛性convergent 收敛的convergent iteration 收敛的迭代convergent sequence 收敛序列convergent series 收敛级数converse 逆(定理)converse of a relation 逆关系converse theorem 逆定理conversion 转换convex 凸convex polygon 凸多边形convexity 凸性coordinate 坐标coordinate geometry 解析几何;坐标几何coordinate system 坐标系系定理;系;推论coplanar 共面coplanar forces 共面力coplanar lines 共面?co-prime 互质; 互素corollary 系定理; 系; 推论correct to 准确至;取值至correlation 相关correlation coefficient 相关系数correspondence 对应corresponding angles (1)同位角;(2)对应角corresponding element 对应边corresponding sides 对应边cosecant 余割cosine 余弦cosine formula 余弦公式cost price 成本cotangent 余切countable 可数countable set 可数集countably infinite 可数无限counter clockwise direction 逆时针方向;返时针方向counter example 反例counting 数数;计数couple 力偶Carmers rule 克莱玛法则criterion 准则critical point 临界点critical region 临界域cirtical value 临界值cross-multiplication 交叉相乘cross-section 横切面;横截面;截痕cube 正方体;立方;立方体cube root 立方根cubic 三次方;立方;三次(的)cubic equation 三次方程cubic roots of unity 单位的立方根cuboid 长方体;矩体cumulative 累积的cumulative distribution function 累积分布函数cumulative frequecy 累积频数;累积频率cumulative frequency curve 累积频数曲?cumulative frequcncy distribution 累积频数分布cumulative frequency polygon 累积频数多边形;累积频率直方图curvature of a curve 曲线的曲率curve 曲线?curve sketching 曲线描绘(法)curve tracing 曲线描迹(法)curved line 曲线?curved surface 曲面curved surface area 曲面面积cyclic expression 输换式cyclic permutation 圆形排列cyclic quadrilateral 圆内接四边形cycloid 旋输线; 摆线cylinder 柱;圆柱体cylindrical 圆柱形的以上便是小编为大家整理的新课标人教版小学数学英语词汇(c 字表)，小编再次请大家注意要把数学学好就得找到适合自己的学习方法。

constrain[1]

constrain[1]


I. I NTRODUCTION Many special purpose imaging systems use coherent demodulation of reflected electromagnetic or acoustic waves; well known examples include ultrasound imaging, synthetic aperture radar (SAR) and sonar (SAS), and laser imaging. Due to the coherent nature of these image acquisition processes, the standard additive Gaussian noise model, so prevalent in image processing, is inadequate. Instead, multiplicative noise models, i.e., in which the noise field is multiplied by (not added to) the original image, provide an accurate description of these coherent imaging systems. In these models, the noise field is described by a non-Gaussian probability density function, with Rayleigh and Gamma being common models. In this introductory section, we begin by briefly recalling how coherent imaging acquisition processes lead to multiplicative noise models; for a more detailed coverage of this topic, the reader is referred to [24], [25], [31], [34]. We then review previous approaches for dealing with images