ࡱ> 35012gf  bjbj LO)wA&A&'''D'''Q( )'H){-{-{-{-@6Z6$6FFFFFFFInLPFA'650@666FA&A&{-{-GBBB6fA&{-'{-FB6FBB:E,/'^OF {-EIY'8;E {FG0HERM@M[FM'[F 66B66666FFB666H6666M666666666 %: Exponents and Roots SECTION A Family Letter: Exponents Dear Family, The student will be learning about exponents and the properties associated with them. An exponent is a number that represents how many times the base is to be multiplied by itself. A number produced by raising a base to an exponent is called a power. Using exponents will allow the student to write repeated multiplication in a more efficient way. This is how the student will write and evaluate exponents. Write in exponential form. 2 2 2 " 2 2 " 2 " 2 " 2 = 24 Identify how many times 2 is a factor. Simplify 43. 43 = 4 " 4 " 4 Find the product of three 4 s. ( 64 Sometimes the exponent will be zero. The zero power of any number except 0 equals 1. When simplifying expressions with exponents, remind the student to follow the order of operations. There are important relationships that exist between exponents and the operations of multiplication and division. The student will learn how to multiply and divide powers with the same base by using some of these basic properties of exponents. Multiplying When multiplying powers with the same base, keep the base constant and add the exponents. Multiply. Write the product as one power. 56 52 56(2 Add the exponents. 58 Dividing When dividing powers with the same base, keep the base constant and subtract the exponents. Divide. Write the quotient as one power.  EMBED Equation.DSMT4  12149 Subtract the exponents. 125 Exponents and Roots SECTION A Family Letter: Exponents continued When multiplying or dividing powers with the same base it is important to remember not to multiply or divide the bases. This property only applies when bases are the same. Powers with unlike bases cannot be combined using the two properties shown in the examples. It is possible to raise a power to a power. To simplify a power raised to a power, keep the base and multiply the exponents. Since it is possible to have a sum or difference that is a negative number, the student will learn how to evaluate expressions with negative exponents. A number raised to a negative exponent equals 1 divided by that number raised to the opposite of the exponent. This is how the student will learn to evaluate expressions with negative exponents. Divide. Write the quotient as one power.  EMBED Equation.DSMT4  5-2 The bases are the same so subtract the exponents.  EMBED Equation.DSMT4  Write the reciprocal and change the sign of the exponent.  EMBED Equation.DSMT4  Simplify. Scientific notation is a shorthand way to write very small or very large numbers. Numbers in scientific notation are written as the product of a decimal and ten with an exponent. To change numbers from scientific notation to standard notation, move the decimal point the number of places indicated by the exponent, to the right for a positive exponent and to the left for a negative exponent. Similarly, to convert numbers from standard to scientific notation, move the decimal point and multiply by ten to the power of the number of places the decimal point moves. Multiplying and dividing numbers in scientific notation works the same way as with other exponents. Have the student explain the purpose of exponents and the many ways they are used in mathematics. Verbalizing this information helps understanding this material. Sincerely, Exponents and Roots SECTION A At-Home Practice: Exponents Write using exponents. 1. ((4) ((4) ((4) 2. 3 3 3 3 3 3 3. 9 9 4. t t t Simplify. 5. 43 6. ((3)4 7. 64 8. ((1)9 9. (2 + 43) 10. (27  32) 11. 25 + (8 " 43) 12. (12 - 72) Multiply. Write the product as one power. 13. 64 " 63 14. 53 " 56 15. 82 " 87 16. k8 " k2 Divide. Write the quotient as one power. 17.  EMBED Equation.DSMT4  18.  EMBED Equation.DSMT4  19.  EMBED Equation.DSMT4  20.  EMBED Equation.DSMT4  Simplify the powers of 10. 21. 10-3 22. 10-6 23. 10-8 24. 10-1 Simplify. 25. 3-3 26.  EMBED Equation.DSMT4  27.  EMBED Equation.DSMT4  28. 74 " 7-5 Write each number in standard or scientific notation. 29. 9,630,000 30. 2.7 ( 10-5 31. 0.0015 Answers: 1. (-4)3 2. 36 3. 92 4. t3 5. 64 6. 81 7. 1296 8. -1 9. 66 10. 18 11. 537 12. -37 13. 67 14. 59 15. 89 16. k10 17. 52 18. r 19. 86 20. p4 21. 0.001 22. 0.000001 23. 0.00000001 24. 0.1 25.  EMBED Equation.DSMT4  26.  EMBED Equation.DSMT4  27. 16 28.  EMBED Equation.DSMT4  29. 9.63 ( 106 30. 0.000027 31. 1.5 ( 10-3 Exponents and Roots Family Fun: Match It Up! Directions Using the numbers in the right-hand column, make the number sentences true in the left-hand column. You may use some numbers more than one time and some numbers not at all. See how well you can match up the correct answers to the number sentences. Number Sentencesx equals ______________Possible Answers for x 1. 3x =  EMBED Equation.DSMT4  0 10 2. 7.2 ( 10x ( 0.072-5 3. x12 ( 1 2 4. 8x ( 83 ( 8(2 7 5. x4 ( 10,000 3 6.  EMBED Equation.DSMT4  ( 49-4 1 7. 0.001 ( 10x 5 8. 5x ( 625-3 9. 12 ( 24 " x(1-210. 6x " 6(3 ( 36 611.  EMBED Equation.DSMT4  ( 1 4 -112.  EMBED Equation.DSMT4  ( 10x-10 Answers: 1. -2 2. -2 3. 1 4. -5 5. 10 6. 6 7. -3 8. 4 9. 2 10. 5 11. 3 12. Exponents and Roots SECTION B Family Letter: Roots Dear Family, The student will be learning about squares and square roots. Although every positive number has two square roots, most of the time you only write the non-negative square root, better known as the principal square root. The student will also learn to recognize a perfect square and use this knowledge to evaluate expressions and estimate the square roots of numbers that are not perfect squares. Find the two square roots of 81.  EMBED Equation.DSMT4  = 9 9 is a solution, since 9 " 9 = 81. - EMBED Equation.DSMT4  = -9 -9 is also a solution since -9 " -9 = 81. Remember to follow the order of operations when simplifying expressions with exponents. Simplify the expression, 4 EMBED Equation.DSMT4  + 9. 4 EMBED Equation.DSMT4  + 9 4(8) + 9 Simplify the square root. 32 + 9 Multiply. 41 Add. You can use the square roots of perfect squares to estimate the square roots of other numbers. The square root of 55 is between two integers. Name the integers. Explain your answer.  EMBED Equation.DSMT4  Think: What perfect squares are close to 55? 72 = 49 49 < 55 82 = 64 64 > 55 7 <  EMBED Equation.DSMT4  < 8  EMBED Equation.DSMT4  is between 7 and 8 because 55 is between 49 and 64. Some square roots can be written as decimals that terminate or repeat. Other square roots, when written as a decimal, go on forever without repeating or terminating. These numbers are called irrational numbers. There is one last set of numbers that encompasses all the sets of numbers the student has studied. The set of real numbers includes the set of whole numbers, integers, rational numbers, and irrational numbers. However, there are some Exponents and Roots SECTION B Family Letter: Roots continued numbers that are not real numbers, like the square root of a negative number. The student will learn to identify the set or sets of numbers to which a given number belongs. The student will also study a special kind of triangle called a right triangle. Right triangles have one right, or 90, angle. The side opposite the right angle, called the hypotenuse, is the longest side. The shorter sides, that form the right angle, are called legs. The student will learn an important formula called the Pythagorean Theorem. This theorem relates the length of the legs of a right triangle to the length of the hypotenuse.  The Pythagorean Theorem states that the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. Sometimes, the formula is a little easier to understand. a2 + b2 = c2 ( ( ( legs hypotenuse Find the length of the hypotenuse. a2 + b2 = c2 Pythagorean Theorem  52 + 122 = c2 Substitute values. 25 + 144 = c2 Simplify powers. 169 = c2  EMBED Equation.DSMT4  =  EMBED Equation.DSMT4  Find the square root. 13 = c The Pythagorean Theorem has many useful applications. One application that the student will learn is finding distance on the coordinate plane. The distance between two points (x1, y1) and (x2, y2) is  EMBED Equation.DSMT4 . 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Powers, roots, real numbers, and the Pythagorean Theorem are all ideas at the foundation of the student math education. Understanding them is essential to his or her progress. Sincerely, Exponents and Roots SECTION B At-Home Practice: Roots Find the two square roots of each number. 1. 36 2. 121 3. 64 4. 900 Simplify each expression. 5.  EMBED Equation.DSMT4  - 4 6.  EMBED Equation.DSMT4  - 9 7.  EMBED Equation.DSMT4  + 5 Each square root is between two integers. Name the integers. 8.  EMBED Equation.DSMT4  9. - EMBED Equation.DSMT4  10.  EMBED Equation.DSMT4  Use a calculator to find each value. Round to the nearest tenth. 11.  EMBED Equation.DSMT4  12.  EMBED Equation.DSMT4  13.  EMBED Equation.DSMT4  Find a real number between each pair of numbers. 14. 4 EMBED Equation.DSMT4  and 4 EMBED Equation.DSMT4  15.  EMBED Equation.DSMT4  and 5 16.  EMBED Equation.DSMT4  and 0 Find the length of the hypotenuse in each triangle.  17. 18. Find the distance between each pair of points. Round to the nearest tenth. 19. (2, 3) and (4, 1) 20. (-4, 2) and (3, (1) Answers: 1. 6, -6 2. 11, -11 3. 8, -8 4. 30, -30 5. 1 6. 0 7. 12 8. 3 and 4 9. -9 and -8 10. 8 and 7 11. 8.5 12. 5.9 13. 28.7 14. 4 EMBED Equation.DSMT4  15. 4 16.  EMBED Equation.DSMT4  17. c = 34 18. c = 19.8 19. 2 EMBED Equation.DSMT4  20. 7.6 Exponents and Roots Family Fun: Be a Square Directions Cut out the cards and shuffle them. Randomly place the cards face down. Taking turns with your partner, choose two cards and try and match the square root to the perfect square. When you find a pair, keep the cards. If you do not have a match, return each card face down in its original spot. The player with the most matches wins.  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2003-07-01T17:49:36Z com.apple.print.ticket.stateFlag 1 com.apple.print.PaperInfo.PMUnadjustedPageRect com.apple.print.ticket.creator com.apple.print.pm.PostScript com.apple.print.ticket.itemArray com.apple.print.PaperInfo.PMUnadjustedPageRect 0.0 0.0 734 576 com.apple.print.ticket.client com.apple.printingmanager com.apple.print.ticket.modDate 2007-11-06T10:49:32Z com.apple.print.ticket.stateFlag 0 com.apple.print.PaperInfo.PMUnadjustedPaperRect com.apple.print.ticket.creator com.apple.print.pm.PostScript com.apple.print.ticket.itemArray com.apple.print.PaperInfo.PMUnadjustedPaperRect -18 -18 774 594 com.apple.print.ticket.client com.apple.printingmanager com.apple.print.ticket.modDate 2007-11-06T10:49:32Z com.apple.print.ticket.stateFlag 0 com.apple.print.PaperInfo.ppd.PMPaperName com.apple.print.ticket.creator com.apple.print.pm.PostScript com.apple.print.ticket.itemArray com.apple.print.PaperInfo.ppd.PMPaperName US Letter com.apple.print.ticket.client com.apple.print.pm.PostScript com.apple.print.ticket.modDate 2003-07-01T17:49:36Z com.apple.print.ticket.stateFlag 1 com.apple.print.ticket.APIVersion 00.20 com.apple.print.ticket.privateLock com.apple.print.ticket.type com.apple.print.PaperInfoTicket com.apple.print.ticket.APIVersion 00.20 com.apple.print.ticket.privateLock com.apple.print.ticket.type com.apple.print.PageFormatTicket 8BIMxHH@Rg(HH(dh 8BIM8BIM&?8BIM 8BIM8BIM 8BIM 8BIM' 8BIM5-8BIM8BIM8BIM8BIM08BIM-8BIM@@8BIM8BIMUhM804FIC06TEC009AhnullboundsObjcRct1Top longLeftlongBtomlonghRghtlongslicesVlLsObjcslicesliceIDlonggroupIDlongoriginenum ESliceOrigin autoGeneratedTypeenum ESliceTypeImg boundsObjcRct1Top longLeftlongBtomlonghRghtlongurlTEXTnullTEXTMsgeTEXTaltTagTEXTcellTextIsHTMLboolcellTextTEXT horzAlignenumESliceHorzAligndefault vertAlignenumESliceVertAligndefault bgColorTypeenumESliceBGColorTypeNone topOutsetlong leftOutsetlong bottomOutsetlong rightOutsetlong8BIM( ?8BIM8BIM Q` 5JFIFHH Adobe_CMAdobed            `" ?   3!1AQa"q2B#$Rb34rC%Scs5&DTdE£t6UeuF'Vfv7GWgw5!1AQaq"2B#R3$brCScs4%&5DTdEU6teuFVfv'7GWgw ?*iM,mUT` kZѵck4IJI$S s`QN]63*t]=ZNE>}S=koo_N[s@2qdMٟ3;Xw3#,4e[/? $n8Iݮn W=ߥWBY3:[O|aSuN$$z9۬_Ĕ)(UmWVi{lǰ5:s}kRI$n԰z^BR%?@=zг2/حɢvw_]{SI$$I)I$JT7>պu$toR{wbl}7'*}Ym%N))IrUu FѰ/v ]]T}2-6u^c'=CZpoMCBmJc 7fV6G,0ݙjIJL-pku$Ϫ*`0gݷ1멪0fL7(~|1ͩ>k1]SKȭS`-湧5wIL'\>Y"FeYd?eNOOvk_ZqKGR~#eۻ9[w?o<Ĕg_abtvH=A염ccw~ŷ)}K199un!ju[uu:zu/YdRwzY5ֻ꽇W1nMwPY 7%sq鮶z7:INI$I$$I)Ż/?ҿO[j}dG"D*} UzN7KV+Ke\vrJxߪUpz/Peu,pϵϥ_so{=5J˱:\~Koc2*/{o\774l s?mbtj-e/l7ee\w[mM:o::R X`3?ղ?aVJRI$I$ faa6quZվIO:z(r>݆$@`u'zXS?(V_n2 K~[};}:]-WuOh?QfE`fcSkvE𴽖$K8Yz,\8/ `?W;iv]wu}=e0riɪClkvٷ+?A 4I%)$IOTI%)$IO7֝՛{2>O{WsM?1qOd"6G,0ݙjINIijƮkcl-h^}ߠ[^n2JRI$I$$I)K?t.ÙW*k~>M[nIO:mct+ f}mO6~W-NֺgW^۽3m^Em=B+/}]JW?sgd6?S?i}b7PzO sۻ;7s￧%kkܾ}y86V?/o1syֲƛ[Y.`|~cAI%)$INGT}RԺfMEnE.m΢s\b5\ç[i$oDު:lf+Kvl^+_f;`I%8f;`_f;`I%8f;`_f;`'֖:5tRf>E͍V7sE3վ[陹xS{rȶ{ØӕMu7Gg\çK\çYYrP/۟e>ۙMg[cSEY[+OeL¶]Y9,zWz+'Xt }Xt m$}Xt }Xt m$}Xt /+qNnV%u3+~um]zI)TI%)$IJI$RI$I%4:Ydok6[n3m-wrVa_pvm"׹ H=k6U]>~R÷:ߋ{vS#湮1 }Cs[^^Mo Qu)η6>}Nmu7ImՑ[?m{뽛b`3~WU-dvR_l~lb#iQ!Z=2ڞuv3w='IèkMud[ tz,INI$I$$I)8BIM!UAdobe PhotoshopAdobe Photoshop CS28BIM:http://ns.adobe.com/xap/1.0/ image/jpeg Adobe Photoshop CS2 Macintosh 2007-11-06T16:19:32+05:30 2007-11-06T16:19:32+05:30 2007-11-06T16:19:32+05:30 uuid:B1750B7F8E1411DCB94BF5801948CE52 uuid:B1750B808E1411DCB94BF5801948CE52 uuid:A62893468DDF11DCB601F0EECED4D3F2 uuid:A62893458DDF11DCB601F0EECED4D3F2 1 Dot Gain 20% 1 2000000/10000 2000000/10000 2 256,257,258,259,262,274,277,284,530,531,282,283,296,301,318,319,529,532,306,270,271,272,305,315,33432;BF9100BA2338E86BD627BA0F687A3886 174 104 -1 36864,40960,40961,37121,37122,40962,40963,37510,40964,36867,36868,33434,33437,34850,34852,34855,34856,37377,37378,37379,37380,37381,37382,37383,37384,37385,37386,37396,41483,41484,41486,41487,41488,41492,41493,41495,41728,41729,41730,41985,41986,41987,41988,41989,41990,41991,41992,41993,41994,41995,41996,42016,0,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,20,22,23,24,25,26,27,28,30;62345EB744C8D0E5A39B78E602B2B844 ICC_PROFILEADBEprtrGRAYXYZ acspAPPLnone-ADBEcprt2descgwtpt\bkptpkTRC textCopyright 1999 Adobe Systems Incorporateddesc Dot Gain 20%XYZ -XYZ curv 0@PaDuRY9.9W" a A )   ,Ee$W2xov'D !q"."#$p%4%&'(U)")*+,e-:../01}2\3=4556789:~;m<^=Q>E?;@3A,B&C"D EF G#H'I-J4K柕I -2zss;GAhv_+8_%حlb^|HR(ݥ5,W=muk;;Y岖[H¾ݻP:*+ Yf:}歬jNDy*AoH*K,UFA>c(#~h*"Ri91 1ѝ6lٳf6lGJ,ğNWf͞nb70|P~oE漂jv6ڌE*8\ =䏓drYviZ["VyCΞQl2l+iW1[^q3Z2NlSOɿ,02&)58xW\ԥ5Ӭ.- bheQ˔Qu:|z't1:痴{h'Lfe6"NS_筳f͛6l9A;8kw~wk&]KFFEf 4H|D ;~e꿜__兦HMFO>bYޟv9?2$?0.?6OOOˋ_*ڟ'5|SԴFyB.E9ROL#r͞uߜ$9<Gu,o ]ONVTuz,;s#%Wg~_Ogf͛<m{Y cˑ&"t΁![;jj#NGhD_(i:[XxMg|td!cky].BV>֏b쵿/z择'u}>xmn"n3#RF|?t#˖z-nx4+Ś!{lbXR)XO,,??ϥ~|A]G~u]~HoQ[R}CV!2G(͛6lٳ91IS͏8~dv]oguMR̰z7sqaŷ8S83 _v\_O"9m~EyOVZޣjs̷RiYG)Ҵ;[Y!Y!Wڟ7<~n^\O2ySΞT3FBF] "ѣf*̏^Y͝}>͛6lؕżpMku w61WxVGVAyY\^{:#yyoh]nB-Z@&QV9Z?,J,|9A?$<{s-+"c}mbmMo V)Fbecnf5& 5usf͛6l_a}Mmiz]y3^ӴXi'N#(wv!UTIg8kW^[.WbT5;im.JMʒ#Pb<ί6G叚Wߗ< 6M\zVzq+KGœyU9_?>)'{^I%Yh]]Υ%%# }u5]Uߗٳf͛66-.DghF KH &*:gfo )y| d3qy6K:ذf]Vݚ:'T};ߙRD4Ȅ GK;VPKSӮz6lٳg6lwdMeu(3?/Iy$g?YL,Ŧ\?^͛6lٲ1%yG@<˺ѵKx`cB.)H9Q-q΃ΞD i$X00ʊ#M%{to#y_v4qY^NkľsSmXo#EH͛?6lޛ_NYŨZ/=>C=dXS+A2WBw8_/'2~syʿPto/Iq6:U76#P4'qIsf͛6lٳg=W4^YaOZ8o($Շy9!2DYZ wVV/U|Tխ*Swr/fZ]0u_Mb4Kϼ $t#;l6lGJ,ğNWg?9>NŞ͛6lٳf͛6r?ȿΛ [o>f+GKekvִK\GĬ6G3)eg[A  t3rKY'JFIF ExifMM*bj(1r2i''Adobe Photoshop CS2 Macintosh2007:11:06 16:19:33&(. LHHJFIFHH Adobe_CMAdobed            " ?   3!1AQa"q2B#$Rb34rC%Scs5&DTdE£t6UeuF'Vfv7GWgw5!1AQaq"2B#R3$brCScs4%&5DTdEU6teuFVfv'7GWgw ?*iM,mUT` kZѵck4IJI$RI$I%)ddŅ?7$@85v'~/~GEUcm/:R%1~z>J{zCF0}' +{XִW Ԛטּ=W^_ZIJI$RI$T5{CC \ )I$JRK7?F?e_?f׸q!USVlhӶcI)\~_ϵI/I$U>{%ҹ%5qq-sqY[]f[I/I$.>̌KM]0l]*?W?_oKx\I%;I,_sv$SwO,0&i$TI%)$IN&'+ϙkms];vqʧYo9V b*҉)_Mis}C?{ɫ)\^>s.]JRI$I$$I)JP7TT5ԫ{oS5XE )?ZX?K>eI%)WffX)/ybY؝?4R%?~X89}k.+4wޚvcUiRpr]}cViǤ5.JuW6ܶP X*IO9~d_e i!rVJ~qXsUTznαk7[[~ONN]xb{m?Y{/G>s. ^DI%)$IOTI%)$IN&'+ϙkmbb⿨,OR|NfnmzFߐ~Rų/.ӏKwYcadVՃCޜnvkƤ~W[ʫzX3?w715W] I$$I)bPrӚlvVI%)$IJI$STI%)$IN&'+ϙkW33̼N=-e\W/.ӏN+eU^[wN3OOײVSKg35tI$I$$I)I$JRI$I$Tʩ$ꤗʩ$z釪:(5WݑwdٻGeeدRIOI/RIOI/RIOI/RIOI/RIOI/RIOI/RIO/2Photoshop 3.08BIM8BIM%F &Vڰw8BIM com.apple.print.PageFormat.PMHorizontalRes com.apple.print.ticket.creator com.apple.printingmanager com.apple.print.ticket.itemArray com.apple.print.PageFormat.PMHorizontalRes 72 com.apple.print.ticket.client com.apple.printingmanager com.apple.print.ticket.modDate 2007-11-06T10:49:33Z com.apple.print.ticket.stateFlag 0 com.apple.print.PageFormat.PMOrientation com.apple.print.ticket.creator com.apple.printingmanager com.apple.print.ticket.itemArray com.apple.print.PageFormat.PMOrientation 1 com.apple.print.ticket.client com.apple.printingmanager com.apple.print.ticket.modDate 2007-11-06T10:49:33Z com.apple.print.ticket.stateFlag 0 com.apple.print.PageFormat.PMScaling com.apple.print.ticket.creator com.apple.printingmanager com.apple.print.ticket.itemArray com.apple.print.PageFormat.PMScaling 1 com.apple.print.ticket.client com.apple.printingmanager com.apple.print.ticket.modDate 2007-11-06T10:49:33Z com.apple.print.ticket.stateFlag 0 com.apple.print.PageFormat.PMVerticalRes com.apple.print.ticket.creator com.apple.printingmanager com.apple.print.ticket.itemArray com.apple.print.PageFormat.PMVerticalRes 72 com.apple.print.ticket.client com.apple.printingmanager com.apple.print.ticket.modDate 2007-11-06T10:49:33Z com.apple.print.ticket.stateFlag 0 com.apple.print.PageFormat.PMVerticalScaling com.apple.print.ticket.creator com.apple.printingmanager com.apple.print.ticket.itemArray com.apple.print.PageFormat.PMVerticalScaling 1 com.apple.print.ticket.client com.apple.printingmanager com.apple.print.ticket.modDate 2007-11-06T10:49:33Z com.apple.print.ticket.stateFlag 0 com.apple.print.subTicket.paper_info_ticket com.apple.print.PageFormat.PMAdjustedPageRect com.apple.print.ticket.creator com.apple.printingmanager com.apple.print.ticket.itemArray com.apple.print.PageFormat.PMAdjustedPageRect 0.0 0.0 734 576 com.apple.print.ticket.client com.apple.printingmanager com.apple.print.ticket.modDate 2007-11-06T10:49:33Z com.apple.print.ticket.stateFlag 0 com.apple.print.PageFormat.PMAdjustedPaperRect com.apple.print.ticket.creator com.apple.printingmanager com.apple.print.ticket.itemArray com.apple.print.PageFormat.PMAdjustedPaperRect -18 -18 774 594 com.apple.print.ticket.client com.apple.printingmanager com.apple.print.ticket.modDate 2007-11-06T10:49:33Z com.apple.print.ticket.stateFlag 0 com.apple.print.PaperInfo.PMPaperName com.apple.print.ticket.creator com.apple.print.pm.PostScript com.apple.print.ticket.itemArray com.apple.print.PaperInfo.PMPaperName na-letter com.apple.print.ticket.client com.apple.print.pm.PostScript com.apple.print.ticket.modDate 2003-07-01T17:49:36Z com.apple.print.ticket.stateFlag 1 com.apple.print.PaperInfo.PMUnadjustedPageRect com.apple.print.ticket.creator com.apple.print.pm.PostScript com.apple.print.ticket.itemArray com.apple.print.PaperInfo.PMUnadjustedPageRect 0.0 0.0 734 576 com.apple.print.ticket.client com.apple.printingmanager com.apple.print.ticket.modDate 2007-11-06T10:49:33Z com.apple.print.ticket.stateFlag 0 com.apple.print.PaperInfo.PMUnadjustedPaperRect com.apple.print.ticket.creator com.apple.print.pm.PostScript com.apple.print.ticket.itemArray com.apple.print.PaperInfo.PMUnadjustedPaperRect -18 -18 774 594 com.apple.print.ticket.client com.apple.printingmanager com.apple.print.ticket.modDate 2007-11-06T10:49:33Z com.apple.print.ticket.stateFlag 0 com.apple.print.PaperInfo.ppd.PMPaperName com.apple.print.ticket.creator com.apple.print.pm.PostScript com.apple.print.ticket.itemArray com.apple.print.PaperInfo.ppd.PMPaperName US Letter com.apple.print.ticket.client com.apple.print.pm.PostScript com.apple.print.ticket.modDate 2003-07-01T17:49:36Z com.apple.print.ticket.stateFlag 1 com.apple.print.ticket.APIVersion 00.20 com.apple.print.ticket.privateLock com.apple.print.ticket.type com.apple.print.PaperInfoTicket com.apple.print.ticket.APIVersion 00.20 com.apple.print.ticket.privateLock com.apple.print.ticket.type com.apple.print.PageFormatTicket 8BIMxHH@Rg(HH(dh 8BIM8BIM&?8BIM 8BIM8BIM 8BIM 8BIM' 8BIM5-8BIM8BIM8BIM8BIM08BIM-8BIM@@8BIM8BIMUM804FIC06TEC010AnullboundsObjcRct1Top longLeftlongBtomlongRghtlongslicesVlLsObjcslicesliceIDlonggroupIDlongoriginenum ESliceOrigin autoGeneratedTypeenum ESliceTypeImg boundsObjcRct1Top longLeftlongBtomlongRghtlongurlTEXTnullTEXTMsgeTEXTaltTagTEXTcellTextIsHTMLboolcellTextTEXT horzAlignenumESliceHorzAligndefault vertAlignenumESliceVertAligndefault bgColorTypeenumESliceBGColorTypeNone topOutsetlong leftOutsetlong bottomOutsetlong rightOutsetlong8BIM( ?8BIM8BIM h LJFIFHH Adobe_CMAdobed            " ?   3!1AQa"q2B#$Rb34rC%Scs5&DTdE£t6UeuF'Vfv7GWgw5!1AQaq"2B#R3$brCScs4%&5DTdEU6teuFVfv'7GWgw ?*iM,mUT` kZѵck4IJI$RI$I%)ddŅ?7$@85v'~/~GEUcm/:R%1~z>J{zCF0}' +{XִW Ԛטּ=W^_ZIJI$RI$T5{CC \ )I$JRK7?F?e_?f׸q!USVlhӶcI)\~_ϵI/I$U>{%ҹ%5qq-sqY[]f[I/I$.>̌KM]0l]*?W?_oKx\I%;I,_sv$SwO,0&i$TI%)$IN&'+ϙkms];vqʧYo9V b*҉)_Mis}C?{ɫ)\^>s.]JRI$I$$I)JP7TT5ԫ{oS5XE )?ZX?K>eI%)WffX)/ybY؝?4R%?~X89}k.+4wޚvcUiRpr]}cViǤ5.JuW6ܶP X*IO9~d_e i!rVJ~qXsUTznαk7[[~ONN]xb{m?Y{/G>s. ^DI%)$IOTI%)$IN&'+ϙkmbb⿨,OR|NfnmzFߐ~Rų/.ӏKwYcadVՃCޜnvkƤ~W[ʫzX3?w715W] I$$I)bPrӚlvVI%)$IJI$STI%)$IN&'+ϙkW33̼N=-e\W/.ӏN+eU^[wN3OOײVSKg35tI$I$$I)I$JRI$I$Tʩ$ꤗʩ$z釪:(5WݑwdٻGeeدRIOI/RIOI/RIOI/RIOI/RIOI/RIOI/RIO8BIM!UAdobe PhotoshopAdobe Photoshop CS28BIM:http://ns.adobe.com/xap/1.0/ image/jpeg Adobe Photoshop CS2 Macintosh 2007-11-06T16:19:33+05:30 2007-11-06T16:19:33+05:30 2007-11-06T16:19:33+05:30 uuid:B1750B848E1411DCB94BF5801948CE52 uuid:B31D09D28E1411DCB94BF5801948CE52 uuid:A62893428DDF11DCB601F0EECED4D3F2 uuid:A62893418DDF11DCB601F0EECED4D3F2 1 Dot Gain 20% 1 2000000/10000 2000000/10000 2 256,257,258,259,262,274,277,284,530,531,282,283,296,301,318,319,529,532,306,270,271,272,305,315,33432;346469BD163FDFA8BAA5FF05F7383BD3 136 133 -1 36864,40960,40961,37121,37122,40962,40963,37510,40964,36867,36868,33434,33437,34850,34852,34855,34856,37377,37378,37379,37380,37381,37382,37383,37384,37385,37386,37396,41483,41484,41486,41487,41488,41492,41493,41495,41728,41729,41730,41985,41986,41987,41988,41989,41990,41991,41992,41993,41994,41995,41996,42016,0,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,20,22,23,24,25,26,27,28,30;258183ED51355AF3007F1ED464A7D557 ICC_PROFILEADBEprtrGRAYXYZ acspAPPLnone-ADBEcprt2descgwtpt\bkptpkTRC textCopyright 1999 Adobe Systems Incorporateddesc Dot Gain 20%XYZ -XYZ curv 0@PaDuRY9.9W" a A )   ,Ee$W2xov'D !q"."#$p%4%&'(U)")*+,e-:../01}2\3=4556789:~;m<^=Q>E?;@3A,B&C"D EF G#H'I-J4K;&'ڈlGF9iyamwU}g5-k)=DOG"-Bj|Kֿ,?2|s9AgO9/kqڨ DuS>:~W^S~\hWߙ^oїWMf=ozjWqgm)o'fw=͛?6l-o~hďN7&K}oKM7T6N[KLr+lǮGx?ܗ[ I?:?h#ՍWG֋'1UƢq\Wqw.u C8?f]˟r]o3..dx?ܗ[ <sKo%7\Aqw.u Ŭ6[IЬ3>kQh\z.g$P36lM__hsM͛6lٳg%䧕W>a[ST.SLg4]wUk{ qoy -5 BVG9.-HأlE{C6lٳfA(7 ?rڦxX@>)$Q6̿&&ykmST{,yb}+T7M'{_묆F>?Vg6lw䗓?˻0[Hn`ʲ FD3iQ$gW~Y,Yߖ<7@Ktu6R \Bʕ4͛6l忛ߛPld-SZ.m;N_imVb8("? ָ>DƛM*}ͥӌ/uMcl6lM__hٳf͛9o?%/<,ǧoz|fTֵKNӭy`U;CC1y/?8Fx$@AqKڟ5O]R:F>/Zf͟HPYUQRNlouK;}CLQ^vֲ,ȿ̒!*l=7R7N-\-I} d^u*q^ǟѳٳf͛9o?%/<,ǧoz|fTֵKNӭy`U;CC1y/?8Fx$@AqKڟ5O]R:F>/Zf͛?9u9tRȺ7彿/.R{b(n$K+[4*h83 _v\/_2y+MW,qߜɤ]2iފ? {(8%O'e\>Ю/Zf͛6K7_129??7sßw_7? ;ҼèZYXzZt2C3*RW=F*9G]䞵c6~ny_&u)-m]ka$RUgj`βcFWf͛9o?%/<,ǧoz|fTֵKNӭy`U;CC1y/?8Fx$@AqKڟ5O]R:F>/Lz7wSZeZDM#N|ӿ$?0 Νoq37/[?!~Gu>Ada(XיV`A*Rg-Zy>juGѯnn \PEr9Ci~NZy;C4%XjޟeY4W:>q_//FX~`^յ ^/O;zQ1WHX!1 yU5'9M__hٳo~oyC[͒;Oo 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8BIMxHH@Rg(HH(dh 8BIM8BIM&?8BIM 8BIM8BIM 8BIM 8BIM' 8BIM5-8BIM8BIM8BIM8BIM08BIM-8BIM@@8BIM8BIMUlM804FIC06TEC003AlnullboundsObjcRct1Top longLeftlongBtomlonglRghtlongslicesVlLsObjcslicesliceIDlonggroupIDlongoriginenum ESliceOrigin autoGeneratedTypeenum ESliceTypeImg boundsObjcRct1Top longLeftlongBtomlonglRghtlongurlTEXTnullTEXTMsgeTEXTaltTagTEXTcellTextIsHTMLboolcellTextTEXT horzAlignenumESliceHorzAligndefault vertAlignenumESliceVertAligndefault bgColorTypeenumESliceBGColorTypeNone topOutsetlong leftOutsetlong bottomOutsetlong rightOutsetlong8BIM( ?8BIM8BIM H JFIFHH Adobe_CMAdobed            H" ?   3!1AQa"q2B#$Rb34rC%Scs5&DTdE£t6UeuF'Vfv7GWgw5!1AQaq"2B#R3$brCScs4%&5DTdEU6teuFVfv'7GWgw ?*iM,mUT` kZѵckHDhE6eUn_EIN/IgIOюN:>ɛ붦+0}eŸU3}NE+)nn38oLڪrS?ZḀדCV=?y5eͦckrzdm ̆3ת4$ ~ׅOSOp>GΨ\_"c>㉖ cq=):Q$IJITA/e'{pɍ_nذ]Hb έGZn1A;=~WO1]GiXSӤI)I$JRI$I$z\/Ϭ XX6[s}ݝU]-źYc>Z,=A}7kq]v;P3ge/y[vl~%6>s]OBowS*]F1A%;E+Dp??JRI$K"*h{`sQIN7گ2zdW7Yi }/}f'XtJ\zGγelGZ:Vmu/knxl{)n@s+O^kGpաEXGhZ8.(ӪևYk_ګ32z\qMOq~=,eJvRXiχ'P BαYD.p1Xk|)nH?uդU$IJI$RI$U[rl.VU^&YPtpމz{_7A)Go_K1v*&,5Ŀ*n?l-O{bI?oINI$I$$I)I$JRF6>U.ʩ`cC?s\Jq􌬎DTcPamFĭSkq-wOc;bW^ŬKje!X8~kQHI<:{~nNMZw$e%i?ԈG}~eܝ?HYzU6 |;_A/O) a2Jqo rcj2ͻ9{w*#]WPXX71G6Pt}C99>M֓W6)枉rseN[v keYT3ֱߤĔT د _O;+_21k, ic:vVS3>_A/O) a$OlWKg}S|/bI%8;S}?d!gnݫY$Tʩ$ꤗʩ$ꤗʩ$ꤗʩ$ꤗʩ$ag[U}zvOM?V&Pd6zڱlԧm"$I^Uxחsr2"˘I?)nq|J~I|J~I|J~I|J8BIM!UAdobe PhotoshopAdobe Photoshop CS28BIM:http://ns.adobe.com/xap/1.0/ image/jpeg Adobe Photoshop CS2 Macintosh 2007-11-06T16:19:31+05:30 2007-11-06T16:19:31+05:30 2007-11-06T16:19:31+05:30 uuid:B1750B7A8E1411DCB94BF5801948CE52 uuid:B1750B7B8E1411DCB94BF5801948CE52 uuid:A62893488DDF11DCB601F0EECED4D3F2 uuid:A62893478DDF11DCB601F0EECED4D3F2 1 Dot Gain 20% 1 2000000/10000 2000000/10000 2 256,257,258,259,262,274,277,284,530,531,282,283,296,301,318,319,529,532,306,270,271,272,305,315,33432;40963ACFFD94DC45969DF447991D3ADB 239 108 -1 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