求课前一分钟,背一段优美语句,关于记忆或青春,看清了再回答

后面每分钟的长度都比前一分钟的长度减少相同的米数
500-420=80就是后两分钟比前两分钟少跑得,是后面每分钟比前一分钟的长度减少米数的4倍
后面每分钟比前一分钟少跑80÷4=20米
第一分钟跑500÷2+20÷2=260,第二分钟跑240米

语文课堂如何加强学生的思想品德教育 加强思想品德教育是各科教学的任务.语文是一门思想性很强的学科,从中加强思想品德教育更是责无旁贷.语文学科课时多,教学时间长,学生几乎天天接触思想性强的课文,耳濡目染,...

解题思路：这个题目是一道等比数列的题目，分段讨论比较简单，讨论每一分钟内两车拉开的距离，进而解决问题．详细过程见解答．

这道题分段讨论比较简单
第一分钟内，甲乙拉开差距（6.6-2.9）×60=222米
第二分钟内，甲的速度是13.2米/秒，乙的速度是8.7米/秒，甲乙拉开差距（13.2-8.7）×60=270（米）
第三分钟内，甲的速度是26.4米/秒，乙的速度是26.1米/秒，甲乙拉开差距（26.4-26.1）×60=18（米）
从第四分钟开始，乙速度超过甲，乙开始追及甲，此前甲乙差距为222+270+18=510（米）
第四分钟内，甲的速度是52.8米/秒，乙的速度是78.3米/秒，甲乙速度差为78.3-52.8=25.5（米/秒），510÷25.5=20（秒），乙用20秒追上了甲，
因此，出发后共用3分20秒乙追上甲．
答：出发后3分20秒乙追上甲．

点评：
本题考点： 追及问题．

考点点评： 此题也可以用列举的办法解答：
甲 第一分钟 行6.6×60=396米
第二分钟 行396×2=792 米
第三分钟 行792×2=1584米
第四分钟的速度1584×2÷60=52.8米/秒
乙 第一分钟 行2.9×60=174米
第二分钟 行174×3=522 米
第三分钟 行522×3=1566米
第四分钟的速度1566×3÷60=78.3米/秒
甲前三分钟共行396+792+1584=396×（1+2+4）=2772米
乙前三分钟共行174+522+1566=174×（1+3+9）=2262米
乙落后与甲2772-2262=510米，这是二车进入第四分钟，乙的速度比甲快了．
速度差为78.3-52.8=25.5米/秒．
所以510÷25.5=20秒
所以出发后3分20秒乙追上甲．

解题思路：这个题目是一道等比数列的题目，分段讨论比较简单，讨论每一分钟内两车拉开的距离，进而解决问题．详细过程见解答．

这道题分段讨论比较简单
第一分钟内，甲乙拉开差距（6.6-2.9）×60=222米
第二分钟内，甲的速度是13.2米/秒，乙的速度是8.7米/秒，甲乙拉开差距（13.2-8.7）×60=270（米）
第三分钟内，甲的速度是26.4米/秒，乙的速度是26.1米/秒，甲乙拉开差距（26.4-26.1）×60=18（米）
从第四分钟开始，乙速度超过甲，乙开始追及甲，此前甲乙差距为222+270+18=510（米）
第四分钟内，甲的速度是52.8米/秒，乙的速度是78.3米/秒，甲乙速度差为78.3-52.8=25.5（米/秒），510÷25.5=20（秒），乙用20秒追上了甲，
因此，出发后共用3分20秒乙追上甲．
答：出发后3分20秒乙追上甲．

点评：
本题考点： 追及问题．

考点点评： 此题也可以用列举的办法解答：
甲 第一分钟 行6.6×60=396米
第二分钟 行396×2=792 米
第三分钟 行792×2=1584米
第四分钟的速度1584×2÷60=52.8米/秒
乙 第一分钟 行2.9×60=174米
第二分钟 行174×3=522 米
第三分钟 行522×3=1566米
第四分钟的速度1566×3÷60=78.3米/秒
甲前三分钟共行396+792+1584=396×（1+2+4）=2772米
乙前三分钟共行174+522+1566=174×（1+3+9）=2262米
乙落后与甲2772-2262=510米，这是二车进入第四分钟，乙的速度比甲快了．
速度差为78.3-52.8=25.5米/秒．
所以510÷25.5=20秒
所以出发后3分20秒乙追上甲．

　　I am Peter.Usually a lot of my hobbies,such as skating,playing 356 Didesmococcus feather,draw,watch extra-curricular book,watch TV and so on,so my life is very rich extra-curricular.Ago is a more introverted person,I have very few words,only and I am very good friends to so many before,but after school at the time of my personality to change slowly,and not,as previously Like very few words,and students are also very harmonious relationship.
In fact,since childhood I dare not interested in English,so my English very poor,then let us hear English,introduce myself,I really do not know how to do,nervous for some time,so I think in the future of English class can have more understanding of English can have more interest in English.Families are.Usually a lot of my hobbies,such as skating,playing 356 Didesmococcus feather,draw,watch extra-curricular book,watch TV and so on,so my life is very rich extra-curricular.Ago is a more introverted person,I have very few words,only and I am very good friends to so many before,but after school at the time of my personality to change slowly,and not,as previously Like very few words,and students are also very harmonious relationship.
I think noting is difficult if you put your heart into it,so I can say will make my English be nice in future.
Thank you!

相信自己 相信明天
朋友,当你胜利时,你充满着喜悦与激情.
朋友,当你失败时,你面带着沮丧与苦恼.
无论成与败,都已是昨天.那么昨天我们可以叫做历史,那么历史也就见证明天,见证未来.
对于成功的你,是否听过这样一句熟语“好汉不提当年勇”.诚然,昨天是你最高兴的日子,可是你是否考虑过明天,考虑过未来,昨天永远都是昨天,它不代表今日的成就与辉煌.所以对于成功的你,应该不松懈,不狂妄,不骄傲,继续保持你努力的干劲儿.相信自己,明天的胜利还是会属于你.
对于失败的你,昨天是一次教训,昨天也许是你人生中重要的一课.人常常在失败中成长,“失败是成功之母”.的确,人不经历风雨,又怎能见彩虹呢?失败是一次积累丰富经验的机会,有的人感谢失败,因为他们的成功建立于失败之上.欧立希的药品“606”经历了数百次的失败终得了成功；居里夫人励精图治,终于在一次次的失败中发现了元素镭.古今中外,无数的成功例子都是最好的证明,所以对于失败的你,应该更努力,更勤奋,不气馁,只要以你的恒心,“有志者事竟成”.相信自己,明天的成功之路一定属于你.
当你在广场上奔跑时,当你在校园里漫步时,仰望蓝天,春风柔和地吹拂着柳枝,阳光洒进教室的每一个角落,太阳笑得依旧那么灿烂.相信自己,因为你身上有自己独特的闪光点.相信自己,因为你的努力,你的恒心,明天的辉煌与成就都在静静地等待着你.
这比较适合你们课前演讲````````````

苦和甜来自外界,坚强则来自内心,来自一个人的自我努力.人生的位置有时是外界赋予的,有时是与生俱来的,重要的不是脚下的位置,而是所朝的方向,这样人生之路不回迷失.爱迪生一开始也只是无名小卒,在最简陋的实验室,默默无闻地做了1000次实验,终于在1001次的时候用坚持和信念发明了电灯点亮了世界!因此,重要的不是所站位置,而是心中的信念,并朝着这个信念的方向坚定地走下去,过得充实,过得从容!

用等比数列求和公式Sn=a1(1-q^n)/(1-q) s甲=6（1-2^x）/(1-2)
s乙 =3（1-3^x）/(1-3)
s甲=s乙 看了下楼下的知道代错了 修改了一下 不过x不是整数,不好解.
另外你也可以把数字列出来加一加就知道了 6 12 24 48 3 9 27 81 可以算到在3-4秒之间,4秒那会乙已经超过了 应该是3秒多一点的时候 可以这样以3秒那会再开始 此时甲跑了6+12+24=42米 速度在第四秒是48米/s 乙跑了3+9+27=39米 速度在第四秒是81米/s 这会列式81*x-48*x=42-39 得11x=1 x=1/11 答案就是3又1/11

没有真的掌握,我孩子开始也这样.后来我到处找,找到《好学拼音》,没想到孩子很喜欢学,很快就全学会了.建议一试.

自我介绍

大家好,我叫...,来自钦州,我很高兴能在这里与大家认识,我是纺织工业学校的一名学生,我的专业是针织,我很荣幸能参加集训营,我参加集训营是因为我喜欢英语,我希望在集训营里学到的用在我以后的工作中,并开始我的职业生涯.因为我坚信将在很多领域都需要英语.
我的英语很差这就是我为什么在这里和大家一起学习,我知道我拿下英语将是一个巨大的挑战,但我坚信,“宝剑锋从磨出,梅花香自苦寒来”,坚持就是胜利,希望就在今后的学习中请大家多多指教,谢谢!
Self-introduction
Hello everyone! My is., from Qinzhou. I’m so glad to meet you, and I’m currently a student at Guangxi Textile Industrial School. my major is knitting. It’s my pleasure to join the CHAMPION training camp, because I love English and I hope I can learn something in the training for my future work. As we all know English is very useful in every field.
My English is limited that’s why I’m here. I know it’s a huge challenge for me to conquer English, but I believe that “No pains, no gains, success belongs to the persevering”, I hope I can learn more from you, Thank you!

1.(1)设n分钟后第1次相遇,依题意得2n+n(n-1)/2+5n=70 整理得：n 2 +13n－140=0,解得：n=7,n=－20(舍去) ∴第1次相遇在开始运动后7分钟． (2)设n分钟后第2次相遇,依题意有：2n+n(n-1)/2+5n=3×70 整理得：n 2 +13n－6×70=0,解得：n=15或n=－28(舍去) 2.1/a(n+1)=(5+an)/5an=1/an+1/5 ∴{1/an}是以1/a1=1为首项,1/5为公比的等比数列 1/an=1+(n-1)/5=(4+n)/5 ∴an=5/(4+n) T2n>Tn + a ∴a

解题思路：这个题目是一道等比数列的题目，分段讨论比较简单，讨论每一分钟内两车拉开的距离，进而解决问题．详细过程见解答．

这道题分段讨论比较简单
第一分钟内，甲乙拉开差距（6.6-2.9）×60=222米
第二分钟内，甲的速度是13.2米/秒，乙的速度是8.7米/秒，甲乙拉开差距（13.2-8.7）×60=270（米）
第三分钟内，甲的速度是26.4米/秒，乙的速度是26.1米/秒，甲乙拉开差距（26.4-26.1）×60=18（米）
从第四分钟开始，乙速度超过甲，乙开始追及甲，此前甲乙差距为222+270+18=510（米）
第四分钟内，甲的速度是52.8米/秒，乙的速度是78.3米/秒，甲乙速度差为78.3-52.8=25.5（米/秒），510÷25.5=20（秒），乙用20秒追上了甲，
因此，出发后共用3分20秒乙追上甲．
答：出发后3分20秒乙追上甲．

点评：
本题考点： 追及问题．

考点点评： 此题也可以用列举的办法解答：
甲 第一分钟 行6.6×60=396米
第二分钟 行396×2=792 米
第三分钟 行792×2=1584米
第四分钟的速度1584×2÷60=52.8米/秒
乙 第一分钟 行2.9×60=174米
第二分钟 行174×3=522 米
第三分钟 行522×3=1566米
第四分钟的速度1566×3÷60=78.3米/秒
甲前三分钟共行396+792+1584=396×（1+2+4）=2772米
乙前三分钟共行174+522+1566=174×（1+3+9）=2262米
乙落后与甲2772-2262=510米，这是二车进入第四分钟，乙的速度比甲快了．
速度差为78.3-52.8=25.5米/秒．
所以510÷25.5=20秒
所以出发后3分20秒乙追上甲．

是3×0.7＋2×0.7＋0.7＝（3＋2＋1）×0.7＝4.2(千米）

全程的平均速度应等于全程的路程除以全程所用时间,全程的路程有两段,第一段是在一分钟运动了30m,第二段是以5m/s的速度运动了20m,所花时间为20m/5m/s=4s.全程所用时间有三个,一个是一分钟=60s,第二个是30s,第三个是4s.
则V平均=S/t=(S1+S2)/t1+t2+t3)=(30+20)/60+30+4)=50/94=0.53m/s

这个题可以转化为2+2×2+2×3+2×4+2×5+2×6+2×7+……
就等于2×（1+2+3+4+5+6+……）=240
1+2+3+4+5+……=120
设要x分钟
1+2+3+4+……+x=（x+1）x÷2=120
x（x+1）=240
240=2×2×2×2×3×5
3×5=15 2×2×2×2=16
答：15分钟后

21*3+5=68
68/12=5……8
商5余8

解题思路：由题意知，兔子5分钟跑路程，25.7×5-3.6×10=92.5，再用路程除以乌龟的速度，可求出乌龟爬完全程用的时间，然后再比较即可．

25.7×5-3.6×10，
=128.5-36，
=92.5（米）；
92.5÷18.8=4[173/188]，
4[173/188]＜5，
答：先到终点的是乌龟，赛程共92.5米．．
故答案为：乌龟，92.5．

点评：
本题考点： 简单的行程问题．

考点点评： 根据兔子的速度求出路程是完成本题的关键．

　　I am Peter. Usually a lot of my hobbies, such as skating, playing 356 Didesmococcus feather, draw, watch extra-curricular book, watch TV and so on, so my life is very rich extra-curricular. Ago is a more introverted person, I have very few words, only and I am very good friends to so many before, but after school at the time of my personality to change slowly, and not, as previously Like very few words, and students are also very harmonious relationship.
In fact, since childhood I dare not interested in English, so my English very poor, then let us hear English, introduce myself, I really do not know how to do, nervous for some time, so I think in the future of English class can have more understanding of English can have more interest in English. Families are. Usually a lot of my hobbies, such as skating, playing 356 Didesmococcus feather, draw, watch extra-curricular book, watch TV and so on, so my life is very rich extra-curricular. Ago is a more introverted person, I have very few words, only and I am very good friends to so many before, but after school at the time of my personality to change slowly, and not, as previously Like very few words, and students are also very harmonious relationship.
I think noting is difficult if you put your heart into it,so I can say will make my English be nice in future.
Thank you!

Manchester United Football Club is an English professional football club, based in Old Trafford, Greater Manchester, that plays in the Premier League. Founded as Newton Heath LYR Football Club in 1878, the club changed its name to Manchester United in 1902 and moved to Old Trafford in 1910.
In 1968, under the management of Matt Busby, Manchester United was the first English football club to win the European Cup, ten years after the Munich air disaster that claimed the lives of eight players. Alex Ferguson is the most successful manager in the club's history, having won 26 major honours since he took over in November 1986.
The club is unique in having won a Premier League, FA Cup and UEFA Champions League Treble, in the 1998–99 season. Having won a joint-record 18 league titles, four League Cups and a record 11 FA Cups, Manchester United is the joint most successful club in the history of English football.
Manchester United is one of the wealthiest and most widely supported football teams in the world. The club is said to be worth ￡1.19 billion, making it the most valuable football club in the world. After being floated on the London Stock Exchange in 1991, the club was purchased by Malcolm Glazer in May 2005 in a deal valuing the club at almost ￡800 million.
这些估计远不止1分钟,你自己按个人兴趣选一些吧.

1、7分钟
2、从第一次相遇到第二次相遇花 7分半钟

20米 此题很有意思 甲比乙每分钟快20米 追上前一分钟 自然是20米

你的回答完美的解决了我的问题，谢谢！

解题思路：这个题目是一道等比数列的题目，分段讨论比较简单，讨论每一分钟内两车拉开的距离，进而解决问题．详细过程见解答．

这道题分段讨论比较简单
第一分钟内，甲乙拉开差距（6.6-2.9）×60=222米
第二分钟内，甲的速度是13.2米/秒，乙的速度是8.7米/秒，甲乙拉开差距（13.2-8.7）×60=270（米）
第三分钟内，甲的速度是26.4米/秒，乙的速度是26.1米/秒，甲乙拉开差距（26.4-26.1）×60=18（米）
从第四分钟开始，乙速度超过甲，乙开始追及甲，此前甲乙差距为222+270+18=510（米）
第四分钟内，甲的速度是52.8米/秒，乙的速度是78.3米/秒，甲乙速度差为78.3-52.8=25.5（米/秒），510÷25.5=20（秒），乙用20秒追上了甲，
因此，出发后共用3分20秒乙追上甲．
答：出发后3分20秒乙追上甲．

点评：
本题考点： 追及问题．

考点点评： 此题也可以用列举的办法解答：
甲 第一分钟 行6.6×60=396米
第二分钟 行396×2=792 米
第三分钟 行792×2=1584米
第四分钟的速度1584×2÷60=52.8米/秒
乙 第一分钟 行2.9×60=174米
第二分钟 行174×3=522 米
第三分钟 行522×3=1566米
第四分钟的速度1566×3÷60=78.3米/秒
甲前三分钟共行396+792+1584=396×（1+2+4）=2772米
乙前三分钟共行174+522+1566=174×（1+3+9）=2262米
乙落后与甲2772-2262=510米，这是二车进入第四分钟，乙的速度比甲快了．
速度差为78.3-52.8=25.5米/秒．
所以510÷25.5=20秒
所以出发后3分20秒乙追上甲．

给你三篇,你选一篇吧.
The Old Cat
An old woman had a cat.The cat was very old; she could not run quickly,and she could not bite,because she was so old.One day the old cat saw a mouse; she jumped and caught the mouse.But she could not bite it; so the mouse got out of her mouth and ran away,because the cat could not bite it.
Then the old woman became very angry because the cat had not killed the mouse.She began to hit the cat.The cat said,"Do not hit your old servant.I have worked for you for many years,and I would work for you still,but I am too old.Do not be unkind to the old,but remember what good work the old did when they were young."
【译文】
老猫
一位老妇有只猫,这只猫很老,它跑不快了,也咬不了东西,因为它年纪太大了.一天,老猫发现一只老鼠,它跳过去抓这只老鼠,然而,它咬不住这只老鼠.因此,老鼠从它的嘴边溜掉了,因为老猫咬不了它.
于是,老妇很生气,因为老猫没有把老鼠咬死.她开始打这只猫,猫说：“不要打你的老仆人,我已经为你服务了很多年,而且还愿意为你效劳,但是,我实在太老了,对年纪大的不要这么无情,要记住老年人在年青时所做过的有益的事情.”
A man was going to the house of some rich person.As he went along the road,he saw a box of good apples at the side of the road.He said,"I do not want to eat those apples; for the rich man will give me much food; he will give me very nice food to eat." Then he took the apples and threw them away into the dust.
He went on and came to a river.The river had become very big; so he could not go over it.He waited for some time; then he said,"I cannot go to the rich man's house today,for I cannot get over the river."
He began to go home.He had eaten no food that day.He began to want food.He came to the apples,and he was glad to take them out of the dust and eat them.
Do not throw good things away; you may be glad to have them at some other time.
【译文】
一个人正朝着一个富人的房子走去,当他沿着路走时,在路的一边他发现一箱好苹果,他说：“我不打算吃那些苹果,因为富人会给我更多的食物,他会给我很好吃的东西.”然后他拿起苹果,一把扔到土里去.
他继续走,来到河边,河涨水了,因此,他到不了河对岸,他等了一会儿,然后他说：“今天我去不了富人家了,因为我不能渡过河.”
他开始回家,那天他没有吃东西.他就开始去找吃的,他找到苹果,很高兴地把它们从尘土中翻出来吃了.
不要把好东西扔掉,换个时候你会觉得它们大有用处.
The City Mouse and the Country Mouse
Once there were two mice.They were friends.One mouse lived in the country; the other mouse lived in the city.After many years the Country mouse saw the City mouse; he said,"Do come and see me at my house in the country." So the City mouse went.The City mouse said,"This food is not good,and your house is not good.Why do you live in a hole in the field?You should come and live in the city.You would live in a nice house made of stone.You would have nice food to eat.You must come and see me at my house in the city."
The Country mouse went to the house of the City mouse.It was a very good house.Nice food was set ready for them to eat.But just as they began to eat they heard a great noise.The City mouse cried," Run!Run!The cat is coming!" They ran away quickly and hid.
After some time they came out.When they came out,the Country mouse said,"I do not like living in the city.I like living in my hole in the field.For it is nicer to be poor and happy,than to be rich and afraid."
【译文】
城里老鼠和乡下老鼠
从前,有两只老鼠,它们是好朋友.一只老鼠居住在乡村,另一只住在城里.很多年以后,乡下老鼠碰到城里老鼠,它说：“你一定要来我乡下的家看看.”于是,城里老鼠就去了.乡下老鼠领着它到了一块田地上它自己的家里.它把所有最精美食物都找出来给城里老鼠.城里老鼠说：“这东西不好吃,你的家也不好,你为什么住在田野的地洞里呢?你应该搬到城里去住,你能住上用石头造的漂亮房子,还会吃上美味佳肴,你应该到我城里的家看看.”
乡下老鼠就到城里老鼠的家去.房子十分漂亮,好吃的东西也为他们摆好了.可是正当他们要开始吃的时候,听见很大的一阵响声,城里的老鼠叫喊起来：“快跑!快跑!猫来了!”他们飞快地跑开躲藏起来.
过了一会儿,他们出来了.当他们出来时,乡下老鼠说：“我不喜欢住在城里,我喜欢住在田野我的洞里.因为这样虽然贫穷但是快乐自在,比起虽然富有却要过着提心吊胆的生活来说,要好些.
请采纳答案,支持我一下.

由v=s1/t1=900/60=15m/s
t=s/v=(1560+240)/15=120s=2min

70 70 运动后约 90 35 呼吸

脑筋急转弯?没看出来,这不是等比数列吗
求和公式：
Sn=a1(1-q^n)/(1-q)
S60=2*Sn
1*(1-2^60)/(1-2)=2*1*(1-2^n)/(1-2)
2^59=2^n
n=59
所以当它下满半筐蛋用了多长时间是59分钟

1、谈笑风生：有说有笑,兴致高.形容谈话谈得高兴而有风趣
奄奄一息：形容呼吸微弱,生命垂危.
2、悠闲 逃窜
3、如果 怎能
4、 B.倒叙
5、

必须要用二元一次方程才可以 设最后一圈跑了a米 ,每圈减速n米 ,则第一圈跑了a+3n,第二圈跑了a+2n,第三圈跑了a+n
a+3n+a+2n=500 ①
a+n+a=420 ②
①-② ：4n=80,n=20
带入 ①式,得a=200
a+3n=260
∴第一圈跑了260米

守株待兔：从前有个农民,有一天,他看见一只兔子一头撞死在一棵树上,于是农民想:如果天天有一只兔子那就好了.于是他天天守在树下等兔子,过了1年兔子没等到,庄稼也因为没锄草也荒了.

70*15+3*[1+2+3+...+(15-4+1)]+[70+3*(15-4+1)]*(30-15)
=1050+3(1+12)*12/2+106*15
=2874
注：70*15+3*[1+2+3+...+(15-4+1)] 是前十五分钟走的路程
[70+3*(15-4+1)]*(30-15) 是后十五分钟走的路程

解题思路：这个题目是一道等比数列的题目，分段讨论比较简单，讨论每一分钟内两车拉开的距离，进而解决问题．详细过程见解答．

这道题分段讨论比较简单
第一分钟内，甲乙拉开差距（6.6-2.9）×60=222米
第二分钟内，甲的速度是13.2米/秒，乙的速度是8.7米/秒，甲乙拉开差距（13.2-8.7）×60=270（米）
第三分钟内，甲的速度是26.4米/秒，乙的速度是26.1米/秒，甲乙拉开差距（26.4-26.1）×60=18（米）
从第四分钟开始，乙速度超过甲，乙开始追及甲，此前甲乙差距为222+270+18=510（米）
第四分钟内，甲的速度是52.8米/秒，乙的速度是78.3米/秒，甲乙速度差为78.3-52.8=25.5（米/秒），510÷25.5=20（秒），乙用20秒追上了甲，
因此，出发后共用3分20秒乙追上甲．
答：出发后3分20秒乙追上甲．

点评：
本题考点： 追及问题．

考点点评： 此题也可以用列举的办法解答：
甲 第一分钟 行6.6×60=396米
第二分钟 行396×2=792 米
第三分钟 行792×2=1584米
第四分钟的速度1584×2÷60=52.8米/秒
乙 第一分钟 行2.9×60=174米
第二分钟 行174×3=522 米
第三分钟 行522×3=1566米
第四分钟的速度1566×3÷60=78.3米/秒
甲前三分钟共行396+792+1584=396×（1+2+4）=2772米
乙前三分钟共行174+522+1566=174×（1+3+9）=2262米
乙落后与甲2772-2262=510米，这是二车进入第四分钟，乙的速度比甲快了．
速度差为78.3-52.8=25.5米/秒．
所以510÷25.5=20秒
所以出发后3分20秒乙追上甲．

设时间为t ,高度为H
则
H=25{1+（80％）^（ t-1）}

解题思路：因为热气球在以后的每一分钟里，它上升的高度是它在前一分钟里上升高度的80%，所以它每分钟上升的高度构成等比数列，而这个热气球上升的最大高度为等比数列前n项和的极限，S=

lim

n→∞

a1(1−qn)

1−q

=

a1

1−q

，即可求出．

由题意可知，热气球每分钟上升的高度构成等比数列，且首项为25，公比为0.8，
各项和S=
lim
n→∞
a1(1−qn)
1−q=
a1
1−q=[25/1−0.8]=125
故答案为125

点评：
本题考点： 等比数列的前n项和；极限及其运算．

考点点评： 本题主要考查了无穷等比数列的所有项的和的求法．属于数列与极限的综合．

　　As food is to the body, so is learning to the mind. Our bodies grow and muscles develop with the intake of adequate nutritious food. Likewise, we should keep learning day by day to maintain our keen mental power and expand our intellectual capacity. Constant learning supplies us with inexhaustible fuel for driving us to sharpen our power of reasoning, analysis, and judgment. Learning incessantly is the surest way to keep pace with the times in the information age, and an infallible warrant of success in times of uncertainty.
　　Once learning stops, vegetation sets in. It is a common fallacy to regard school as the only workshop for the acquisition of knowledge. On the contrary, learning should be a never-ending process, from the cradle to the grave. With the world ever changing so fast, the cease from learning for just a few days will make a person lag behind. What's worse, the animalistic instinct dormant deep in our subconsciousness will come to life, weakening our will to pursue our noble ideal, sapping our determination to sweep away obstacles to our success and strangling our desire for the refinement of our character. Lack of learning will inevitably lead to the stagnation of the mind, or even worse, its fossilization, Therefore, to stay mentally young, we have to take learning as a lifelong career.
　　学习之于心灵,就像食物之于身体一样.摄取了适量的营养食物,我们的身体得以生长而肌肉得以发达.同样地,我们应该日复一日不断地学习以保持我们敏锐的心智能力,并扩充我们的智力容量.不断的学习提供我们用不尽的燃料,来驱使我们磨利我们的推理、分析和判断的能力.持续的学习是在信息时代中跟时代并驾齐驱的最稳当的方法,也是在变动的世代中成功的可靠保证.
　　一旦学习停止,单调贫乏的生活就开始了.视学校为汲取知识的唯一场所是种常见的谬误.相反地,学习应该是一种无终止的历程,从生到死.由于世界一直快速地在变动,只要学习停顿数日就将使人落后.更糟的是,蛰伏在我们潜意识深处的兽性本能就会复活,削弱我们追求高贵理想的意志,弱化我们扫除成功障碍的决心,而且扼杀我们净化我们人格的欲望.缺少学习将不可避免地导致心灵的停滞,甚至更糟地,使其僵化.因此,为了保持心理年轻,我们必须将学习当作一生的事业.
　　2．heavy schoolwork【课业繁重】
　　In my opinion, the schoolwork now being assigned to high school students is too heavy. While it is true that students need to study, they need other things as well if they are to grow into healthy and well-rounded adults. High should be allowed more time for play. Playing is not wasting time, as some think. It gives them physical exercise, and also exercise their imagination. Which tends to be stifled by too much study. Finally, the pressure put on high school students by excessive schoolwork can cause serious stress, which is unhealthy physically and mentally. I do not advocate the elimination of schoolwork. I do think, however, that a reduction of the current heavy load would be beneficial to students and to the society as a whole.
　　我认为目前高中生的课业实在太重了,虽然说学生的确应当念书,但是要想长大成为健全的人,他门还需要一些其它的东西,所以应该给高中生较多从事娱乐的时间.娱乐并不如某些人所想的,是在浪费时间,它可以让学生锻炼身体,发挥被繁重课业扼杀的想象力.此外,繁重的课业加诸在高中生身上的压力可能引起严重的情绪紧张,这对身心都有害.我并非主张废除学校课业,但是我认为减轻目前繁重的课业对于学生和整个社会都是有益的.
　　3．Time【时间】
　　Lost time is never found again. This is something which I learned very clearly last semester. I spent so much time fooling around that my grades began to suffer. I finally realized that something had to be done. It was time for a change.
　　Now I have a new plan for using my time wisely. I have set my alarm clock ahead half an hour. This will give me a head start on the day. I have also decided to keep a log of what I do and when I do it. Looking back on what I’ve done will give me some ideas on how to reorganize my time.
　　时光一去不复返,这是我上学期清楚学到的教训.我浪费很多时间四处游荡,以致于我的成绩开始退步.最后我终于了解到我必须有所作为；该是痛改前非的时候了.
　　现在我有一个明智运用时间的新方法.我已将闹钟早拨半小时,这将使我这一天的作息提前开始.我也决定将我所做的一切及做这些事的时间记录下来.回顾我所做的事情会启发我如何重新安排我的时间.
　　4．Work and Play【工作与娱乐】
　　Work and play do not contradict each other; in fact, they complement each other. As the saying goes, "All work and no play makes Jack a dull boy." A life burdened with work leads you nowhere, for you would get tired and bored with your daily routine work. On the other hand, proper recreation will relieve the tension and discomfort of our monotonous life because it offers you various ways to let out your pent-up emotions.
　　What I usually do to relax after school is jogging and seeing movies. Usually I don't spare time for exercise, but I value the physical education class at school. Jogging several rounds in the field certainly relieves the day's pressure. On weekends, I'll catch the morning movie for my visual enjoyment. I feel revived and energetic for another week's work-load.
　　工作与娱乐并不互相冲突,事实上,它们之间的关系还相辅相成.有句格言说：「整日工作而没有休闲娱乐,会令人变得沉闷乏味.」被工作重担压得喘不过气来的生活,将使你一事无成,因为你将对一成不变的例行公事感到厌烦.由另一方面来说,适度的娱乐活动能提供各种管道,来渲泄你被压抑的情绪,减轻单调生活中的紧张与不悦.
　　放学之后,我最常做的休闲活动,便是慢跑与看电影.通常我并不特地拨出时间来做运动,但是我很重视学校的体育课.在操场上慢跑几圈,无疑地可以减轻一天的压力.在周末时,我都去看早场电影,享受视觉飨宴.如此一来,我将有如再生般的充沛活力,去面对下一星期的工作量.
　　5．My first Job【我的第一份工作】
　　My first job was at a cramming school. It was three years ago when I just graduated from junior high school and finished the entrance examination. since I had nothing to do that summer, I decided to find a job, tasting the joy of independence.
　　I was responsible for answering the telephone and taking the message. I worked eight hours a day, six days a week. The work was not difficult nor heavy to me and I guess I did well. The most delighted thing was perhaps that I could spend the money I earned all by myself.
　　我的第一份工作是在一家补习班做事.那是三年前我刚从国中毕业,考完联考时的事了.既然我那整个夏天都闲着没事,倒不如找份差事,尝尝独立赚钱的快乐.
　　我负责接听电话且纪录留言的工作.我一天工作八小时,一星期工作六天.那份工作对我而言既不困难亦不沉重,所以我想我还满称职的.而最令人快乐的事大概莫过于花全部由自己赚来的钱了!
　　6．My Favorite Sports【我最喜爱的运动】
　　Sports help everyone to keep healthy, happy, and efficient. So I pay special attention to games, especially table-tennis. Table tennis is my favorite game. I play it almost every day.
　　Table-tennis is an ideal game us because it brings the whole body into action. It strengthens our muscles, expands our lungs, promotes the circulation of the blood, and causes a healthy action of the skin. Besides, it is very amusing and does not cost us much money. Table-tennis is very moderate; it is not so rough as football. It is an indoor game and can be played even on rainy days. Thus, it is my favorite kind of exercise.
　　运动能帮助每一个人保持健康、快乐和有效率.所以我特别重视运动,特别是桌球,桌球是我最喜欢的运动.我几乎每天玩.
　　桌球对我们而言,是一项理想的运动,因为它可以使我们全身运动,它可以增强我们的肌肉,扩张我们的肺部,促进血液循环,并且使肌肤产生健康作用,此外,它很有趣而且所费不多.桌球是相当温和适中的,它不像足球那么粗野.它是一种室内运动,甚至在下雨天也能玩.因此,桌球是我最喜爱的一种运动.
　　One day, a father and his little son were going home. At this age, the boy was interested in all kinds of things and was always asking questions. Now, he asked, "What's the meaning of the word 'Drunk', dad?" "Well, my son," his father replied, "look, there are standing two policemen. If I regard the two policemen as four then I am drunk."
　　"But, dad," the boy said, " there's only ONE policeman!"
　　醉酒
　　一天,父亲与小儿子一道回家.这个孩子正处于那种对什么事都很感兴趣的年龄,老是有提不完的问题.他向父亲发问道：“爸爸,‘醉’字是什么意思?” “唔,孩子,”父亲回答说,“你瞧那儿站着两个警察.如果我把他们看成了四个,那么我就算醉了.” “可是,爸爸, ”孩子说,“那儿只有一个警察呀!”

解题思路：因为热气球在以后的每一分钟里，它上升的高度是它在前一分钟里上升高度的80%，所以它每分钟上升的高度构成等比数列，而这个热气球上升的最大高度为等比数列前n项和的极限，S=

lim

n→∞

a1(1−qn)

1−q

=

a1

1−q

，即可求出．

由题意可知，热气球每分钟上升的高度构成等比数列，且首项为25，公比为0.8，
各项和S=
lim
n→∞
a1(1−qn)
1−q=
a1
1−q=[25/1−0.8]=125
故答案为125

点评：
本题考点： 等比数列的前n项和；极限及其运算．

考点点评： 本题主要考查了无穷等比数列的所有项的和的求法．属于数列与极限的综合．

2的最大倍数是98
3的最大倍数是99
甲最后得分98+3*2=104分
乙最后得分99+4*1=103分
最终是甲获胜