问题 解答题

某工厂用7万元钱购买了一台新机器,运输安装费用2千元,每年投保、动力消耗的费用也为2千元,每年的保养、维修、更换易损零件的费用逐年增加,第一年为2千元,第二年为3千元,第三年为4千元,依此类推,即每年增加1千元.

(Ⅰ)求使用n年后,保养、维修、更换易损零件的累计费用S(千元)关于n的表达式;

(Ⅱ)问这台机器最佳使用年限是多少年?并求出年平均费用(单位:千元)的最小值.(最佳使用年限是指使年平均费用最小的时间,年平均费用=(购入机器费用+运输安装费用+每年投保、动力消耗的费用+保养、维修、更换易损零件的累计费用)÷机器使用的年数 )

答案

(I)∵第一年为2千元,第二年为3千元,第三年为4千元,每年增加1千元

故每年的费用构造一个以2为首项,以1为公差的等差数列

∴前n年的总费用S=2+3+…+n+1=

n(n+3)
2

(II)设使用n年的年平均费用为y,则

y=(72+2+2n+

n(n+3)
2
)÷n

=

72
n
+
n
2
+
7
2
2
36
+
7
2
=
31
2

72
n
n
2
,即n=12时取等号.

故最佳使用年限是12年,这时年平均费用最小,为

31
2
千元/年

完形填空

Advertising is used to make something such as a product, service, or idea known to the public. Many types of advertising are used for the purpose of building brands and increasing product sales. Advertising is present everywhere in our daily life.

Print media like magazines and newspapers allows advertisements to reach their readers. Magazines include articles and images intended to attract a specific(特定的)type of consumers. Newspaper advertising is not as effective as it was before because of the appearance of other types of advertisements.

Broadcast advertising includes TV and radio messages. Traditional forms of these types of advertisements are commercials(商业广告)shown during a television program or before a movie. Product placement advertising(植入式广告)is a less obvious way to promote a product. With product placement advertising, companies pay to have their product ‘used’ by an actor or actress in the program. When you see someone in a TV show or movie using a specific brand, this is product placement.

Internet advertising is one of the new types and can be achieved in a number of ways. Flash advertising refers to messages that jump onto your computer screen and often move around. They can be hard to close and are annoying, but a useful way of gaining your attention.

Outdoor advertising often uses advertising boards as its main way. Of course, the type of advertising also includes using cars with messages on them, or large signs placed on the sides of buses. They can also be signs in stadiums drawing the attention of large crowds.

小题1:What’s the purpose of advertising? (no more than 8 words)   (2 marks)

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小题2:What is product placement advertising? (no more than 11 words)   (2 marks)

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小题3:How does flash advertising draw your attention? ( no more than 15 words)  (3 marks)

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小题4:What does the passage mainly talk about? (no more than 6 words)      (3 marks)

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