maths F.5問題

2010-04-11 7:26 pm
1. 若4個蘋果的成本與3個蘋果的售價相同,找售10個蘋果的盈利百分率.
ans. 33.3%

2. 在triangle ABC中,則1+cos(B)cos(-A-C)=
ans. sin^2 B

3. sin^2 2 + sin^2 4 + sin^2 6 +......+ sin^2 86 + sin^2 88=
ans. 22

4. (2-5cos 2 A)^2 + 1 的極小值為
ans. 1

i would like to have the solution ..thz^^

回答 (3)

2010-04-11 8:30 pm
✔ 最佳答案

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2010-04-12 07:45:38 補充:
當cos2A=2/5時,
可得極小值=[2-5(2/5)]²+1
=1
2010-04-11 9:36 pm
SOMUCH你第一題錯左...應該係4C=3P
2010-04-11 8:20 pm
3. sin^2 2 + sin^2 4 + sin^2 6 +......+ sin^2 86 + sin^2 88

=sum(k=1,22) ((sin(2k))^2+(sin(90-2k))^2

=sum(k=1,22) ((sin(2k))^2+(cos(2k))^2

=sum(k=1,22) 1

=22//

4. -1<cos2A<1

=>-5<-5cos2A<5

=>-3<2-5cos2A<7

=>9<(2-5cos2A)^2<49

=>10<(2-5cos 2 A)^2 + 1<50

minimum = 10//

1+cos(B)cos(-A-C)

=1+cosBcos(B-180)

=1-cosBcosB

=sin^2B//

1. let cost = C and price = P

then 3C=4P => P=3/4C

profit percentage

=(P-C)/C x100%

=(3/4C-C)/C x100%

=25%//



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