數學既幾條問題 - Ans.fyi 參考答案

數學既幾條問題

2012-01-15 2:29 pm

請教我數學,有6題
唔該列詳細步驟,唔好跳步啊
1.the speed of train is deceased by r%. Find the percentage change
in the time taken to travel the same distance
answer: ( r÷(100-r) )%
2 A sum of $P is invested at r% p.a. , compounded yearly. after
2years ,the total interest is $ K. Find P
answer: 10000K÷(r(r+200))
3. Andy 's weight is measured to be 64kg and the percentage error
is 0.78125%. Which of the following cannot be his actual weight
answer: 64.53kg
4.if the percentage error in the length of a spuare is 1%, whist is the
percentage error in the area of the square
answer:2.01%
5. The measurement is correct to the nearest 0.1cm.The radius is 5.2cm
The height is 6.1cm. Find the greatest possible surface area of the cylinder.
answer:376 cm2

唔該哂啊~~

回答 (1)

waiting

2012-01-15 8:11 pm

✔ 最佳答案

1. Let the distance it travels be A km,original speed : 1>>> originaltime needed : A/1 (hrs)new speed : ( 1- r% ) >>> newtime needed : A/ (1-r%) (hrs)The percentage change in the time :{[A/(1-r%)-A/1]÷A/1}x100%= {[A/(1-r%)-A]÷A}x100%= {[A(1/(1-r%)-1]÷A}x100%= [(1/(1-r%)-1]x100%= [(1-(1-r%)/(1-r%)]x100%= [(1-1+r%)/(1-r%)]x100%= r%/(1-r%)x100%=r/100÷(100/100-r/100)X100%= r/(100-r)%2.P x (1+r%)2 – P = KP[ (1+r%)2 – 1] = KP[ (1+r/100)2 – 1] = KP [(1+2r/100+r2/10000) –1] = KP (2r/100+r2/10000) = KP (200r/10000+r2/10000) = KP [(200r+r2)/10000] = KP (200r+r2) =10000 KP = 10000 K/(200r+r2)P = 10000K÷(r(r+200)) 3. Maximum absoluteerror / 64 x100% = 0.78125%Maximum absoluteerror / 64 = 0.0078125%Maximum absoluteerror / 64 = 0.0078125%Maximumabsolute error = 0.49984 The lower limit is 63.50 ( 4.s.f.)The upper limit is ( 64. 50 ( 4.s.f.)
4. [(1.01 x1.01 – 1x1)/1x1]x 100% = (1.0201 –1) x 100%= 2.01%
5. The radiuslies between (5.2±0.05)cm, the height lies between(6.1±0.05)cm;The upperlimit of surface area of the cylinder:2Πr2 + 2 Πrh= 2Πr(r+h)= 2Π(5.25)(5.25+6.15)=119.7Π=376.05

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