Maths problems!明天考試!!唔該20point

question 1:Find the length of the bookmark in the figure correct to the nearest (a) cm (b) 0.5 cm,如果個measured value係12.9 cm,correct to the nearest 0.5 cm 即係點?同correct to the nearest 0.1 cm,0.2 cm,0.3 cm,0.4 cm......有什麼不同?
correct to the nearest 0.5 cm 姐係話要揀個個度到既數最近既0.5cm既倍數12.9係12.5同13.0之間佢近13.0所以係13.0而唔係12.5
通常會用correct to nearest 1cm/ 0.5cm, 0.1cm都會, 0.2 0.3 0.4就好少你當你睇把間尺你度野通常唔會真係岩岩好個個刻度正常D人會大約估下個個位係個2個刻度之間近邊個估個數出黎, 就好似12.9咁差"一格"但係數學黎講, 我地要搵最近個個刻度, 因為你靠肉眼估出黎個個數字冇意思. 用同一把間尺, A同學同B同學都度到佢地本書厚度4.0到4.5之間, 但係一個覺得4.2 一個覺得係4.3 咁佢地就以為B個本大D, 但係其實可能根本一樣, 甚至B個本仲薄D所以只會睇最近個刻度而寫得做13.0, 就已經知道佢係correct左寫13會冇分
question 2:16^2+17^2+18^2+...+30^2點做?
呢題你要知道1^2+2^2+3^2+....+n^2=n(n+1)(2n+1)/6
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證明:考慮(k+1)^3-k^3=[(k+1)-k][(k+1)^2+(k+1)k+k^2] <<a^3-b^3=(a-b)(a^2+ab+b^2) 係書到有寫=(k+1)^2+2k^2+k
代k=1, 2^3-1^3=2^2+2*1^2+1代k=2, 3^3-2^3=3^2+2*2^2+2代k=3, 4^3-3^3=4^2+2*3^2+3
一路代到去n, 代k=n, (n+1)^3-n^3=(n+1)^2+2*n^2+n你會見到咁多條式加哂之後左面差唔多約哂, 得番(n+1)^3-1^3右面就係2^2+3^2+4^2+...+(n+1)^2 + 2( 1^2+2^2+3^2+...+n^2 ) + 1+2+3+...+n
(n+1)^3-1^3= [2^2+3^2+4^2+...+(n+1)^2 ] + 2( 1^2+2^2+3^2+...+n^2 ) + (1+2+3+...+n)(n+1)^3-1^3= [1^2 + 2^2+3^2+4^2+...+(n)^2 -1^2+(n+1)^2 ] + 2( 1^2+2^2+3^2+...+n^2 ) + (1+2+3+...+n) <<前面個括號加D野減D野變番1^2+2^2+...+n^2(n+1)^3-1^3= 3( 1^2+2^2+3^2+...+n^2 ) -1^2+(n+1)^2 + (1+2+3+...+n)(n+1)^3-1^3= 3( 1^2+2^2+3^2+...+n^2 ) -1^2+(n+1)^2 + (n+1)n/2 << 1+2+3+...+n係人都知係"頭加尾乘項數除2"...要證明上網SEARCH3(1^2+2^2+3^2+...+n^2)=(n+1)^3-1^3+1^2-(n+1)^2 - (n+1)n/21^2+2^2+3^2+...+n^2=1/3((n+1)^3-(n+1)^2 - (n+1)n/2)拆番開RHS就會計到

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n=30, 1^2+2^2+3^2+....+30^2=30(30+1)(2*30+1)/6 ___________(1)n=15, 1^2+2^2+3^2+....+15^2=15(15+1)(2*15+1)/6 ___________(2)
(1)-(2)就係答案16^2+17^2+18^2+...+30^2=30*31*61/6-15*16*31/6=8215
或者仲有其他方法...因為佢減走個到岩岩好係30/2



2012-01-05 22:57:40 補充：
過左字數限制...
Q3Q4: http://i44.tinypic.com/w82djd.png
Q5: http://i42.tinypic.com/34fkzyc.png

for inequalities, try to keep the direction sign all the way...
(4-3x)/5 > 2
4 - 3x > 10
-3x > 6
-6 > 3x
-2 > x