麻煩幫幫忙,解決數學上的問題!!!!
Factorize
(1)6mn^2+9m^2n
(2)16x^2y-24xy^2
(3)20mn-21+15m-28n
(4)(a)x^3-64
(b)Hence factorize[x^3-(64/x^3)]
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(refer toQ5&6)
Salaries tax rates fot the year 2009-2010
Net chargeable income($) Rate
On he next 40000 2%
On he next 40000 7%
On he next 40000 12%
Rmainder 17%
(5)Tom has to pay salaries tax of $8400 in the year 2009-2010.Find his monthly salary in the yer 2009-2010.Given that the basic allowance is $108000.
(6)Sue borrowed $50000 fom the bank at an interest rate of 15%p.a.The interest was compounded monthly.Staring from the first month,she repaid $3000 to the bank at the end of each month.Can she repay the loan after 2 years?Explain your ide.
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Prove the trigonomeric identities.
(7)sin^3θ+cos^3θ=(sinθ+cosθ)(1-sinθcosθ)
(8)(a)Find the value of (cos^2 10º+cos^2 20º+cos^2 30º+...+cos^2 80º)^2
(b)Hence ecaluate (cos^2 1º+cos^2 2º+cos^2 3º+...+cos^2 89º)^2.Explain how you can get the answer.
F3.maths
2012-08-24 12:39 am
回答 (1)
2012-08-24 3:02 am
✔ 最佳答案
Factorize(1)6mn^2+9m^2n=3mn(2n+3m)
(2)16x^2y-24xy^2=8xy(2x+3y)
(3)20mn-21+15m-28n=20mn+15m-28n-21=5m(4n+3)-7(4n+3)=(4n+3)(5m-7)
(4)(a)x^3-64=(x-4)(x^2+4x+16)
(b)[x^3-(64/x^3)]=(x-4/x)(x^2+4x/x+16)=(x^2+4)(x^2+20)/x
(5)
40000x2%=$800
40000x7%=$2800
40000x12%=$4800
800+2800+4800=$8400
∴The yearly salary=40000x3+108000=$228000
∴The monthly salary=228000/12=$19000
(6)
After 1 month, the amount she borrowed=50000x(1+15%/12)-3000=$50750
After 2 months, the amount she borrowed=50750x(1+15%/12)-3000=$51556.25
After 3 months, the amount she borrowed=51556.25x(1+15%/12)-3000=$52422.97
From the above, we can see that the total amount of money she borrowed is increasing.
∴She can't repay the loan after 2 years.
(7)sin^3θ+cos^3θ=(sinθ+cosθ)(1-sinθcosθ)
L.H.S.
=sin^3θ+cos^3θ
=(sinθ+cosθ)(sin^2θ-sinθcosθ+cos^2θ)
=(sinθ+cosθ)(1-sinθcosθ)
=R.H.S.
(8)(a)
(cos^2 10º+cos^2 20º+cos^2 30º...+cos^2 80º)^2
=(cos^2 10º+cos^2 80º+cos^2 20º+cos^2 70º+...)^2
=(cos^2 10º+sin^2 10º+cos^2 20º+sin^2 20º+...)^2
=(1x8/2)^2
=16
(b)
(cos^2 1º+cos^2 2º+cos^2 3º+...+cos^2 89º)^2
=(cos^2 1º+cos^2 89º+cos^2 2º+cos^2 88º+...)^2
=(cos^2 1º+sin^2 1º+cos^2 2º+sin^2 2º+...+cos^2 45º)^2
=[1x(89-1)/2+(√2/2)^2]^2
=(44+1/2)^2
=7921/4
參考: me
收錄日期: 2021-04-20 13:13:34
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