F.4 MATHS - Ans.fyi 參考答案

F.4 MATHS

Please show all the steps in the problems below:
1. The sum of the
圖片參考：http://pooito.edu.mo/middleschool/maths/ift/2010/IFT2011/IFTmaths%202010%7E2011%28chinese%29.files/image006.gif
term of a geometric sequence is -4.If the sum of the first two terms is 32, find the first term of the sequence

2. If
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3. If x=
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and k, n≠0, then
A.log y=
圖片參考：http://pooito.edu.mo/middleschool/maths/ift/2010/IFT2011/IFTmaths%202010%7E2011%28chinese%29.files/image026.gif
and y=x + k has only one solution, then what is k?
5.If log x, log y, log z are in arithmeticsequence,I. x, y, z are in arithmetic sequence. II. x, y, z are all integers. III. x, y, z are in geometric sequence. 6. The perimeter of a square is twice the circumference of a circle.Find the ratio of the area of the square to that of the circle.

回答 (1)

用戶2053

2011-03-26 6:14 pm

✔ 最佳答案

1)
1st term = a
Common ratio = r ar^3 + ar^4 = - 4....(1)
a + ar = 32....(2)(2)*r^3 / (1) :1 = (32r^3) / - 4
1 = - 8r^3
r = - 1/2Sub into (2) :
a + a(-1/2) = 32
a (1 - 1/2) = 32
a = 64
2)(x+3)² - (x+1)(x-3) ≡ P(x+1) + QPutting x = - 1 :
4 = Q(x+3)² - (x+1)(x-3) ≡ P(x+1) + 4Putting x = 3 :
36 = 4P + 4
P = 8
3)x^n = y/ky = k x^nlog y = log k + nlogx(D)
4)Sub y = x+k into x² + y² = 8 :x² + x² + 2kx + k² = 8
2x² + 2kx + k²-8 = 0△ = 4k² - 4*2(k²-8) = 0 for only 1 solution.k² - 2(k²-8) = 0
k² = 16
k = 4 or - 4
5)logx + logz = 2logy
log (xz) = log y²
xz = y²The answer is :
III. x, y, z are in geometric sequence.
6)Let r be the radius of the circle :The circumference = 2πr ,
The perimeter of a square = 4(2πr) means a side of the square = 2πr ,S : C= (2πr)² : πr²= 4π²r² : πr²= 4π

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