f.4 maths - Ans.fyi 參考答案

f.4 maths

2009-08-23 12:55 am

有幾題數唔識,希望大家幫幫手

1a. rewrite the equation
12sin^2x-11sinxcosx+2cos^2x=0
in the form of atanx+c=0,
where a,b,c are integers.

1b. hence,solve for x,where 0°≦x＜360°

2. The area of a square is (x+3)cm^2. if the length of each side of the square is increased by 1 cm,the area is increased by x/2 cm^2. find the length of a side of the original square.

3. If x is 60％ more than y,by what percentage is y less than x?

thanks

回答 (1)

用戶9112

2009-08-23 3:42 am

✔ 最佳答案

1a. 12sin2x – 11sinxcosx + 2cos2x = 0
(3sinx – 2cosx)(4sinx – cosx) = 0
3sinx – 2cosx = 0
3tanx – 2 = 0
OR
4sinx – cosx = 0
4tanx – 1 = 0
1b. 3tanx – 2 = 0
3tanx = 2
tanx = 2/3
x = 33.69 degrees or x = 213.7 degrees
4tanx – 1 = 0
tanx =
x = 14.04 degrees or x = 194.0 degrees
2. Let the length of a side of the original square = z cm
z2 = x + 3 => x = z2 – 3 … (1)
(z + 1)2 = x + 3 + x/2 … (2)
Sub(1) into (2) => (z + 1)2 = z2 + (z2 – 3)/2
z2 + 2z + 1 = z2 + 0.5z2 – 1.5
0.5z2 – 2z – 2.5 = 0
z2 – 4z – 5 = 0
(z – 5)(z + 1) = 0
z = 5 or z = -1 (rejected)
The length of a side of the original square = 5 cm
3. x = (1 + 60%)y = 1.6y
(x – y)/x * 100%
= (1.6y – y)/1.6y * 100%
= 0.6y/1.6y * 100%
= 37.5%
y is 37.5% less than x

2009-08-22 19:44:10 補充：
1b second part, tanx = 1/4
x = 14.04 degrees or x = 194.0 degrees

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