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[匿名]

2010-05-18 11:48 am

Q2. B10. Find the equation of the perpendicular bisector of the line segment joining
A(–5, 6) and B(9, –12).

Q3 A rectangular container is made up by cutting out squares of side x cm from
each corner of a piece of rectangular cardboard measuring 16 cm by 12 cm.

(a) If the area of the base of the completed box is 96 cm^2.write down an
equation in terms of x and show that it reduces to x^2 – 14x + 24 = 0.
(b) Solve the equation in part (a). 附圖了~

Q4. Refer to the figure below; given that 角CDB = 角ABD = 角AC'C = 90°, AB and
CD are of heights 45 m and 30 m respectively. The angle of elevation of A
from D is 30°.

(a) Find the length BD.
(b) Find the angle of elevation of A from C. 附圖了~

圖片係~ http://lsforum.net/board/thread-138038-1-1.html

回答 (1)

用戶10012

2010-05-18 1:50 pm

✔ 最佳答案

1.
Mid-point of AB is (-5 +9)/2, (6 - 12)/2, that is (2, -3).
Slope of AB = (-12 - 6)/(9 + 5) = -18/14 = -9/7.
so slope of perpendicular bisector = 7/9.
so equation of perpendicular bisector is
y - (-3) = (7/9)(x - 2)
9y + 27 = 7x - 14
7x - 9y - 41 =0.
2.
Length of base = 16 - 2x
Width of base = 12 - 2x
so area of base = (16 -2x)(12 - 2x) = 96
(8 - x)(6 - x) = 24
48 - 14x + x^2 = 24
x^2 - 14x + 24 = 0
(x - 2)(x - 12) = 0
x = 2 or 12 ( rej.)

2010-05-18 06:00:59 補充：
Cannot see the figure, but guess to be the following: AB/DB = tan 30 , DB = AB/tan 30 = 45 sqrt 3.
Angle of elevation of A from C = arc tan [(AB - CD)/DB] = arc tan (15/45 sqrt 3) = arc tan (1/3 sqrt 3).

2010-05-18 06:02:47 補充：
A from C is 10.9 degree.

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