help!!!Maths(1)

2010-02-28 5:07 am

a) Solve log'base8'(x-13)+log'base8'(x-1)=2

b) The distance between Airport A and Airport B is 189 km. An aeroplane flies from Airport A at the speed of 72 km per hour. Another aeroplane slowly flies from B and its speed is 54 km per hour.
If the departure time is the same for both aeroplanes and they are flying in the directions towards each other, how many hours later will they meet?

c) An iron box with an open top is to be constructed by cutting 3-cm squares from the corners of a rectangular sheet of tin whose length is twice its width. What size sheet will produce a box having a volume of 60 cm^3?

回答 (1)

老爺子

2010-02-28 5:57 am

✔ 最佳答案

a)
log8(x - 13) + log8(x - 1) = 2
log8(x - 13)(x - 1) = 2
(x - 13)(x - 1) = 8^2
x^2 - 14x + 13 = 64
x^2 - 14x - 51 = 0
(x - 17)(x + 3) = 0
x = 17 or x = -3 (rejected)

(x = -3 is rejected because log8(-3 - 13) and log8(-3 - 1) are both indefinite.)

b)
Let t hours be the time required.

Total distance that the two planes fly = Distance between A and B
72t + 54t = 189
126t = 189
t = 1.5

Time required = 1.5 hours

c)
Let w cm be the width of the sheet.
Then the length of the sheet = 2w cm

Volume of the box :
3 x (w - 3 x 2) x (2w - 3 x 2) = 60
3(w - 6)(2w - 6) = 60
3(2w^2 - 18w + 36) = 60
w^2 - 9w + 18 = 10
w^2 - 9w + 8 = 0
(w - 8)(w - 1) = 0
w = 8 or w = 1 (rejected)
2w = 16

Width of the box = 8 cm
Length of the box = 16 cm

參考: 老爺子

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