F.3 Maths ........

2007-04-10 11:29 pm

1. In a two-digit number, the units digensions of a rectit is greater than the tens digit by 3, and the sum of the squares of two digits is grater than the two-digit number by 3. Let the units digit be x.
a) Express, in terms of x,
(i) the tens digit,
(ii) the value of the two-digit number.
b) Hence find the two-digit number.

更新1:

2. A ladder of length 5m leans against a vertical wall, and the foot of the ladder is 3m from the wall. a) Find the distance between the top of the ladder and the ground.

更新2:

b) If the foot of the ladder is pulled x m away from the wall so that the top of the ladder slides the same distance down the wall, find x. Answer : 1a - i ) x - 3 ; 1a - ii) 11x - 30 ; b) 14 2a) 4m ; b) 1

回答 (1)

用戶3614

2007-04-10 11:53 pm

✔ 最佳答案

1.
a) (i) the tens digit = x – 3 ( because the unit digit is greater than the tens digit by 3)
(ii) the value of the two-digit number = 10*(x-3) + x = 10x – 30 + x = 11x-30
b) (x-3)^2 + x^2 – 3 = 11x – 30
x^2 – 6x +9 + x^2 – 3 = 11x – 30
2x^2 -17x +36 = 0
(2x-9)(x-4)=0
X = 9/2 (rejected because x must be integer) or x = 4
The unit digit is 4
The ten digit is 4-3=1
Therefore, the number is 14.

2.
a) Distance between the top of the ladder and the ground
= square root (5^2 – 3^2) (using Pythagoras's theorem)
= 4m
b)
The foot of the ladder is 3+x from the wall.
The top of the ladder is 4-x from the ground.
(3+x)^2 + (4-x)^2 = 5^2
9 + 6x + x^2 + 16 -8x + x^2 = 25
25 -2x + 2x^2 = 25
2x^2 – 2x = 0
X(x-1) = 0
X = 0 (rejected because x must be greater than 0) or x = 1
Therefore, If the foot of the ladder is pulled 1 m away from the wall.

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