幾條數學題(F1數,20POINT)

1.) Solve the following equations.
-25/4 = 5/-2x
50x = 20
x = 2/5
2.) Solve the following inequalities
a.) 2(x+1)>4
2x+2>4
2x>2
x>1
b.) 7x-9>9x+7
-16>2x
x<-8
3.) Consider the sequence -3, 9,-27
Write down the general term, hence the 100 tern.
R = -27/9 = 9/-3 = -3, a = -3
General term = -3(-3)^(n-1)
The 100th term
= -3(-3)^(100-1)
4.) Given a rectangle of dimensions 3cmX4cm.If this rectangle is a scaledrawing to a scale of 1:250, find its actual area in m2.
Its actual area
= (3*250)(4*250)/(100*100)
= 75m2
5.) A car is parked in a car-park 9 hours and 25min on the same day. Find the parking fee if the rate of charges is$12.5 for the first hour and $5 foreach half hour or part of a halfhour thereof.
The parking fee
= 12.5 + 5[2(9-1)+1]
= 12.5 + 5(16+1)
= 12.5 + 5(17)
= $97.5
6.) A and B are two consecutive numbers (B<A). Half of B exceedsone-fourth of A by 1. Find the values of A and B.
Let B be x, i.e. A is (x+1),
x/2 - 1 = (x+1)/4
(x-2)/2 = (x+1)/4
4(x-2) = 2(x+1)
4x-8 = 2x+2
2x = 2+8
2x = 10
x = 5
Therefore, B = 5, A = 5+1 = 6


2010-08-08 17:41:48 補充：
For supplymentary,
The 100th term
= -3(-3)^(100-1)
= -3(-3)^99
= (-3)^100 <== even number
= 3^100

1.) -25/4 = 5/-2x
20 = 50x
x = 0.4



2.)a.) 2(x+1)>4
2x + 2 > 4
2x > 2
x > 1

b.) 7x-9>9x+7
-16 > 2x
-8 > x
x < -8


3.)General term: -3^n
the 100 term = -3^100 = 3^100


4.)Actual area = [3 x (250/100)] x [4 x (250/100)]
= 75m^2


5.) Fee = $(9 x 12.5 + 5) = $117.5


6.) B = A - 1
1/2 x B - 1 = 1/4 x A
1/2 x (A - 1) - 1 = 1/4 x A
A = 3
B = 2

2010-08-08 16:51:14 補充：
amendment:
3.)General term: (-3)^n
the 100 term = (-3)^100 = 3^100

2010-08-08 16:56:13 補充：
5.) Fee = $[12.5 + 2(9 - 1) x 5 + 5] = $97.5

6.) B = A - 1
1/2 x B - 1 = 1/4 x A
1/2 x (A - 1) - 1 = 1/4 x A
A = 6
B = 5