2) The original formula =1-1/2+1/3+1/3-1/4+...+1/.
2 . x *[ 1/( 1×2)+ 1/(2×3)+ 1/(3×4)+...+ 1/(2005×2006)]=2005
x*( 1- 1/2006)=2005
X=2006
3. Fill in the middle number 3, and the numbers at both ends of each connecting line are -5 and 2 respectively; -4, 1; -3,0; -2,- 1.
4.∫| a-b | = b-a
∴b>； a
a=-3
The original formula = 7a2-2b-a2+3b-1/2 = 6a2+b-1/2 = 6 * 32+3 * 2-1/2 = 59 and1/2.
5.3x-5(-x)=2a
2x+7(-x)=a+ 18
4x=a
-5x=a+ 18
a=-8
6.( 1) Formula 1- Formula 2: 3x-2z=0
x:z=2:3
(2)z=3/2x, obtained by substituting into the second formula:
x-3y-3/2x=0
x:y=6:- 1
x:z=2:3=6:9
x:y:z=6:- 1:9
(3)x=-6y，z=-9y
(xy+2yz)/(x^2+y^2-z^2)=(-6y*y-2y*9y)/[(-6y)^2+y^2-(-9y)^2=6/ 1 1
7. The sum of the two formulas is: 4009x+4009y=4009.
x+y= 1
Two types and one type:
x-y=3
(x+y)？ +(x-y)？ = 1? +3? =28
8. Do you want to find the △BEF area?
S△BEC = S△BED+S△CED = 1/2S△BAD+ 1/2S△CAD = 1/2S△ABC = 2cm？
S△BEF= 1/2S△BEC= 1cm？
9. City A: 8+1.5 (n-3) =1.5n+3.5; B city: 5+1.4 (n-1) =1.4n+3.6.
1.5n+3.5-( 1.4n+3.6)= 0. 1(n- 1)
10.M+N=7x？ +x- 1
N=7x？ +x- 1-(3x？ ﹣6x+5)=4x？ +7x-6
M-N=3x？ ﹣6x+5-(4x？ +7x-6)=-x？ - 13x+ 1 1
1 1. Let the original road be x kilometers long, and the equation can be listed as follows:
x/8=(x+3)/9- 1/8
X =15km
12. suppose class a transfers x boys to class b and class b transfers x girls to class a, and the equation can be listed:
(32-x):( 10+x)=( 1 1+x):33-x
x？ -65x+ 1056=x？ +2 1x+ 1 10
x= 1 1
Transfer from Class A to 1 1 Boys to Class B, and Class B to1/girls to Class A.
13. Because 2.4 must be multiplied by a multiple of 5 to become an integer, there are two schemes:
Adults and children
5 sets 13 sets
10 set
14.2+6-2x+3y=3×4
-5-3x+ 12+4y=3×4
Solution: x= 1, y=2.
xy(x+y)= 1 * 2 *( 1+2)= 6
15. If X individuals are arranged to produce bolts, 60-x individuals are arranged to produce nuts. Countable equation:
14 * x:[20 *(60-x)]= 1:2
x=25
60-25=35 people
16. suppose that the single digit of the automobile mileage at 8:00 is a, then the ten digits are 7-a, and the mileage is 10(7-a)+a=70-9a.
The mileage seen at 8:30 is 10a+7-a=9a+7.
The mileage seen at 9 o'clock is: 100(7-a)+a=700-99a.
9a+7-(9a)=700-99a-(9a+7)
a=6
700-99× 6-(70-9× 6) = 90km
17. When checking in at the station, there is a (a>0) waiting room with 100 tourists waiting in line to check in. After the check-in started, passengers still came to check in. Assuming that the number of passengers increases at a fixed speed, the ticket checking speed at the ticket gate is also fixed. If you open a ticket gate, it will take 30 minutes to check the tickets of the passengers in line. If two ticket gates are opened, it will take 10 minutes to check the tickets of the passengers in line. If three more ticket gates are opened, how long will it take to check the tickets of the passengers in line, so that the passengers who arrive later can check them on the spot?
If x people are added every minute, the number of people checking at a ticket gate is: a+30x; The number of ticket takers at the two ticket gates is: a+ 10x.
(a+30x)/30 =(a+ 10x)/ 10/2
A = 30x times
It takes t minutes to open three ticket gates, so:
(a+30x)/30=(a+tx)/t/3
(30x+30x)/30=(30x+tx)/t/3
T=6 minutes
18.225-150× (1+10%) = 60 (yuan)
19. An enterprise has 80 workers, each of whom can create an output value of one yuan per year on average. In order to adapt to the reform of market economy, it is decided to divert some personnel from IT department to engage in service industry. After the diversion, the average annual output value of enterprise employees can be increased by 30%, and the average annual output value of service employees can be increased by 2.5a yuan. It is necessary to make the annual output value of the employees in the diversion enterprise not lower than the original annual output value, and the annual output value created by the service personnel not lower than half of the original annual output value. Suppose you are a business manager, please determine the number of people who are diverted to the service industry.
Assuming that X people are diverted to the service industry, the unequal groups can be listed:
(80-x)( 1+30%)a≥80a
2.5ax≥80a/2
14≤x≤ 18.5
Diverted to the service industry 14~ 18 people.
20.
( 1)( 1-5%)( 1+5%)- 1 =-0.25% & lt； 0
Therefore, the supermarket is losing money.
(2) ( 1+20%)/( 1-5%)- 1≈26.3%