Engineering problems of linear equation with one variable To process a batch of parts, workers a need 15 hours, workers B need 20 hours, and workers C need 10 hours. Now, workers a and B process 5 hours at the same time, and then workers C do it alone. How many more hours to complete!

(1-5 / 15-5 / 20) = 5 / 12 10x 5 / 12 = 25 / 6 hours

The problem of linear equation with one variable,
1. The tree planting day is coming. There is a barren mountain where trees need to be planted. It takes 10 days for team a to plant trees alone, and 6 days for team B to plant trees alone. Now it takes two days for team a to plant trees first, and then team B to join. How many days will it take to complete the tree planting?

If the average efficiency of a is 1 / 10 and the efficiency of B is 1 / 6, then the equation can be formulated as 1 / 10x2 + (1 / 10 + 1 / 6) XA = 1, and the solution is a = 3, so it takes 5 days to complete the tree planting

The following engineering problems and interest rate problems are solved by linear equation of one variable
1. For a job, it takes 10 days for Party A to complete it alone, 12 days for Party B to complete it alone, and 15 days for Party C to complete it alone?
2. In order to promote the sales of a certain brand of air conditioner, the store promised to buy the air conditioner on New Year's day in 2010, which can be paid in two installments. A sum of money will be paid in advance, and the remaining part and the loan interest (annual interest rate is 5.6%) will be paid off on New Year's day in 2011?
3. Party A and Party B contract a project. Party a works for 10 days and Party B works for 13 days. The total reward is 6100 yuan. Because Party A's technology is better than Party B's, it is agreed in advance that Party A's salary for 4 days is 400 yuan more than Party B's salary for 5 days. How much yuan do Party A and Party B get each?
4. A batch of saplings will be collected by each class according to the following methods: 100 saplings and the remaining 1 / 10 in the first class, 200 saplings and the remaining 1 / 10 in the second class, 300 saplings and the remaining 1 / 10 in the third class Finally, all the saplings are taken, and the number of saplings in each class is the same
5. The price of a refrigerator sold in shopping malls is 2190 yuan, and the daily power consumption is 1 degree. Although the price of B energy-saving refrigerator is 10% higher than that of a refrigerator, the daily power consumption is only 0.55 degree. Now we sell a refrigerator at a discount. How much discount can consumers get when they buy a refrigerator and B refrigerator? (the service life of refrigerator is calculated as 10 years, 365 days per year, 40 yuan / kWh)
6. On Sunday, Xiaohui asked Xiaohong to type a document for the neighborhood committee. It takes 6 hours for Xiaohui to type the document alone, and 4 hours for Xiaohong to type it alone. Xiaohui and Xiaohong work together. Xiaohong has to leave for an hour on the way. How many hours does it take to type the document?

It will take X days to complete the design
(1\10+1\15)x+1\15+(1\12+1\15)x=1
X = 4
A: omitted. If IQ is OK, I don't need to write it
2. Set X Yuan for each payment
x=8224-x+5.6%×（8224-x）
Solution: x = 4224
Answer
three
Let a pay x yuan per day, then B (4x-400) / 5
10X+（4X-400）/5*13=6100
The solution is x = 350
A = 350 * 10 = 3500 yuan
B = 200 * 13 = 2600 yuan
A: 3500 yuan for a and 2600 yuan for B
4. Set the total number of saplings as X,
The number of saplings taken in the first shift is 100 + (X-100) / 10,
The number of saplings taken in the second shift was 200 + [x-200-100 - (X-100) / 10] / 10,
According to the condition that the number of seedlings in each class is equal, the formula is as follows:
100＋（X-100）/10＝200＋[X-200-100-(X-100)/10]/10
The results are as follows
X＝8100
That is, the total number of saplings is 8100. Substituting 100 + (X-100) / 10, the number of saplings taken by the first shift is 900,
According to the condition that the number of seedlings in each class is equal, the number of classes can be listed as follows:
8100÷900＝9
There are nine classes
5. Set up a market to sell a refrigerator at a discount of X
2190*x/10+0.4*365*10*1=3212
The solution is: x = 8
6. Design
Wait for me. I want to sleep
Let's sleep on it

Characteristics and formulas of triangle square rectangle trapezoid circular parallelogram
Features must be written clearly, only in one sentence, the formula, no matter what the area or perimeter!

Just remember the trapezoid area formula (bottom and top) times height divided by 2
The area formula of triangle
The area formula of parallelogram
I only know so much

This sin2a + sin2b = sin2c, how to get 2Sin (a + b) cos (a-b) = 2sinccosc?

The sum difference product formula sin2a + sin2b = 2Sin (a + b) cos (a-b) you see my derivation sin2a + sin2b = sin [(a + b) + (a-b)] + sin [(a + b) - (a-b)] = sin (a + b) cos (a-b) + cos (a + b) sin (a-b) + sin (a + b) cos (a-b) - cos (a + b) sin (a-b) = 2Sin (a + b) cos (a-b)

6.25: (x + 30) = 1.3:4 of 8 = (7-x): x.x: 3 and 5 of 16 = 5 of 16

6.25: (x + 30) = 1 / 8
6.25x8=x+30
x+30=50
x=50-30
x=20
3:4=(7﹣x):x
4(7-x)=3x
28-4x=3x
4x+3x=28
7x=28
x=4
x: 3 and 1 / 5 = 5 / 16
x:16/5=5/16
x=16/5x5/16
x=1

Square difference formula method
1.(a-1)+a^2 ·(1-a)
2.7m^2 ·a^4-7m^2 · b^4
3.-2m^8+512
4.x^2·(x-y)+y^2·(y-x)
5.18a^2 -32b^2-18a+24b

1、（a-1）（1－a^2）＝－（a-1）^2（a＋1）
2、7m^2（a^4－b^4 ）＝7m^2（a^2＋b^2）（a＋b）（a－b）
3、－2m^8＋2*2^8＝2*（m^4+2^4）（m^2+2^2）（m+2）（m-2）
4、(x-y)（x^2－y^2）＝（x-y)^2（x＋y）
5、(3a-4b)(6a+8b-6)

If the function image y = a * x + B-1 (a > 0, and a ≠ 1) passes through the first three or four quadrants, then there must be a > 1 and B < 0
Why do you have the following results,
Who can tell me

Draw an image
If 0

1/1×2×3+1/2×3×4+…… +1 / 20 × 21 × 23 (simple calculation)

In general, there are:
1/[k*(k+1)*(k+2)]
=1 / 2 * [(K + 2) - k] / [k * (K + 1) * (K + 2)] → substitute molecule 1 with [(K + 2) - k] / 2
= 0.5 / [k*(k+1)] - 0.5 / [(k+1)*(k+2)] ①
1 / [K (K + 1)] = 1 / K - 1 / (K + 1) 2 -------- you can't use this topic
So: 1 / 1 × 2 × 3 + 1 / 2 × 3 × 4 + +1 / 20 × 21 × 22
=0.5 * {[1 / (1 × 2) - 1 / (2 × 3)] + [1 / (2 × 3) - 1 / (3 × 4)] +. + [1 / (20 × 21) - 1 / (21 × 22)]} used in ①
= 0.5 * {1/(1×2) - 1/(21×22)}
= 115/462
More generally:
1/(1×2×3) + 1/(2×3×4) +…… + 1/[(n×(n+1)×(n+2)]
= 1/2 {1/2 - 1/[(n+1)*(n+2)]

Equation 4.6x = 7.5 and Ax = 5.8 have the same solution. What is the value of a

From 4.6 + x = 7.5, x = 7.5-4.6 = 2.9
Because of the same solution, we substitute x = 2.9 into AX = 5.8, that is, 2.9a = 5.8a = 2

Engineering problems of linear equation with one variable To process a batch of parts, workers a need 15 hours, workers B need 20 hours, and workers C need 10 hours. Now, workers a and B process 5 hours at the same time, and then workers C do it alone. How many more hours to complete!