Help explain a super difficult math problem, and if you don t dare to challenge it, you ll be out

This is actually the sum of the applied series of equal differences, where the first term is 1+2+3+...y can be seen as the sum of a series of numbers with an equal difference of 1, and this series of numbers with an equal difference of 1 has a formula that can be written as the upper bottom plus the lower base multiplied by the height divided by two (as with the formula for triangles, the top base refers to the smallest number, here 1; The bottom is the largest number, and here is y; High is the number of exponents, and there are obviously y numbers here). So you can get 1+2+3+...

y=（1+y）y/2

In the same way, 3 (33-x) + 3 (32-x) + ....6+3=3[(33-x)+(32-x)+.2+1] (extract 3).

of which (33-x) + (32-x) +2+1 is also the sum of a series of numbers with an equal difference of 1; It can be obtained using the above formula.

33-x)+(32-x)+.2+1=(33-x+1)(33-x)/2=(33-x)(34-x)/2

In the same way, 1+2+3+......x-y-2)=(1+x-y-2)(x-y-2)/2=(x-y-1)(x-y-2)/2

Taken together, it gets:

3(1+2+……y)+ 3（33-x）+3（32-x）+…6+3]+[1+2+3+……x-y-2)]

3y(1+y)/2+3(33-x)(34-x)/2+(x-y-1)(x-y-2)/2

This is the process of de-parentheses and merging similar items.

Original = (3y+3y) 2+3(x -68x+1122) 2+[(x-y)(x-y)-3(x-y)+2] 2

3y+3y²）/2+(3x²-204x+3366)/2+[x²-2xy+y²-3x+3y+2]/2

3y+3y²+3x²-204x+3366+x²-2xy+y²-3x+3y+2)/2

4x²-2xy-204x+4y²+6y+3368)/2

2x²-xy-102x+2y²+3y+1684

This is the test question of the National Junior High School Mathematics League in 02 or 01!

(1) When I first read the first question, I was also dizzy, so we might as well set the corner AOC as X. x<90

So isn't EOC half of AOB + AOC? （90+x）/2

If EOD is required, just subtract DOC from EOC, and OD is the angular bisector of AOC, then DOC=X 2, EOD=EOC-DOC=(90+X) 2-X 2=45+X 2-X 2=45°

2) When the angle AOB = M°, how many degrees is the angle doe equal to? We have already solved the above, replace x with m, the result is not the same, the problem condition AOB is an acute angle, and DOE is always equal to 45°

2.The term that does not contain xy is (2x) 3-3[(x) 2]y+kxy-5x[(y) 2]+4xy-3 without k*x*y, we write the formula better, 2x 3-3x y+kxy-5xy +4xy-3, that is, we kxy+4xy=0, and the rest don't worry about it, so k=-4, how about it, it's simple

3.The expression of the title is a bit vague, but it should be like this, mx (2a+2)y +5 2xy (3b+4), if this is the case, then it is simple, look at it, m=-5 2

2a+2=1

3b+4=2, then put m=-5 2

a=-1/2

b=-2 3 generations will go in.

I'll write it carefully for you.

1.(as an auxiliary line OA with respect to the OE symmetry line).

Set the angle aoc=x

angular aoe=y

So the angle boc=90+x, the angle boe=90-y;

So 2(90-y)=90+x; (0 degrees, since the angle doe = x 2 + y, the angle doe = 45 degrees 2.)Same as question 1, the angle aoc=x, the angle aoe=y, so the angle doc=angle doa=x 2;

So the angle boc = x + m, so the angle eoc = angle boc 2 = x + y;

So we get (x+m) 2=x+y;

Simplified m=x+2y;

Since the angle doe=x2+y=m2;

Final Result. The degree of the angle doe is 45°, and when the angle aob=m°, the angle doe is equal to m 2 The answer on the first floor is wrong!! ～

There is also the first question and the second question, don't do this during the exam, you should write it.

When the angle AOB=M°, the angle DOE is equal to (90+M)2-M2=45

Solution: Set the cost of each refrigerator to be X yuan.

480 - x = x * 20% - according to the equation of the first three sentences: ** - cost = profit.

Solution: x = 400 -- the cost of each refrigerator is 400 yuan.

--In the above equation, the first three numbers calculate the income of 110 good refrigerators, the middle three numbers calculate the income of 10 broken refrigerators, and the last two numbers calculate the cost of 120 refrigerators.

Then, revenue - cost = profit (that is, 7680 yuan).

Answer: The take-home profit is 7680 yuan.

If you don't understand, you can ask

The cost of each unit (calculated according to good) 480 (1 + 20%) = 400 yuan, the profit of each unit (calculated according to good) 480-400 = 80 yuan, all good profits, 80x (120-10) = 8800 yuan, the unit price after 6% discount of damage.

The profit of 10 broken units is 10x (288-400) = -1120 yuan, and the final profit is 8800 + (-1120) = 7680 yuan.

Hello first calculate the cost of each unit: 480 (1 + 20%) = 400 yuan, then according to 480 yuan sold per unit profit = 480-400 = 80 yuan 480 60% = 288 yuan.

400-288 = 112 yuan, that is to say, ten of them were sold at a loss of 112 yuan each, so the actual profit = (120-10) 80-112 10 = 7680 yuan, please ask.

480 (1+20%)=400, the cost of refrigerators per day is 120*400=48000, the total cost of all refrigerators (120-10)*480+10*480*60%=52800+2880=55680, the total selling price of all refrigerators.

55680-48000=7680, actual profit.

480 yuan per unit, 20% profit, that is, cost 480 80% = 384 yuan, profit 480 20% = 96 yuan.

The profit of 110 refrigerators is 96 110 = 10560 yuan 10 broken refrigerators, 6% off**, 480 yuan per unit, 384-288 = 96 yuan per unit, a total loss of 960 yuan.

Therefore, the take-home profit of this batch of refrigerators: 10560-960 = 9600 yuan.

One: 480 (1 + 20%) = 400 yuan (purchase price) two: (120-10) * (480-400) = 8800 (** profit) three: 10 * 480 * 60% - 10 * 400 = -1120 (10 broken machine profits).

Four: 8800-1120 = 7680 (take-home profit).

Calculate the total cost first.

480*120 (1+20%)=48,000 yuan This is the money spent on these refrigerators, and then how much money is sold in total.

480 * 110 = 52,800 yuan This is the normal sale of 480 * 10 * yuan This is the 10 units discounted.

52800 + 2880 = 55680 This is how much money was sold in total, 55680-48000 = 7360 This is the profit.

480 (1+20%)=400 yuan, 480-400=80 yuan.

480 60% = 288 yuan.

400-288 = 112 yuan, actual profit = (120-10) 80-112 10 = 7680 yuan.

Step 1: Ask for a selling price.

According to the profit margin = (selling price - purchase price) purchase price.

Part 2: Profit = Total Selling Price - Total Purchase Price...

This question... It's so hard ... What grade are you? Little Six?

Solution: When the monthly income is 2000 yuan, you need to pay tax: (2000-800) * 10% = 120 (yuan);

When the monthly income is 5,000 yuan, you need to pay tax: 120 + (5000-2000) * 15% = 570 (yuan);

When the monthly income is 10,000 yuan, you need to pay tax: 570 + (10,000-5,000) * 20% = 1,570 (yuan) > 1,200 yuan.

That is, his monthly income is between 5,000 and 10,000 yuan.

Suppose his monthly income is $x, then:

570+(x-5000)*20%=1200.

Solution: x=8150

Therefore, his monthly income after paying taxes is: 8150-1200 = 6950 (yuan).

First of all, you need to determine how much he earns. You see, if his income exceeds 2000, 800 2000 taxes paid are 1200x10% = 120 yuan. If the income exceeds 5000, the tax paid is the part of the previous 120 + 2000 5000.

That's 120 + 3000 x 15% = 120 + 450 = 570But the title says he paid 1,200 in taxes, so his taxes must have exceeded 5,000

And the tax paid for the part exceeding 5000 is 1200-570=630Suppose his income is x, (x-5000) x20%=630The solution is x=

Remember to add 70 to me. You don't know how to ask me again.

Suppose his monthly income is X yuan, if it is calculated according to 10%, then his salary is 800 + 1200 10% = 12800 yuan, but it does not meet the standard of 800-2000 yuan; If calculated according to 15%, his salary is 800 + 1200 15% = 8800 yuan, but does not meet the standard of 2000-5000 yuan; If calculated according to 20%, his salary is 800 + 1200 20% = 6800 yuan, which meets the standard of 5000-10000 yuan, so his salary is 6800 yuan, and the after-tax balance is 6800-1200 = 5600 yuan; Another algorithm: 1200 = [(x-800)*10%(800 x 2000),(x-800)*15%(2000 x 5000),(x-800)*20%(5000 x 1000)], then x=6800 yuan, so there is 6800-1200=5600 yuan left after paying taxes.

According to the provisions of China's tax law: personal monthly income does not exceed 800 yuan, exempt from personal income tax, more than 800 yuan not more than 1300 yuan need to pay 5% of the individual income tax, try to write out the monthly income between 800 yuan and 1300 yuan should pay tax Y yuan and monthly income X yuan between the functional relationship.

y=(x-800)*5%

1200* yuan) has 1080 yuan left.

Because it's 10%, it's multiplied.

1200-800=400 This 400 is the part that needs to be taxed 400*10%=40 (tax) 1200-40=1160

According to the narrative, the formula listed is:

x^（m-2)*y^2+m*x^(m-2)*y+n*x^3*y^(m-3)-2*x^(m-3)*y+m+n

Because this formula is simplified to a quadratic trinomial, and now the formula is six, then it must be combined with similar terms, so observing the formula, we can see:

The second term and the fourth term are both 1 degrees, which may be the same term, then m=2, but the substitution results are quadrive, so this may be excluded.

Therefore, the second term and the fourth term are two different terms, and after adding the constant term (m+n), there are already three terms, so the first term and the third term must be opposite numbers, according to which the idea can be obtained:

m-2=3 m=5

n=-1 and then substitute the original test:

5x 3*y-2x 2*y+4 is a quadratic trinomial, and this answer is preferable.

。。。Landlord.

The topic is really too profound.

I can't read ......What are you writing about.

As a 6th grader, I-. - Scared to pee ......

It doesn't take 10 minutes...

Number the holes as shown below...

Set the farmer's number as A, B, C... In the initial state, A accounts for 4, B accounts for 5, and C accounts for 6.

1min: B to 2

2min: None of them move.

3min: B back 5

4min: B to 8

5min: No movement. (If the gopher is not found at this time, the gopher must be in the 2nd place.)

6min: B back 5(Gopher in 1, 3).

7min: None of them move. (Gopher back 2).

8min: A to 1, C to 3(Catch the gopher).