Using description method to represent set M = {(0,3) (3,0) (1,2) (2,1)}

Using description method to represent set M = {(0,3) (3,0) (1,2) (2,1)}

(0,3), (3,0), (1,2), (2,1) are all points on the line y = - x + 3,
The coordinates are natural numbers
So the set M = {(x, y) | y = - x + 3, X ∈ n} is represented by description

How to express the set 0 2 4 6 8 by description

x/x=2n 0

The set {(O, radical 2), (0, - radical 2), (1,1), (1, - 1), (- 1,1), (- 1, - 1)} can be expressed as

{(x,y) | x²+y²=2,x∈Z }

Fill the bottle with a bottle of water, pour out 12% of all the water, then pour in the same amount of alcohol, pour out 13% of all the solution, fill it with alcohol, then pour out 14% of all the solution, and fill it with alcohol, then the alcohol accounts for 30% of all the solution______ %．

1-12 = 12; 12 × (1-13) = 13; 13 × (1-14) = 14; 1-14 = 34.34 × 100% = 75%

There is water in three barrels. If one third of the water in the first barrel is poured into the second barrel, then one fourth of the water in the second barrel is poured into the third barrel, and finally one seventh of the water in the third barrel is poured into the first barrel, then the water in each barrel is 12 liters. How many liters of the original water in each barrel?

One seventh of the water in the third bucket is poured into the front of the first bucket
Third barrel = 12 ÷ (1-1 / 7) = 14 liters
First barrel = 12 - (14-12) = 10 liters
A quarter of the water in the second bucket is poured into the front of the third bucket
Second barrel = 12 ÷ (1-1 / 4) = 16 liters
Third barrel = 14 - (16-12) = 10 liters
original
First barrel = 10 ÷ (1-1 / 3) = 15 liters
Second barrel = 16 - (15-10) = 11 liters
Third barrel = 10 liters

How many liters of alcohol are there in the liquid when one third of a liter of alcohol is poured out and the same amount of water is added?
Stir well, then pour out a third of the mixed liquid, and add the same amount of water. Then stir well, pour out a third of the mixed liquid, and add the same amount of water. At this time, how many liters of alcohol are still in the obtained mixed liquid?

One third of a liter of alcohol is poured out from one liter of alcohol, and the same amount of water is added to the liquid. The alcohol in the liquid is 1-1 / 3 = 2 / 3L
Stir well, pour out a third of a liter of the mixture, and add the same amount of water. There is still alcohol in the liquid = 2 / 3-2 / 3 * 1 / 3 = 4 / 9L
Then stir well, pour out one third of the mixture, and add the same amount of water. At this time, there is 4 / 9-4 / 9 * 1 / 3 = 8 / 27L alcohol in the mixture
I don't know how to ask

Is the third a polynomial or a monomial?

Monomials, of course

It is known that (A-1) x2ya + 1 is a polynomial of degree 5 of X and Y. try to find the value of the integral: (1) A2 + 2A + 1; (2) (a + 1) 2. What conclusion do you find from the results of (1) (2)? Randomly take several a values to verify your conclusion

∵ (A-1) x2ya + 1 is a polynomial of degree 5 of X and y, 2 + A + 1 = 5, the solution is a = 2, (1) A2 + 2A + 1 = 4 + 4 + 1 = 9; (2) (a + 1) 2 = 32 = 9. Conjecture: A2 + 2A + 1 = (a + 1) 2, prove: when a = 1, A2 + 2A + 1 = 4, (a + 1) 2 = 4, the equation holds; when a = 2, A2 + 2A + 1 = 9, (a + 1) 2 = 9, the equation holds; when a = 3, A2 + 2A + 1 = 16, (a + 1) 2 = 16, the equation holds;

If the monomials 2mxay and - 5nx2a-3y are monomials about X and y, and they are of the same kind, (1) find the value of (4a-13) 2003; (2) if 2mxay + 5nx2a-3y = 0 and XY ≠ 0, find the value of (2m + 5N) 2003

(1) ∵ the monomials 2mxay and - 5nx2a-3y are monomials of X and y, ∵ 2a-3 = a, the solution is a = 3, ∵ 4a-13) 2003 = (4 × 3-13) 2003 = - 1; (2) ∵ 2mxay + 5nx2a-3y = 0, ∵ 2mx3y + 5nx3y = 0, ∵ XY ≠ 0, ∵ 2m + 5N = 0, ∵ 2m + 5N) 2003 = 02003 = 0. So the answer is: - 1, 0

It is known that the order a + 1 of the square y of (a minus 2) x is a binomial with respect to x, y, then the value of a is?

(A-2) x ^ 2Y ^ A + 1 is a binomial of degree six about X, y
That is, the sum of the times of X and Y is 6
2+a=6
a=4