The following is an explanation of some common heat phenomena in our life A. In winter, put a few buckets of water in the vegetable cellar to prevent the vegetables from freezing. B. the camphor pill in the wardrobe becomes smaller because it evaporates. C. The dew on the flowers and plants in the morning is formed by air liquefaction. D. rub some alcohol on the body to cool down when you have a fever because the temperature of alcohol is low

The following is an explanation of some common heat phenomena in our life A. In winter, put a few buckets of water in the vegetable cellar to prevent the vegetables from freezing. B. the camphor pill in the wardrobe becomes smaller because it evaporates. C. The dew on the flowers and plants in the morning is formed by air liquefaction. D. rub some alcohol on the body to cool down when you have a fever because the temperature of alcohol is low

Solution: A. put a few barrels of water in the vegetable cellar in winter. When the water solidifies, it will release heat to the vegetable cellar, so that the temperature will not be too low and the vegetables will freeze; B. camphor pill becomes smaller and becomes gaseous, the process from solid to gaseous is called sublimation; C. dew is formed by the water vapor in the air liquefying when it is cold; D. alcohol can vaporize rapidly at room temperature, and the vaporization needs heat absorption

Milk powder factory to make milk powder, milk moisture through the evaporation process to dry
But without destroying the nutrients in the milk, the method of vacuum distillation is adopted, that is, the water is evaporated at a lower temperature?
Why?

Because the space pressure of milk powder is small under the condition of low temperature and vacuum, the boiling point of water vapor is very low, and it can be evaporated at low temperature?

X tends to PI, find the limit of (Pi-X) cos1 / (x-pi),

1 / (x-pi) tends to infinity
Then cos1 / (x-pi) is bounded
Pi-X tends to zero
So limit = 0

Substitution method (x + 1) (x + 3) (x + 5) (x + 7) + 15
Factorization (A-1) (A-2) (A-3) (A-4) - 24
One can also be!!!

(x+1)(x+3)(x+5)(x+7)+15
=(x+1)(x+7)（x+3）（x+5）+15
=(x²+8x+7)(x²+8x+15)+15
=(x²+8x)²+22(x²+8x)+15×7+15
=(x²+8x)²+22(x²+8x)+120
=(x²+8x+12)(x²+8x+10)
=(x+2)(x+6)((x²+8x+16)-6)
=(x+2)(x+6)(x+4+√6)(x+4-√6);
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Mathematical logic problems in Discrete Mathematics
Construct the proof of the following reasoning in P system: p125
If today is Saturday, we will go to the summer palace or Yuanmingyuan. If there are too many visitors in the summer palace, we will not go to the summer palace. Today is Saturday, and there are too many visitors in the summer palace. So we will go to the Yuanmingyuan or the zoo

First, the simple proposition is symbolized
Lingp: today is Saturday,
q: We went to the summer palace,
r: Let's go to Yuanmingyuan,
s: There are too many tourists in the summer palace
Premise: P → (Q ∨ R), s → Q, P, S
Conclusion: R
It is proved that: (1) P → (Q ∨ R) premise is introduced
② P-premise introduction
③ Hypothetical reasoning
④ The introduction of s → Q premise
⑤ S premise introduction
⑥ Hypothetical reasoning
⑦ Disjunctive syllogism

Sequence {an} = 2 ^ n, ask whether there is an arithmetic sequence {BN}, so that A1B1 + a2b2 +. Anbn = (n-1) 2 ^ (n + 1) + 2 holds for all n belonging to n *?
If it exists, find out the general formula of {BN}; if not, explain the reason

AnBn=(n-1)2^(n+1)-(n-2)2^n
2^nBn=n2^n
Bn=n

Finding the definite integral of function f (x) = √ (4-x ^ 2) on interval [- 2,2]

y=√(4-x^2)
x^2+y^2=4
so answer is 2π.

The first line? The second line? The third line 10.9.8.8.8 the fourth line 10.9.8.7.7 the fifth line 10.9.8.7.6
10 9 8 8 8
10 9 8 7 7
10 9 8 7 6

First line 10 10 10 10 10
The second line 10 9 9
As for the rules, put them in a 5 * 5 square lattice and connect the upper left and lower right diagonals

Find the minimum value of natural number a such that the inequality 1 / (n + 1) + 1 / (n + 2) +... + 1 / (2n + 1)

1/(n+1)+1/(n+2)+...+1/(2n+1)

If a natural number is divided by 7, the remainder 2 is divided by 6, and the remainder 5 is obtained

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