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Arrived in the seventh middle school.

The first and second classes in the morning were math classes, and the math teacher was still the sick old teacher, who spoke like a woman. The students sitting in the back row could barely hear it. However, Wang Tian's personal level has now reached level 15, and the increase in his muscles and bones attributes has improved his own abilities a lot, and he can barely hear it when he is sitting in the back row.

Leng Xinxin next to her took out her mobile phone to play cool running as soon as she started class, and the math teacher didn't care about her at all. What he thought in his heart was that he was going to retire anyway, and it didn't matter if the students listened or not, as long as he lectured on it, he would complete the task.

But it doesn't matter if she listens to the class coldly or not, anyway, her father is the president of the group company, and when she reaches a certain age, she can go to work directly in the company, and she is not an ordinary employee. Even if she says she wants to go now, I'm afraid Leng Qian will arrange a good position for her.

Wang Tian listened carefully, he used to give up studying for money, but now he doesn't need it. Now the money in his package is unlimited, and it stands to reason that it doesn't matter if he doesn't study. But he still has to study seriously, first, because he thinks this opportunity is rare. Second, he believes that learning knowledge is his own business, and learning is not for further education, but for improving personal quality. People who are knowledgeable are better than others in every aspect.

These two lessons are about mean inequalities: hn≤gn≤an≤Qn. That is, the harmonic mean is no more than the geometric mean, and the geometric mean is no more than the arithmetic mean.

1. Harmonic mean: hn=n/(1/a1+1/a2++1/an)2, geometric mean: gn=(a1a2an)^(1/n)3, arithmetic mean: an=(a1+a2++an)/n4, square mean: Qn=√[(a1^2+a2^2+++an^2)/n] These four averages meet hn≤gn≤an≤Qn, where a1, a2、...、an∈R+, if and only if a1=a2=...=an, take "=" Number.

Then the math teacher talked about the various deformations of mean inequality, and the sophomore mathematics basically has the following three deformations: (1) For the real numbers a, b, there are a^2+b^2≥2ab (take the "=" sign if and only if a=b).

(2) For non-negative real numbers a,b, there is a+b≥2√(a*b)≥o, that is, (a+b)/2≥√(a*b)≥o.

(3) For negative real numbers a,b, there is a+b&1t;o&1t;2√(a*b).

In the second lesson, the teacher talked about how to prove the mean inequality. There are many methods: mathematical induction (first or reverse induction), Lagrange multiplier, piano-born inequality method, ranking inequality method, Cauchy inequality method, etc.

Proving by mathematical induction requires an auxiliary conclusion. Lemma: Let a≥o, B≥o, then (a+B)^n≥a^n+na^(n-1)B. Note: The correctness of the lemma is obvious, and the conditions a≥o, B≥o can be weakened to a≥o, a+B≥o.

The original question is equivalent to: ((a1+a2+... ＋an)／n)^n≥a1a2… an。 When n=2, it is easy to prove. Let the proposition hold when n=k, i.e. ((a1+a2+... ＋ak)／k)^k≥a1a2… ak。

Then when n=k+1, you might as well let a(k+1) be the largest of a1,a2,...,a(k+1), then ka(k+1)≥a1+a2+... ＋ak……

Although this math teacher is not in good health, his academic attainments are still quite good, listening to his lectures, Wang Tian has always thought that he was a wreck, but now he knows that he still has two children.

Now Wang Tian's intelligence is over 13o, and he has the ability to never forget, although he has basically not learned high school courses, but his foundation in junior high school is relatively good, and once he learns seriously, he doesn't know how much faster than others. This mean inequality is easy to understand, and some elementary school students can play with it, but after a lesson, only a few people can understand it. I have to admit that no matter what aspect there is, there is a gap between people and people.

The third and fourth classes were physics, and the lecture was given by a male teacher in his thirties.

At present, the current situation of the college entrance examination is that each province independently formulates the questions, or uses the national unified test paper. Then the admission is based on high and low scores, and the second year of high school in major provinces across the country has been divided into liberal arts and science classes. Jianghuai City adopts independent propositions, and the college entrance examination is still the ancient comprehensive of arts and sciences, which requires students to have relatively high basic knowledge. The comprehensive volume of arts and sciences has 3oo points, which is definitely a big head.

In class, the teacher gave everyone a question.

There was a bear that fell into a trap that was 19 deep. 617 meters, with a fall time of exactly 2 seconds. What color is the bear?

A. Brown, Brown Bear B. White, Polar Bear C. Black, Black Bear D. Black Brown, Malayan Bear E. Gray, Grizzly Bear......

Everyone was at a loss for this question, and finally the physics teacher gave an answer.

s=1/2gt^2(t=2,s=19.617) This is the formula for homogeneous addition, and the initial degree is o to calculate g=9.8o8. And g = 9.8O8, then the latitude is about 44 degrees. According to the geographical distribution of bears, there are no bears in the southern hemisphere, and it can be known that it should be 44 degrees north latitude. According to the title, since it is a trap, it is a trap that bears can fall into. Because there are few rare animals on the ground that are bigger than bears, they can be pushed out, and this trap is designed for bears.

Secondly, since the ground trap is designed for bears, it must be 6 perched bears. Moreover, most of the 6-perched bears have poor eyesight and are difficult to distinguish traps, so they are easy to fall into traps. Since the trap is deep 19. 617 meters, the soil must be the impact parent material, so that it is easy to excavate. Although brown bears have geographical distribution, they are mostly at high altitudes, and they are fierce, and the risk factor of hunting is large, and the value is not as high as that of black bears. The general bear paws and bear bile are taken from black bears. And because the geographical distribution of black bears basically does not coincide with brown bears. It can be determined that the correct answer to this question is a black bear. To sum up, bears are black.

After listening to the teacher's explanation, everyone suddenly realized. It turns out that this question is not random, but has a precise solution idea. In other words, physics teachers and chemistry teachers have to take other courses at the same time. In this way, I can keep up with the pace of the times, and the teacher is not so easy to be.

Two history classes and two geography classes in the afternoon, these two subjects are Wang Tian's strengths.

As long as he used the skills that he could not forget, all those basics entered his mind, and as for the flexible application, with his 13o intelligence, this question was not a problem.