There are 56 students in a class. If they all shake hands once, how many times do they shake hands________ ?

There are 56 students in a class. If they all shake hands once, how many times do they shake hands________ ?

Sum formula with arithmetic sequence: (first term + last term) * number of terms / 2 = (55 + 1) * 55 / 2 = 1540 times

At a meeting, everyone shook hands with each other. A total of 66 times, how many people?

If x people shake hands once, then each person will shake hands (x-1) times. Because there are x people, so we need to shake hands x (x-1) times (assuming that everyone goes to shake hands with other people in person) and because it is enough to shake hands once, so here x (x-1) is repeated once, so the equation: X (x-1) / 2 = 66, and the solution is x = 12

I haven't seen you for more than one year. I met you two and shook hands 28 times. How many people attended the party? 2 there is a big tree. I can see the top of the ball from point a
I haven't seen each other for more than one year. We shake hands 28 times. How many people are there?
2. There is a big tree. The elevation of C at the top of the ball is 35 degrees from point a, and 45 degrees from point B. the distance between a and B is 4.5 meters
For the circle inside the equilateral triangle, Xiao Ming randomly throws a needle, and the probability of puncturing the circle is 0

I haven't seen each other for more than one year. We shake hands 28 times. How many people are there?
Suppose there are x people at the party
x*(x-1)/2=28
2x²-x-56=0
(x-8)(x+7)=0
X = 8 (x = - 7, rounded off)
A: there were eight people at the party
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2. There is a big tree. The elevation of C at the top of the tree is 35 degrees from point a, and 45 degrees from point B. the distance between AB and CD is 4.5 meters
Let the height of the tree be x M
AD=x/tan∠CAD,BD=x/tan∠CBD
x/tan35°=x/tan45°+4.5
x*(1/0.7-1)≈4.5
x≈10.5
A: the height of the tree is about 10.5 meters
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3. The inscribed circle of an equilateral triangle. Xiao Ming randomly throws a needle into the equilateral triangle, and the probability of getting into the circle is
Geometric probability
Let the length of an equilateral triangle be 1,
Then the area of equilateral triangle is 1 * √ 3 / 2 * 1 / 2 = √ 3 / 4
The radius of inscribed circle is 1 / 2 * Tan 30 ° = √ 3 / 6
The area of the inscribed circle is π / 12
Xiao Ming randomly throws needles into an equilateral triangle, and the probability of puncturing the circle is π / 12 △ (√ 3 / 4) = √ 3 / 9 * π

At a meeting, every two participants shake hands with each other once. According to statistics, if they shake hands 66 times, the number of people present at the meeting is______ People

Suppose there are x participants in the meeting, according to the meaning of the question: 12x (x-1) = 66, sorting out: x2-x-132 = 0, solving: X1 = 12, X2 = - 11, (rounding off). Answer: there are 12 participants in the meeting